Math is Figure-Out-Able!: Recent Episodes
Pam Harris, Kim Montague
Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what? Join them for ~15-30 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able. See www.MathisFigureOutAble.com for more great resources!
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 29, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Rich Tasks are a powerful lesson structure and can be challenging to implement effectively. In this episode, Pam and Kim discuss the preparation and approach needed to facilitate a successful Rich Task.
Talking points:
- Know your content, know your students
- Importance of knowing who engages or shuts down, students' prior math experiences, who seeks extra challenge, and what's going on in their lives.
- Need to set expectations
- Understanding the vertical and the horizontal math progressions
- Shifting your goals in real time
- Try Problem Strings first
Links:
- Math is FigureOutAble Challenge Registration
- Math is Figureoutable Blog
- Pam's Books
Check out Pam's social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 29, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How do you cultivate flexibility in your classroom? In this episode Pam and Kim discuss expectations, perspectives, and techniques that help students develop mathematical flexibility.
Talking Points:
- The subtle messages of "That's not what we are doing right now."
- Difference between feeling invited vs. feeling commanded
- Crafting the conversation
- Honoring students' thinking
- Responding to,"Can't I just solve it this way?"
- Helping students access what they already know
Links:
- DMR Registration Link
- Math is Figureoutable Blog
- Pam's Books
Check out Pam's social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 22, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
You already know that we seek for flexibility, efficiency, being clever, and owning a variety of mathematical strategies. But what about grading students based on how many strategies they own to solve a problem? And what does "clever" even mean? Tune in as Pam and Kim discuss their definitions of "clever" and how we can help students seek for clever math strategies.
Talking Points:
- The meaning of 'clever' and how to encourage it in students.
- How 'seeking for clever' is a mathematical behavior and mindset
- Caution with requiring multiple solutions for a grade
- Importance of experience in mentoring kids to represent their thinking
- Nudging students to reflect on a strategy they want to do 'next time'
Links:
- NumberClub FREE Webinar Registration
- DMR Registration Link
- Math is Figureoutable Blog
- Pam's Books
Check out Pam's social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 15, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How can we equip students to tackle problems that do not fit a standard algorithm? In this episode, Pam and Kim experience a Problem String intended to engage fraction reasoning without traditional algorithms.
Talking Points:
- Equivalences
- Percents and fractions
- Genuine reasoning about fractional relationships
- Playing versus commanding
- Drawing fraction models just in case versus just in time
Links:
- NumberClub FREE Webinar Registration
- DMR Registration Link
- Math is Figureoutable Blog
- Pam's Books
Check out Pam's social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 8, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
We love being with mathematics educators! In this episode Pam and Kim recount their experiences at CAMT 2026.
Talking Points:
- Feeling at home at CAMT
- Experiencing math at conferences
- Bullding relationships at conferences
- Should a goal be to make math 'easier'?
- Real world math from real questions from students
- Language matters
- Explicit vs Inquiry
DMR Registration LinkPam's BooksMath is FigureOutAble Blog
Check out Pam's social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 1, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Developing Mathematical Reasoning FREE workshop
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Shout out to our leaders! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.
Talking Points:
- Ep 65: The power of shared math and teaching experiences
- Ep 104: What is Math Is Figure-Out-Able?
- Ep 165: Caution with manipulatives
- Ep 201: Are algorithms bad?
DMR Registration LinkPam's BooksMath is FigureOutAble Blog Check out Pam's social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 24, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Shout out to our 9-12 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.
Talking Points:
- Ep 294: Introducing Logarithms
- Ep 69: Equations of Lines are Figureoutable!
- Ep 6: Developing Functional Reasoning
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
Check out Pam's Books
Math is FigureOutAble Blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 17, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Shout out to our 6-8 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.
Talking Points:
- Ep 45 - 5 Interpretations of Rational Numbers
- Ep 183 - Integer Subtraction
- Ep 266 - Solving Proportions - Within & Between
Check out Pam's Books
Math is FigureOutAble Blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 10, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Shout out to our 3-5 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.
Talking Points:
- Ep 174 - Double/Half: The Most Sophisticated Multiplication Strategy
- Ep 29 - Ratio Tables!
- Ep 34 - Knowing vs Memorizing Multiplicaiton Facts
Check out Pam's Books
Math is FigureOutAble Blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 3, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Shout out to our K-2 teacher friends! Let's take a peek at some important conversations Pam and Kim have had over the years, just for you.
Talking Points:
- Ep 16 - Names of Teens
- Ep 85 - Moving Past Counting
- Ep 195 - Main Strategies for 1st Grade
- Ep 281 - How Strategies Grow Up
Check out Pam's Books
Math is FigureOutAble Blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 27, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How would you describe the difference between a classroom that emphasizes memorization and a classroom that develops mathematical reasoning? In this episode, Pam and Kim wrestle with an analogy for math classrooms.
Talking Points:
- Importance of letting students play with what they know to learn the real game of math
- The significance of choice in math class
- Pitfalls of labeling students
- Value of providing equal opportunities in math class
- What does "natural talent" mean in math?
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out Pam's Books
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 20, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
What benefits have you found from teaching reasoning and mathing in your classroom? In this episode, Pam shares with Kim things she learned in her recent trip to South Korea.
Talking Points
- Learning with your students
- Importance of turn and talks to capture internal "aha" moments
- Value of vulnerability and openness in the classroom
- Math content vs math content for teaching
- How open-ended problems and real math-ing naturally differentiates
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out our social mediaTwitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 3, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Can your students confidently reason about fraction multiplication? In this episode, Pam and Kim facilitate a Problem String that develops two strategies for fraction multiplication and discuss the thoughts that went into designing the string.
Talking Points:
-
TryThisTuesday and #TryThisThursday
- Scaling with fractions
- Building fraction relationships
- Goal of math is to build mathematical reasoning, not just get answers.
- Reasoning is the reason!
- Designing Problem Strings for multiple outcomes
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out our social mediaTwitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 6, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Is there a 'correct' way to name math concepts? In this episode, Pam and Kim discuss different naming conventions for fractions from different cultures.
Talking Points:
- Cultural difference in how fractions are expressed in Korean, where the denominator is said and written first.
- Cultural convention influences the way students think about and express fractions.
- Social conventions can influence mathematical understanding and the importance of being aware of these differences.
- Many languages use a part-whole approach, while others use a whole-part approach.
- Importance of being flexible in how we express fractions to support students' understanding and avoid confusion.
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out our social mediaTwitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 29, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Can you use an algorithm to solve every type of problem, or are there some problems for which algorithms leave you stranded? In this episode, Pam and Kim answer that question and share a Problem String to build fractional fluency.
Talking Points:
- Importance of understanding the relationships between different fractions.
- Making sense of equivalent fraction values through experiences rather than memorized procedures.
- Problem Strings provide continual building and strengthening of relationships and skills.
- Problems Strings send the message it is not about one and only one way.
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 22, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Looking for useful games and materials for your classroom? In this episode, Pam and Kim discuss some of the classroom materials and games they love and what makes them great.
Talking Points:
- Games and resources that do NOT lead towards an algorithm
- The value of games with strategy choice and without time/speed
- Hand2mind Foundations for Strategies
- Number Hive games for differentiation and to practice facts
- Math For Love games
- NumberClub games to build understanding
- Wipebooks for Rich Tasks
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 15, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How should context and models be used to build strategy? In this episode, Pam and Kim share a sequence of tasks regarding area to demonstrate a better approach for building understanding, abstraction, and strategy as a natural outcome.
Talking Points
- Hand2mind Foundations for Strategies
- Use of manipulatives to feel the meaning of area
- Guiding students to become more sophisticated, both in models and in strategies
- The importance of context for clarity and developing strategy
- Moving from concrete, to representational, to abstract to deepen understanding, strategy, and independence, NOT to apply an algorithm
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 8, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
If multiplication facts are so fundamental, why do students who memorize them struggle with multiplicative reasoning? In this episode, Pam and Kim take a hard look at what students need to succeed multiplicatively.
Talking Points
- What does it mean to 'know' multiplication facts?
- Using multiplication to solve subtraction problems
- Memorizing facts doesn't build complex multiplicative reasoning
- Redefining the mathematical 'basics'
- Applications to algebra
- How "productive practice" engages students in meaningful activities to build knowledge
Ep.139: Factor to Add and Subract!?
Math is FigureOutAble Blog: https://www.mathisfigureoutable.com/blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 1, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How can we prepare students to grapple with algebraic concepts? In this episode, Pam and Kim further adapt factor puzzles for developing understanding of both decomposing and combining expressions.
Talking Points:
- Helping students understand algebraic expressions
- Differences in adding and multiplying variables
- Relationships between terms in algebraic expressions
- The need for multiplicative reasoning in algebra
- Advanced Factor Puzzles for high school
Links:
1) Ep.139: Factor to Add and Subract!?
2) Factor Puzzle Blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 25, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Why is practice sometimes not enough for students to become comfortable multiplying and adding integers? In this episode, Pam and Kim explore more with Factor Puzzles, this time with integers!
Talking Points:
- Gaining experience multiplying and adding with negative integers
- Purposefulness of keeping certain numbers constant in the factor puzzles
- Practical applications of when to do Factor Puzzles
- Importance of understanding the absolute value of numbers
- Connection between Factor Puzzles and factoring quadratic trinomials
Link to Blog: https:https://www.mathisfigureoutable.com/blog
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 11, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
What is a great way for student's to increase their factor fluency and move from additive reasoning to multiplicative reasoning? In this episode, Pam and Kim play with factor puzzles and describe their many benefits.
Talking Points:
- Kim loves podcast reviews!
- Factor Puzzles routine
- Generalizing patterns to develop algebraic reasoning
- Building multplicative reasoning
- Fluency with factor pairs
- Ties to factoring quadratics
Link to Blog: https://www.mathisfigureoutable.com/blog
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 11, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
What does the day-to-day of a math is figureoutable classroom look like? In this episode, Pam and Kim discuss the new book for teachers of Grades 3-5 to transform their teaching.
Talking Points:
- New book release for Grades 3-5!
- Development of Mathematical Reasoning
- Additive Reasoning
- Multiplicative Reasoning
- Problem String walkthroughs and videos
- Rich tasks, routines, models and modeling
- Next steps for teachers, specific to their needs and experience
Shark Metaphor Podcast episode: Ep 245: Three Distortions that Ruin Math Teaching
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 4, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Using strategies to solve problems sounds good, but what if my students don't know the basics? In this episode, Pam and Kim dispel the myth that "the basics" needed for mimicking algorithms are the same as the fundamentals for math-ing.
Talking Points
- The limitations of rote memorization and the benefits of strategic thinking
- The challenges of shifting away from traditional math teaching methods
- Redefining what constitutes "basic math knowledge"
- "The basics" needed for mimicking algorithms are not the same as "the basics" for math-ing.
- Students need to understand underlying properties and relationships rather than isolated facts
- Putting algorithms before reasoning gatekeeps who gets to reason
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 25, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
What does it take to make real change in a school's math program? In this episode, Pam and Kim share what does and doesn't work to make lasting, systemic change in mathematics teaching for schools and school districts.
Talking Points:
- Teachers should not have to be expert teachers and expert curriculum writers at the same time.
- Good curriculum change alone is not enough
- Lock-step plans backfire
- Teachers need math-ing experiences
- Teachers need to analyze mathematics for teaching
- Teachers need bite-off-able tasks
- Gradual, differentiated shifts over time last
- Get in touch with us to make lasting impact in your schools at https://www.mathisfigureoutable.com//solution
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 18, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
It's great to learn from other educators. In this episode, Pam and Kim relay their experience at NCTM Spring 2026, giving their unique perspective of modern teaching trends.
Talking Points:
- The need to define the terms curriculum, resources, scope and sequence, standards, content
- Clarity before competence
- Mathematics as both a noun and a verb
- Caution around "research" and the "science of math"
- The micro-routine "Interpret with Intention"
- Different types of strategies
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 11, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How can you tweak a Problem String to work perfectly for your class? In this episode, Pam and Kim share a subtraction Problem String, and then unpack what changes they'd make for different audiences.
Talking Points:
- A subtraction Problem String with the Over strategy
- The purpose of "what could a Helper be"?
- When to provide a Helper problem
- Adult-ish Problem Strings can cover more content
- Making a Problem String appropriate for your grade level
Link to blog: Differentiating Problem Strings for Your Grade Level
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 4, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Introducing new math concepts can be tricky. In this episode, Pam and Kim do a Problem String to introduce logarithms in a natural, figureoutable way.
Talking Points
- Problem String to introduce students to logarithms
- Differences between logarithms and algorithms
- Relationship between logarithms and exponents
- Developing exponential equations
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 28, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Are your Number Talks purposeful? In this episode, Pam and Kim discuss the when, how, and why of Number Talks, which they call Problem Talks.
Talking Points:
- Problem Talk vs. Problem String
- When and why to use a Problem Talk
- Example Problem Talk of 15 x 36
- Deciding whose strategy to represent
- Problem Talks are still instructional
- How many students to choose
- Choosing a rich problem
For more about Problem Talks and Problem Strings, check out episodes 33 and 241. Episode 33 , Episode 241
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 21, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
There is much more to fractions than "cross multiply and divide". In this episode, Pam and Kim facilitate a Problem String to explore the partitive meaning of fractions.
Talking Points:
- Fractions and division
- The partitive meaning of fractions
- Equivalent fractions
- Relational reasoning in understanding fractions
- Scaling up or down to find equivalent, simpler problems
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 14, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Part of being a good teacher is teaching with integrity and consistency. In this episode, Pam and Kim discuss the importance of knowing your beliefs about teaching and learning math to guide your choices and decision making.
Talking Points:
- Mathematics is hierarchical
- Development of Mathematical Reasoning framework
- Know your content, know your kids
- Success Map framework
- Developing a cohesive vision for math and math teaching
- Decision making about the what and how of teaching math
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 7, 2026.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How did you grow in 2025? What are your goals for 2026? In this podcast, Pam and Kim reflect on 2025 and share the exciting things they are working towards in 2026.
Talking Points:
- Recapping highlights of 2025
- Problem String book series completed
- Development of Mathematical Reasoning anchor and companion books
- Foundations for Strategies
- New workshops in 2025 and 2026
- Free opportunities in 2026
- Conferences in 2026
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 31, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
All teachers are different, but we should all teach intentionally. In this episode, Kim surprises Pam with a collection of favorite "Pam-isms" and asks Pam to elaborate on whether each one is an intentional teacher move and why it is important, or if it is just her personality.
Talking Points
- Ninety-niiiiiiiiine...
- Is that legal?
- Isn't it nice, when the answer is the question?
- Sit up tall, you just mathed!
- Math is Figure-Out-Able!
- Bam!
- Could I invite you to consider...
- I know you didn't, but could you?
- Tell us more about that.
- Who wants their brain to think like that?
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 24, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In the season of giving, Math is Figure-Out-Able is giving some free stuff to you! In this episode, Pam and Kim discuss free opportunities to learn and grow as a teacher.
Talking Points:
- Join the Teacher Facebook Group
- Podcast Episodes 156 "Start Here"
- Development of Mathematical Reasoning Episodes 5, 6, 67, 68
- Focus on Fluency in Episode 277
- Math is FigureOutAble Blog
- Problem String Videos
- Numberclub Webinar
- Our Free Developing Mathematical Reasoning Workshop
Link to all 12 Days of FREE: https://www.mathisfigureoutable.com/blog/12-days-of-christmas-math-is-figureoutable
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 17, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Who does not love free? We do, and know you do too!
In this episode, Pam and Kim kick of the 12 Days of Free, Math is Figureoutable style! Tune in to hear the first 6 FREE opportunities for supporting your math teaching.
Talking Points:
- The Most Important Numeracy Strategies ebook
-
MathStratChat
- TryThisTuesday/Thursday
- Problem Strings Guide
- Math if Figure-out-Able Podcast favorite 3 episodes
- How to receive our weekly email newsletter
- Instructional Routines Hub
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
FREE Resources:
Most Important Numeracy Strategies https://www.mathisfigureoutable.com/big
Problem Strings Guide https://www.mathisfigureoutable.com/problem-string
Instructional Routines Hub https://www.mathisfigureoutable.com/instructionalroutines
Podcasts https://podcast.mathisfigureoutable.com/ (Check out episodes #245, #276, #277)
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 10, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Why do we listen to student thinking? In this episode, Pam and Kim discuss how listening is a powerful tool for both coaching and teaching.
Talking Points:
- Why do we listen?
- What do we do after listening?
- Listening in service of moving the student or teacher forward
- The Success Map and Developing Mathematical Reasoning
- Affirming Learning Walks
- Distinguishing methods from end goals
- Mathematical and Community Building purposes for listening
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 3, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Sometimes a little shift makes all the difference. In this episode, Pam and Kim describe the new mini workshop for introducing secondary teachers to the small shifts in their teaching that can bring reasoning into their classrooms.
Talking Points:
- Cathy Fosnot's 'Young Mathematicians At Work'
- Introducing new 'mini' workshops on Transforming Teaching 6-12
- Bridging the gap between K-5 and secondary teachers
- How these workshops are accessible and affordable for both teachers and leaders.
- The importance of small shifts and manageable chunks of information
Register for the workshop that's right for you at: https://mathisfigureoutable.com/mini-hub
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 26, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
As the end of the year gets closer, it's a great time to reflect what and who we are grateful for! In this episode, Pam and Kim pause to give thanks for the wonderful work being done around the world to make math more figureoutable.
Talking Points:
- Grateful for YOU, listeners!
- Grateful for our amazing teacher Facebook group
- Grateful for our Journey and JourneyLeader communities
- Grateful for the Math is FigureOutAble team
- Grateful for hard questions
- Grateful for each other
- Grateful for the journey!
Check out our social media
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Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 19, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
With so many models, what role do equations play? In this episode, Kim takes Pam through a Problem String that can only be modeled with equations and shares why.
Talking Points:
- Fibonacci Day
- Utilizing choice is a mathematical behavior
- Differentiating instruction through strategies
- Swapping, not a major strategy, but a fun one
- Models vs. Strategies
- Equations as models for equivalance strategies
Check out our social media
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Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 12, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Understanding math is important, and fun. In this episode, Pam and Kim discuss the necessity of play in mathematics education and share when, where, and why they each play differently with math.
Talking Points:
- Dr. Brad Ballinger's view that algorithms are...playful??
- The fun and educational value of simply playing with mathmatics
- How Pam and Kim differ in their purposes and preferences when playing with math
- How #MathStratChat can help you!
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 5, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
There's a brand new book for K-2 teachers! In this episode, Pam and Kim discuss how strategies in early mathematics build upon each other and increase in sophistication for future learning.
Talking Points:
- Strategies build on each other, algorithms do not
- The importance of building relationships and mental actions in students' brains
- Get to Ten grows up to Get to a Friendly Number
- Add Ten grows up to Add a Friendly Number
- How the Over and Give and Take strategies help students think outside the problem
- Ways developing strategies allows for differentiation
Purchasing Information: Developing Mathematical Reasoning: The Strategies, Models, and Lessons to Teach the Big Ideas in K-2https://www.mathisfigureoutable.com/dmrk2
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 29, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How can we adjust our teaching to meet the needs of our students? In this episode, Pam proposes a series of rapid-fire pedagogical scenarios for Kim to respond to with her best advice. What will Kim say in 90 seconds or less?
Talking Points:
- What to do about a student who only solves addition problems left to right?
- How to handle a student who always signals to pass during Problem Strings?
- Ways to encourage students to use strategies learned in Problem Strings when doing independent math work.
- Managing students who always yell out answers.
- Using Hint Cards/Clue Cards effectively
- Suggestions for students who have additional time accommodations
- The importance of knowing your students
For additional information on Hint Cards, listen to Podcast Episode 38: Multiplication Facts: The Good, the Bad, and the Ugly Pt. 5
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 22, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Pam and Kim went to NCSM and NCTM in Atlanta! In this episode, they share some of their favorite moments, biggest take-aways, and new insights gleaned from the sessions they attended and the people they met.
Talking Points:
- Discussing the meaning of "algorithm" with Sarah Bush and Karen Karp, authors of The Math Pact
- Importance of talk moves and listening moves, with Elham Kazemi and Allison Hintz, authors of Intentional Talk And Listening
- The joy of celebrating someone else's learning from Vanessa Vakharia
- How the Science of Reading does not correlate or correspond with what the people who call themselves the Science of Math are suggesting
- The importance of Affirming Learning Walks
- Clarifying the meaning of the word "procedural", as in "procedural fluency"
- The misleading nature of much of the math research currently being approved by What Works Clearinghouse
- Shout-out to James Tanton for being intellectually curious!
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 15, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
What role can technology play in mathematics education? In this episode Pam and Kim explore a Problem String for solving systems of equations using Desmos.
Talking Points:
- Graphing systems of equations
- Where lines intersect with different parent functions
- Using graphing to understand the behavior of a cubic function and more
- Using technology as a tool to understand what's happening, not as a crutch just to get answers.
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 8, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
What is the difference between "knowing" and "owning" facts? In this episode Pam and Kim discuss how to help all students make the most of multiplication facts.
Talking Points:
- How different people respond when asked to "memorize facts"
- "Own the facts" versus "Know the facts" - Do they mean the same thing?
- Napkin Math
- Using Problem Strings to teach facts and more
- How reasoning about facts builds important multiplicative relationships
- How reasoning in Problem Strings supports reasoning in word problems
- Redefining what "memorization" means
- Teaching for operational fluency
Facts Problem Strings: www.mathisfigureoutable.com/factsps
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 1, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Facilitating a Problem String is much more than providing a list of problems. In this episode Pam shares the moment to moment decisions she makes when facilitating a "Sticks of Gum" proportional realtionship building Problem String.
Talking Points:
- Setting the stage
- How to pull out thinking
- Using this string to math with teachers in professional development
- Reinforcing mathematical behaviors
- Strategically determining wait time
- Using potential misunderstandings as learning opportunities
- Applying models to student thinking
- Deciding the order of strategies to elicit
- Choosing the numbers in the Problem String
Check out the Sticks of Gum Problem String here:
https://www.mathisfigureoutable.com/ratio-tables
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Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 24, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Mathematics is everywhere, but if students don't know how to reason they may not want to engage and play with numbers or see all the opportunities to do so. In this episode Pam and Kim discuss scenarios where they play with mathematical concepts in their daily lives.
Talking Points
- Playing with numbers...double, half, factors, multiples, etc.
- What numbers do they play with? House numbers, license plates, time, prices, interstate signs
- I Have, You Need with time and distance
- Which is a better deal? Cost per ounce
- Mindset to engage in play with math
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 17, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Have students that struggle with word problems? In this episode Pam and Kim discuss the best way to help students succeed when faced with a word problem.
Talking points:
- Why mimicking makes word problems harder
- Reasoners develop greater stamina
- Developing the feel of actions of the operations
Check out our social media
Twitter: @PWHarris
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 10, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Is the goal of math class all about getting answers? In this episode Pam and Kim discuss how their work differs from those who promote traditional math classrooms and even some conceptual inquiry based classrooms.
Talking Points:
- Teaching algorithms as the goal is detrimental
- What is the goal?
- Teachers need their own math learning experiences
- We want students to own relationships to develop strategies that they will use in math class and throughout life
Check out our social media
Twitter: @PWHarris
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 3, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How does the definition of fluency change when your goal for math class changes? In this episode Pam and Kim discuss in some areas of mathematics they aim for fluency and how students use those relationships to build from.
Talking Points:
- Buzzwords
- What are our goals?
- Does automaticity need to be drilled or can it develop naturally?
- Strategies are synergistic
- Fluency with decomposing numbers
- Functional fluency
- Fluency with prime and square numbers
- Fluency in mathematical behaviors
Check out these episodes to learn more about "working with multiplication facts".
- Ep 97: If Not the Multiplication Algorithm, Then What?
- Ep 34 - 38: Multiplication: The Good, The Bad, And the Ugly
Check out our social media
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Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 27, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How can we bridge from proportional reasoning to functional reasoning? In this episode Pam and Kim talk through a Problem String that moves students from proportional reasoning into linear functions.
Talking Points:
- Building Proportions Problem String
- Thinking about "between" and "within" relationships in a ratio table
- Slope, rate of change, similar triangles, equivalence: all figure-out-able
- Ratios and proportional reasoning to functional reasoning
- Slope is a ratio
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 20, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How do mathy people approach mathematics? In this episode Pam and Kim discuss different mathematical behaviors and the value of engendering them in students.
Talking Points:
- Reflecting about what else you could have done that might be more sophisticated
- Seeking the "ooh" factor or the "aha" moment
- Compare strategies and make connections
- Making choices based on numbers or the structure
- Seeking efficiency and making generalizations
- Start with "What do I know?"
- Seek understanding and asking for more
- The importance of acknowledging mathematical behaviors
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 13, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Does inquiry mean leaving students to their own devices? In this episode Pam and Kim share their thoughts on the debate teaching reasoning vs. teaching procedures.
Talking Points:
- We all want what's best for students
- Sometimes educators talk past each other, using words without examples to give meaning
- Experiencing mathing is different from helping students learn to do the mental actions of mathing
- Is there a continuum of how to teach?
- Examples of "direct" and "inquiry based" instruction
- Should we ever be explicit?
- Why is it so important to have a common experience?
See the debate here: https://www.youtube.com/watch?v=CANtr9OHAvU
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 6, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How can teachers help students be more sophisticated additive reasoners? In this episode Pam and Kim discuss the major addition strategies, what properties they use, and how to model student thinking.
Talking Points:
- Addition strategies and models
- Addition strategies modeled with equations
- Proporties that the addition strategies are based on
- When manipulatives are appropriate
- Why teachers need to own the major strategies addition
Get the free ebook of Major Strategies at: https://www.mathisfigureoutable.com/big
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 30, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
If your only focus is answer getting, students may never experience and grapple with and understand multiplicative properties. In this episode Pam and Kim discuss how to use models to help students progress to more sophisticated strategies using multiplicative properties.
Talking Points:
- Modelling different strategies on area models, ratio tables, and equations
- Using models to visualize properties
- Strategies that use the associative property are more multiplicative than the those that use the distributive property
Get the free ebook of Major Strategies at: https://www.mathisfigureoutable.com/big
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 23, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How does proportional thinking prepare students for reasoning with variables? In this episode Pam and Kim explore the transition from proportional reasoning to functional reasoning.
Talking Points:
- Connecting proportional reasoning to linear functions
- Scaling triangles
- Proportions "within" and "between"
- Introducing tricks stifles students' opportunity to build sophisticated reasoning
- Rich task with non-unit rates
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 16, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Should you require student's to show their work in mathematics? Whose work? When? How much work? For what purpose? In this episode Pam and Kim discuss classroom culture and the importance of communication in mathematics, diving into these questions and more.
Talking Points:
- Whose work are you asking student to show?
- Motivations for showing work
- Don't fix the math, mentor the mathematician - Cathy Fosnot
- Communication is a mathematical behavior
- Determining 'just enough' is a mentoring opportunity
Check out our social media
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Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 9, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How can Problem Strings help build big ideas? In this episode Pam and Kim walk through a Problem String that helps students dig into area and multiplicative equivalence and helps you know how to expertly facilitate.
Talking Points:
- Facilitating the string
- Teacher moves during the string
- Modeling the string
- Equal products means total area is the same
- Why we want students to have lots of experience with concepts rather than just direct teaching.
Check out our social media
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Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 2, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How does a Problem String look in front of real students? In this episode Pam and Kim give a play by play for how a Problem String could be facilitated.
Talking Points:
- When to circulate and when to ask for choral response
- Helping students communicate thinking
- How and when to engage students in conversations
- When to anchor strategies
- When to be intentionally curious to solidify thinking
Check out our grade level Problem String books!
Grade 1 Problem Strings: https://www.mathisfigureoutable.com/nps-1
Grade 2 Problem Strings: https://www.mathisfigureoutable.com/NPS-2
Grade 3 Problem Strings: https://www.mathisfigureoutable.com/nps-3
Grade 4 Problem Strings: https://www.mathisfigureoutable.com/nps-4
Grade 5 Problem Strings: https://www.mathisfigureoutable.com/nps-5
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 25, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What if finding equivalence between fractions, decimals, and precents wasn't just a task for students to do, but a tool making them more efficient in rational number computations? In this episode Pam and Kim talk about code switching with rational numbers to make complex problems more figure-out-able.
Talking Points:
- What is code switching in rational numbers?
- A Problem String using equivalence to think about multiplication
- Tasks that use equivalency to solve problems rather than just practicing conversions
See episode 219 for learning about finding the mean: https://www.buzzsprout.com/1062400/episodes/15561786
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 18, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Five years of important conversations, lots of laughs and a blooper every once in a while. In this episode Pam and Kim revisit some important moments of the podcast from the last 5 years.
Talking Points:
- Clips from the past 5 years!
- Types of questioning
- Student compliance
- Problem Strings vs Problem Talks
- Math distortions
- Wait time and Private signals
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 11, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How can you get the most out of I Have, You Need in your classroom? In this podcast Pam and Kim answer some common questions and dig deeper into one of their favorite routines, I Have You Need.
Talking Points:
- Do cars speak the language of fractions?
- I Have, You Need (See also Ep 7 and 164)
- Why it is helpful to know partners of 1, 10, 100, 1000, etc.
- Common misconceptions
- Why it is important for the teacher to call the numbers
- Is it about creativity or efficiency?
- Discussing strategy is a big part of I Have, You Need
Get the free download at:
https://www.mathisfigureoutable.com/youneed
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 4, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We've got a lot to say about screeners! In this episode Pam and Kim dig a bit more into why we screen and what we do with the results.
Talking Points:
- Are screeners useful for diagnosing and grouping students?
- Are assessments important?
- What would be a helpful way to spend the first few weeks of school with students?
- What to do with required screeners
- Some recommended screeners
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 28, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Are Universal Screeners worth the time and effort? What do we gain? In this episode Pam and Kim begin their discussion about using Universal Screeners and raise some wonders for consideration.
Talking Points:
- Defining screeners
- Limitations of screeners
- What we screen reveals what we value
- Screeners don't always reflect the content in the classroom
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 21, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Do Problem Strings and Thin Slicing achieve the same results? In this episode Pam and Kim discuss the differences between Problem Strings and Dr. Liljedahl's Thin Slicing.
Talking Points:
- Different purposes, different facilitation
- The importance of recording student thinking
- When non-permanent surfaces can be helpful
- Problem Strings are strategically planned sequences and not always 'easy to more complex'
- Differences in the teacher's role, questioning, math relationships
- Word problems are natural extensions of Problem Strings
- Problem Strings and Thin Slicing: Some similarities, but not the same.
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 14, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Are Problem Strings the same thing as Thin Slicing? In this episode Pam and Kim talk about the similarities between Problem Strings and Dr. Peter Liljedahl's Thin Slicing.
Talking Points:
- Example Problem String:
- Calling on students strategically in a Problem String
- Strategic seating arrangements for partner talk
- Similarities between Problem Strings and Thin Slicing:
- Purposefully designed sequence of related problems
- Problems given one at a time
- Increasing challenge
- Critical teacher planning
- Open access for all students
- Purposeful variation to keep students challenged
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 7, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
You facilitated a Problem String! ... Now what? In this episode Pam and Kim share they think about after facilitating a Problem String and what their next steps for their classroom might be.
Talking Points:
Ways to up the ante
- Echo strings
- How much to change at once
- Next Step strings
- When to move on
- When to anchor
Get Problem String books here: https://www.mathisfigureoutable.com/books
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 30, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
You've chosen a Problem String to teach, but does it need any preparation? In this episode Pam and Kim discuss how they prepare to facilitate a Problem String.
Talking Points:
- Is it ok to adjust a pre-written Problem String?
- What should you include in your 'Kim's Notes'?
- What will your final board layout look like?
- Naming specific teacher moves
- Practice using models ahead of time
- Are pre-created models ok?
- Where can you find pre-written strings complete with facilitation notes and final display? https://www.mathisfigureoutable.com/big
Check out our social media
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Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 23, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Which Problem Strings are appropriate for your students? In this episode Pam and Kim discuss what they consider when choosing a Problem String for a classroom.
Talking Points:
- A fraction addition example string
- Things to consider when choosing a Problem String:
- Prewritten vs write your own
- Time of year
- Strategies students already own
- Building a model vs building a strategy
- Order of sophistication of strategies
- Building a model vs strategy
- New content versus review/reteach
See episodes 33, 71, 72, 163, 226, 241 for more on Problem Strings!
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 16, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What kinds of tasks help students build multi-digit multiplication and division strategies? In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for multi-digit multiplication and division: Scaling, Over and Adjust, Partial Products, Factoring
Talking Points:
- Benefits of using diverse task types
- Sample of three "messy" tasks to develop:
- Ratio tables
- Area model
- 2 different kinds of division
- Relationship between multiplication and division
- Practice ideas
Get your kit from Hand2mind here: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-multiplication-division-small-group-kit
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 9, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What kinds of tasks help students build multi-digit addition and subtraction strategies? In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for multi-digit addition and subtraction: Friendly numbers, place value, adjusting, the commutative property, decomposing
Talking Points:
- Sequencing tasks is more than just moving from one page to the next in the teacher guide
- Sample of three "messy" tasks to:
- develop number lines
- make connections between addition and subtraction
- analyze strategies
- solidify a strategy
For more sequences, check out the Foundations for Strategies from Hand2mind!: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-addition-subtraction-small-group-kit
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 2, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Math class is richer and more fun when the goal is more than answer-getting!
In this episode Pam and Kim discuss how to sequence tasks to develop the foundational strategies and relationships for single digit multiplication and division: doubling, making use of ten, and partial products/quotients.
Talking Points:
Three sample sequence of tasks that use:
- A product approach
- Student exploration of patterns
- Just in time vocabulary
- Differentiation
- Foundations of multiplicative reasoning, area, geometry
- Contexts to develop 3 major models
- Useful fact practice
- Anchoring the learning
For more sequences, check out the Foundations for Strategies from Hand2mind!: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-addition-subtraction-small-group-kit
Check out our social media
Twitter: @PWHarris
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 26, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What should the bulk of math class look like? In this episode Pam and Kim discuss sequencing tasks to build foundational relationships that develop into major strategies.
Talking Points
- Major relationships that build the major strategies
- Problem Strings are one kind of task
- Foundational Relationships for young learners
- Rich tasks that get kids messing with relationships
- What does practice look like? (See Episode 38 for more information on Hint Cards)
- Check out pre planned sequence of tasks in the Foundation for Strategies small group kit
Order information for Foundation for Strategies here: https://www.hand2mind.com/item/foundations-for-strategies-multi-digit-addition-subtraction-small-group-kit
Order your copy of Avoiding the Trap of Algorithms here: https://www.mathisfigureoutable.com/avoidthetraps
Check out our social media
Twitter: @PWHarris
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Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 19, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Why do students give up on learning math? In this episode Pam and Kim discuss how using algorithms as teaching tools is distorting students' perception of what the definition of math is, which results in a poor mathematical identity.
Talking Points:
- A mysterious five pound bag
- A proportional reasoning Problem String
- Trap #1 and #2 (see Ep 246 and 247 for more details)
- Trap #3 a false definition of math that leads to Identity Definition of Math Trap
- Read Pam's new book for more information: Developing Mathematical Reasoning: Avoiding the Trap of Algorithms
Purchase Book here: http://www.mathisfigureoutable.com/avoidthetraps
Check out our social media
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Facebook: Pam Harris, author, mathematics education
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 12, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Why do students not realize their incorrect answers are completely unreasonable? In this episode Pam and Kim discuss another trap students fall into when taught to mimic algorithms as 'the way' to solve problems.
Talking Points:
- The patterns in Remove a Friendly Number Over strategy
- Important place value conversations
- How students can be stuck dealing with only digits rather than magnitude
- Reasonableness, or "Ish", numbers
- Parsing out polynomials into too many pieces
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 5, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
If a student can perform an algorithm, have they developed the mathematical reasoning that operation calls for? Or are they answer-getting? In this episode Pam and Kim discuss a major trap students fall into when we teach mathematics as a series of steps to rotely memorize.
Talking Points:
- A closer look at the multiplication algorithm and a major trap.
- Problem String that helps give students a high does of patterns for a multiplicative strategy.
- Algorithms disregard reasonableness.
- Memorizing an algorithm is forgetable but every strategy learned helps build mental maps to the make subsequent strategies easier to develop.
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 26, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
If math is figure-out-able why does the world not always teach it that way? In this episode Pam and Kim discuss the three major distortions holding back math education today.
- Autostereograms as a metaphor
- How the distortions are learned
- How the distortions create frustration
- How classrooms transform without distortions
- We want all kids to "see the shark"!
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 19, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
There are so many way to participate in math professional learning! In this episode Pam and Kim discuss some benefits of choosing your own learning and engaging in free opportunities.
Talking Points:
Traditional forms of professional development
Benefits of multi-day online summits/conferences
The value of a shared experience
Join in on these great math summits from other fantastic educators!
Bulid Math Minds Free Virtual Math Summit, sponsored by Christina Tondevold: https://virtualmathsummit.com/
Make Math Moments FREE Virtual Summit sponsored by Jon Orr and Kyle Pearse: https://makemathmoments.com/summit/
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 12, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
In this episode Pam and Kim use what students know about integer multiplication to tackle integer division (without mismatching rules or randomly switching signs).
Talking Points:
- Reasoning about integer multiplication is ground work for integer division
- An integer division Problem String
- Teacher move: time to pause and consider
- Using the quotative meaning of division
- Thinking about opposites and reflection
- Using the partitive meaning
See episode 64 for the equivalent ratio strategy
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 5, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
One of our most requested topics! In this episode Pam and Kim discuss integer multiplication without mismatching rules or randomly switching signs.
Talking Points:
- Whole number multiplication strategies + meaning of integers leads to integer multiplication.
- The meaning of integers (See episodes 169, 181, 182, 183, 186)
- An integer multiplication Problem String and how to model
- Important noticings about modeling and context
- The importance of distance, reflection and opposites
- The importance of equivalence and commutative property
Free downloads!
https://www.mathisfigureoutable.com/factsps
https://www.mathisfigureoutable.com/big
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Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 29, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Is mathing just about allowing students to solve problems their way? Aren't Probem Strings and Problem Talks really just the same routine? In this episode Pam and Kim discuss how Problem Strings move beyond Problem Talks to develop student's mathematical reasoning at a more sophisticated level.
Talking Points:
- Example of a Problem Talk
- What do we gain from Problem Talks?
- Example of a Problem String
- Problem Strings are more focused conversations
- Problems Strings allow for constant feedback, a high dose of patterning
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 22, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Math may be figureoutable, but communication can be tricky! In this episode Pam and Kim discuss things to consider in order to be clear in the message we send when we speak about mathematics education.
Talking Points:
Duking it out!
- Are algorithms fake math?
- A better word than mathing?
- What do mathematicians think about algorithms?
- Do the math in mathematics education discussions so we have a common experience.
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 15, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
People across the world are changing math education. In this episode Pam and Kim discuss the documentary Counted Out that they were fortunate to see. They spotlight some of the thoughts of a few of the great researchers and add their thoughts about affecting change.
Talking Points:
- Spoilers!
- The effects of algorithms today
- What needs to change?
- How do we contribute to change?
- Math is everywhere
- Giving students choice
- Jo Boaler will be on the January 2025 Math is Figureoutable Challenge!
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 8, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Are inverse functions figureoutable? In this episode Pam and Kim go more into the nuance of when and how we want students to tackle inverse relationships.
Talking Points:
- When to introduce inverse proportions
- Experience versus instruction
- Allowing students to grapple to in order to experience those aha moments
- Problem String design
Check out our social media
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Facebook: Pam Harris, author, mathematics education
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 1, 2025.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What does it mean for something to be an inverse, or to be inversely proportional? In this episode Pam and Kim look at a specific kind of proportional reasoning.
Talking Points:
- It's worth thinking before doing
- Inversely proportional vs direct variation with non-unit scaling
- Common misunderstandings
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 25, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Did you know that students can understand negative exponents without being told what they mean? In this episode Pam and Kim wrap up their series on exponent relationships.
Talking Points:
- New listeners, where to start? Episode 156 Start Here
- Discovering Negative Exponents
- Give students experiences first and let them make sense of it
- Using equivalent expressions to help students visualize and make generalizations
- What grade levels are these strings for?
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 18, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What if students actually understood using common factors to simplify complex division expressions? In this episode Pam and Kim divide exponents without reciting a rule.
Talking Points:
- Thinking versus reasoning
- Problem String Dividing Exponents
- "Canceling" vs "Dividing out to equal 1"
- Focus on left over factors vs mimicking a rule
- Why start with smaller bases?
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 11, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
When variables and exponents start mixing, we need to memorize the rules, right? In this episode Pam and Kim develop exponential relationships, not rules.
Talking Points:
- How "Kim's Notes" became "Half Sheets"
- Problem String to explore multiplicative relationships when working with exponents.
- Generalizing multiplication of exponents
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 4, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Would you believe I'm more comfortable dealing with exponents because I haven't memorized the rules? In this episode Pam and Kim continue building exponentiation with a great problem string
Talking Points:
- Problem string to help build exponentiation
- When and how to introduce vocabulary
- Teacher move: Choosing who shares, and in what order
- More confident reasoning without the rules
- Teacher Move: Generalizing
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 27, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Can we prepare students for really hairy exponent problems without resorting to memorized rules? In this first episode of a series, Pam and Kim share a task that could get kids and teachers thinking more and more multiplicatively and understandably about exponents.
Talking Points:
- Can a task have too many layers for students to be successful?
- Can we sequence a task that works for 3rd grade to Algebra?
- Problem String to connect prime factorization to exponents.
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 20, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Should high school mathematicians be given choice of which strategy to use? In this episode Pam and Kim wrap up their exploration of systems of equations.
Talking Points:
- What is needed to understand 3x?
- Where students mess up using substitution
- How do different systems lend themselves to different strategies?
- Ketchup problems
- Next step Problem Strings and comparing strategies
- Giving students choice
Check out our social media
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Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 13, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Don't you think math needs more cookies in it? In this episode Pam and Kim use Desmos graphing calculator to go through a routine to make sense of systems of equations before doing any elimination or substitution.
Talking Points:
- Kim going to a Cafe for sandwiches and cookies
- Graphing on Desmos graphing calculator
- Understanding x and y intercepts
- Understanding where the lines intersect
- Relating systems of equations to each other
Link to Desmos Graphing Calculator: https://www.desmos.com/calculator/qq59ey0bub
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 6, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Do we flip the sign when its negative? Or is it we keep the sign and flip the minus? I'm confused! In this episode Pam and Kim avoid all that confusion and make solving inequalities figureoutable!
Talking Points:
- Open Number Lines for Inequalities
- Using "Reflecting the inequality" vs "flipping the sign"
- Reasoning about balancing the equation
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 30, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Solving equations is figureoutable! In this episode Pam and Kim do a follow up string to last week's episode to further develop algebraic reasoning.
Talking Points
- Using a double open number line to build proportional reasoning
- Using what you know to find x and explore multiple relationships
- Understanding equations vs mimicking steps
- Simultaneity can be tricky
- Additive vs Multiplicative thinking showing up
- Operator meaning of fractions comes into play
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 23, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Do we need to memorize a bunch of rules to solve linear equations or can we reason about them? In this episode Pam and Kim use a model to make thinking visible and keep students reasoning!
Talking Points:
- Modeling on a double open number line
- Finding where x lies on a double open number line.
- Grappling with the opposite of x
- Building integer sense as well as building equation solving sense
- Reasoning about an equation versus balancing an equation
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 16, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
How can we help students who have always mimicked learn to reason through the content we need to teach? In this episode Pam and Kim lay out their approach to getting students up to speed while preparing them for the content of the day.
Talking Points:
- How to avoid students feeling belittled
- Using a 1/3, 2/3 mindest to planning
- Planning with the entire year in mind
- Layering in complexity to build a single strategy
- Only change one thing at a time
- It may take longer in the beginning or when you switch a strategy
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 9, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Do your students struggle with place value? In this episode Pam and Kim discuss great tasks to build real place value understanding for students of all ages.
Talking Points:
- "Adding a zero" vs shifting place value
- Place Value versus Place Labeling
- Avoiding rules that expire
- Build a Number activity
- Place Value Mini-Workshop!
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 2, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We love the math teaching community! In this episode Pam and Kim are live from NCTM and discuss the many things they are learning from other math teaching educators at NCSM and NCTM in Chicago.
Talking Points:
- Too many great sessions to list! But here are a few.
- Announcing: Developing Mathematical Reasoning: Avoiding the Trap of Algorithms
- Announced: Foundations for Strategies Small Group Lessons
Pre order Developing Mathematical Reasoning: Avoiding the Trap of Algorithms here: https://us.corwin.com/books/dmr-289132?srsltid=AfmBOor-iPP6FJaP0vQS7MWXGMzv6U6psI-ZbqBwxYbE_y4rGgPHU4fU
Pre order Foundations for Strategies Small Group Lessons here: https://www.hand2mind.com/supplemental-curriculum/math/math-fluency/daily-math-fluency-foundations-for-strategies-small-group-lessons
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 25, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How do you plan for the content you teach? In this episode Pam and Kim discuss task sequencing and a new resource for every classroom.
Talking Points:
- Determining the big ideas, strategies, models
- Alternating between instructional routines
- Leading into and getting out of a rich task
- Introducing Foundations For Strategies Small Group Lessons a collaboration with hand2mind!
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 18, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
You all know we love playing games in the classroom. In this episode Pam and Kim discuss the advantages of playing games to change students attitudes and beliefs about math, and just have some fun.
Talking Points:
- The benefits of games
- They don't even have to be math games
- Multiple Machine by Michael Minas
Check out more of Michael Minas' games at Love Maths: https://www.lovemaths.me/games
Other Games: Cubit, Balance Beans, Quarto, Dimension, Blockus
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Facebook: Pam Harris, author, mathematics education
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 11, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
In this episode Pam and Kim discuss a fun way for students to practice their geometry vocabulary and relationships.
Talking Points:
- Geometry riddles
- Hierarchies of polygons
- Practice vocabulary in a meaningful way, in context
Check out our social media
Twitter: @PWHarris
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 4, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How can you intentionally build a Math is FigureOutAble culture in your classroom? In this episode Pam and Kim discuss Pam's recent month long trip to Australia and the important teacher moves she showcased in the lab lessons while she was there.
Talking Points:
- Pam's time Down Under
- Wait time
- Private Signal
- Focus on thinking verses focus on the answer
- A challenge for some students: What hint could you give?
- Teacher engaged with students the entire time
- Does every kid need to finish the problem?
- Do you need more time or help?
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 28, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Statistics Problem Strings? Yes Please! In this episode Pam and Kim demonstrate a Problem String that helps students develop intuition for the meanings of mean, median, and mode.
Talking Points:
- Names are social knowledge, but the feel for what they mean in the data is logical mathematical knowledge
- Experience with data helps students develop real understanding of mean, median, mode
- Changing the data values and comparing how that affects the measures of central tendency deepen understanding
Check out our social media
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Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 21, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Is statistics figureoutable? In this episode Pam and Kim explore a Problem String to build logical mathematical sense for the meaning of mean.
Talking Points:
- What is the mean?
- Just in time vocabulary
- Social vs Logical Mathematical knowledge
- Understanding mean/average is much more than performing an averaging procedure
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 14, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We were joined by Jenna Laib at our last challenge where she facilitated an amazing routine called Slow Reveal Graphs. In this episode Pam and Kim share that same Slow Reveal Graph and explain along the way why it makes for such an impactful tool to teach data analysis and interpretation for students K-12.
Talking Points:
- Shout out to Jenna Laib for currating the Slow Reveal Graphs website
- Questions that focus on Strategy vs Answers
- High level of engagement
- Natural extensions built into the routine
- Building thinking to analyze data representations and notice critical information or bias of the creator
- The advantages to using routines
Follow along with the podcast with the Slow Reveal Graph here: https://slowrevealgraphs.com/2022/04/22/how-loud-is-too-loud-english-espanol/
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 7, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Its a great time to be a math teacher! In this podcast episode Pam and Kim share a super useful tool for organizing and collecting free online math teaching materials for your classroom.
Talking Points:
- An amazing tool for finding and organizing tasks and other math content
- Great to find new math education creators
- Organize and share in and between schools
- We probably should mention we don't benefit monetarily from promoting tools like this, we just like them :)
Check out Semble! https://www.sembl.app/
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 31, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
There's so much to learn once teachers discover that math is figureoutable! In this episode Pam and Kim discuss planning and sequencing to keep the math moving forward in your classroom.
Talking Points
- The stages help teachers focus their energy
- Writing an echo Problem String
- Write an 'Up the Ante' Problem String
- Sequencing Strings
- Sequencing different routines within a task
- Sequencing Tasks
- Understand the progression of models
- Understand the connections between strategies
- The different structures of Problem Strings
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 24, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
You've worked hard to build your numeracy and already own the strategies and models for your operation that you're working on. What's next?
In this episode Pam and Kim discuss Teacher Moves, the fourth stage on the Success Map.
Talking Points:
- Differentiate for teachers' needs like they differentiate for students
- Great teacher moves are only helpful when there's great math conversations happening
- Model teacher moves in professional development
- Using a private signal
- Using a neutral response
- Using focusing patterns for questions vs funneling patterns
- Using partner talk appropriately
- Using teacher moves appropriately
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 17, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Becoming a better teacher is hard work, so we'll make it easier by helping you know where you are and what to work on next. In this episode Pam and Kim discuss the third stage for improving your mathematics teaching: representing student thinking.
Talking Points:
- The stages layer on each other
- Teacher's may be in different stages for areas of math
- The teacher chooses the model to best facilitate discussion and understanding
- Learn to listen, elicit thinking, and represent it.
- Share your experiences on the Math is Figureoutable Facebook group!
- The How Do You Reason? downloadable: https://www.mathisfigureoutable.com/reason
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 10, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What's next on the landscape for teachers after they've built their own math understanding in a particular area? In this episode Pam and Kim discuss math for teaching, the next layer on the Success Map that teachers should consider as they are learning how to make math more figure-out-able for themselves and their students.
Talking Points:
- Math for teaching is different body of math than the math anyone does
- Understanding and naming the major strategies and models for each operation
- Judiciously using the major strategies and models
- Crafting rich problems
- Build understanding in this stage alongside your students
Register for a workshop: https://www.mathisfigureoutable.com/workshops
Register for free Developing Mathematical Reasoning Workshop: https://www.mathisfigureoutable.com/freeworkshop
Download the free Major Strategies ebook: https://www.mathisfigureoutable.com/big
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 3, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What does developing as a math-teacher look like? In this episode Pam and Kim discuss one stage of a math teacher's journey.
Talking Points:
- Designing the Success Map
- Building Numeracy - a step in the cycle
- Understanding models versus strategies
- Owning partners of 10, 100, 1000, and 1
- Describing mathematical relationships correctly
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 26, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Can students gain fluency without long sheets of problems? In this episode Pam and Kim discuss Number Hive, a game that builds students multiplication fact fluency.
Talking Points:
- Better than the Product Game
- Good for classroom discussion
- Low cost of failure
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 19, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Developing multiplicative reasoning, let alone learning multiplication facts, has never been more fun. In this episode Pam and Kim discuss Stick and Split, a simple digital game your students or own kids can explore to learn multiplication in a whole new way.
Talking Points:
- We don't recommend products lightly - Stick and Split is amazing!
- Taking the product approach - How is that different?
- Noticing the commutative property
- Using common factors as tools
- What do the levels look like?
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
What does it look like when students confidently and efficiently reason through fraction multiplication problems? In this episode Pam and Kim discuss more sophisticated and efficient strategies for solving fraction multiplication problems.
Talking Points:
- How to model the commutative property in fraction multiplication.
- How to reasoning through "slash and burn".
- In a classroom, we would expect for students to have a variety of strategies to solve a rich problem.
- It's not about multiple representations but about connections between multiple representations so that kids have a series of connections in their head.
Help us reach 1 million downloads! Share the podcast with a friend!
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 5, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Can students reason through fraction multiplication beyond unit fractions? In this episode Pam and Kim finish out last week's Problem String and build on those relationships to reason through more complex fraction multiplication problems.
Talking Points:
- Can building Additive and Multiplicative reasoning with whole numbers help with fraction multiplication?
- Does the area model just explain a procedure or can you actually reason with it?
- How does building reasoning about multiplying fractions using scaling impact future learning (like slope)?
Help us reach 1 million downloads! Share the podcast with a friend!
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 12, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Registration is open for workshops is open for a limited time!
https://www.mathisfigureoutable.com/workshops
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 29, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Registration is open for workshops is open for a limited time!
https://www.mathisfigureoutable.com/workshops
This week we're kicking off our series on fraction multiplication! In this episode Pam and Kim describe a classroom's experience discovering unit fraction multiplication.
Talking Points:
- Learning requires multiple experiences
- Layers of Reunitizing
- The limitations of memorized procedures
- When teaching the use of a model, is actually teaching a procedure
Registration is open for workshops is open for a limited time!
https://www.mathisfigureoutable.com/workshops
This week we're kicking off our series on fraction multiplication! In this episode Pam and Kim describe a classroom's experience discovering unit fraction multiplication.
Talking Points:
- Learning requires multiple experiences
- Layers of Reunitizing
- The limitations of memorized procedures
- When teaching the use of a model, is actually teaching a procedure
Registration is open for workshops is open for a limited time!
https://www.mathisfigureoutable.com/workshops
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 22, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Registration is open for workshops is open for a limited time!
https://www.mathisfigureoutable.com/workshops
When should students use calculators? In this episode Pam and Kim discuss how to help students determine when and for what reasons to turn to technology.
Talking Points
- Help students learn judicious use of technology
- Great game: Beat the Calculator
- Do you know enough to put that in your calculator?
- What about competition?
- What about speed?
- An easy extension for Beat the Calculator
Help us reach 1 million downloads! Share the podcast with a friend!
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
Registration is open for workshops is open for a limited time!
https://www.mathisfigureoutable.com/workshops
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 15, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Register for the FREE Math is FigureOutAble Challenge: https://www.mathisfigureoutable.com/challenge
Is your classroom a place where students' thinking is valued? In this episode Pam and Kim discuss building a healthy classroom culture.
Talking Points:
- Know your content, but also know your kids
- Me versus us statements
- Walking the line of planning for the community and being part of the community
- A great place to start is recognizing 'hidden' students
- Names are important, learn them, use them
Help us reach 1 million downloads! Share the podcast with a friend!
The free Math is Figure-out-able Challenge is coming soon! You can register here: www.mathisfigureoutable.com/challenge
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
Register for the FREE Math is FigureOutAble Challenge: https://www.mathisfigureoutable.com/challenge
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 8, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Register for the FREE Math is FigureOutAble Challenge: https://www.mathisfigureoutable.com/challenge
What kind of instructional routines should you use in your classroom? In this episode Pam and Kim describe why instructional routines are useful and what makes some of their favorites shine.
Talking Points:
- Unlocking creativity and reasoning with routine
- Content flexibility within routines
- The downside to one and done routines
- How to decide which routines are worth establishing
- What makes Problem Strings a great routine
- Are games routines?
- Each of our 3 favorite routines
Help us reach 1 million downloads! Share the podcast with a friend!
The free Math is Figure-out-able Challenge is coming soon! You can register here: www.mathisfigureoutable.com/challenge
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
Register for the FREE Math is FigureOutAble Challenge: https://www.mathisfigureoutable.com/challenge
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 1, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
All students can learn more math when it is taught as figure-out-able! In this episode Pam and Kim wade into trigonometry and make sense of it as they go.
Talking Points:
Making sense of Pi and angle measure of a circle
- Defining radians
- Understanding the unit circle
- A Problem String using a unit circle
- The importance of modeling
- I Have, You Need with angles
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 24, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Got questions about the Math Is Figureoutable movement? In this lightning round episode, Pam and Kim answer questions and address misconceptions they've heard people have.
Talking Points:
Is it only about Problem Strings?
- Does math-ing have be done in all in your head?
- Is "one and done" desirable?
- Are we doing "Pam Harris Math"?
- Are algorithms bad?
- Is Math is Figuroutable appropriate for all grades K-12?
- Is Math is Figuroutable only numeracy?
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 10, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We're so excited to celebrate our 200th episode with you! In this episode Pam and Kim change up their intro and discuss how the things they've learned continue to shape how they spread the Math is FigureOutAble movement today.
Talking Points:
200 Episodes!!!
- Is the math mathing?
- Pam, a former mimicker
- Perspectives versus distortions
- Kim, a reasoner who can now share her thinking
- Algorithms are amazing historical feats, but not good teaching tools!
- The reason for math class
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 10, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Real math is never fun and cute, or is it? In this episode Pam and Kim discuss a cartoon they've fallen in love with that builds number sense intuitively and entertainingly.
Talking Points:
- What is Numberblocks? What makes it stand our?
- Different representations of numbers
- Squares
- Doubling
- Math symbols
- Odd and even
- Who is Numberblocks for?
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 3, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What can schools use to create a shared vision for math instruction? In this episode Pam and Kim discuss the New York Department of Education's Look Fors for School-Wide Mathematics Teaching and Learning.
Talking Points
- Who is this Look For for?
- Specifics for equity around scheduling teachers with an eye on content knowledge and pedagogy
- Making space for observing, sharing, and discussing teaching practices that engage students with challenging mathematics
- Share the school's vision throughout all parent communication and events
- The importance of shared vision about pathways for students to have access to high quality math
Find the Look Fors here:
For Students
For Teachers
For Schools
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 27, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What conversations can teachers and coaches have about improving instruction in the classroom? In this episode Pam and Kim discuss the Look Fors for Teachers provided by the New York Department of Education.
Talking Points:
- Coaching requires more than observation or modeling a lesson
- Avoid analysis paralysis
- Coaching through conversation
- How to inform your in-the-moment decisions
- Maintain students' opportunities to develop their own ideas and understandings
- Creating a shared vision
Find the Look Fors here:
For Students: https://drive.google.com/file/d/1spWxDFP_FRVGFkNmWAjGxKnDscGSctYD/view
For Teachers:
https://drive.google.com/drive/u/0/folders/1zZI4Y1MLr1DzSwtm_EK3KDC6Re3L62zn
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 20, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What goals do you have for your classroom? How do you measure your success? How to plan to achieve those goals? In this episode Pam and Kim discuss New York City's Look Fors for Students and how they can help us focus on the changes we want to see in our classrooms.
Talking Points:
- Kim and Pam have different styles and personalities as the approach planning a lesson or session
- Taking time to think deeply about a lesson
- New York City's Look Fors
- Kim and Pam highlight a Look For
- To avoid burnout, innovate in bursts
Find the Look Fors for Students here: https://drive.google.com/file/d/1spWxDFP_FRVGFkNmWAjGxKnDscGSctYD/view
Find other resources from New York City here: https://sites.google.com/view/nyc-math-resources/home
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 13, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
When should you start developing which relationships? In this episode Pam and Kim discuss the important addition relationships for first grade and how to develop them throughout the year.
Talking Points:
When do I teach what?
- Download The Most Important Numeracy Strategies Free Ebook!
- We want students to understand relationships so that strategies are natural outcomes, not memorized procedures.
- Partners of Ten
- Doubles
- Plus ten
- Modeling is super important
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 6, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Can we really be efficient in solving multiplication problems without algorithms? What about the really cranky ones? In this episode Pam and Kim discuss the quarter strategy- a clean, efficient, figureoutable way of solving traditionally difficult multiplication problems.
Talking Points:
- Baby strategies! What?!
- A problem string for the Quarter Strategy
- COMING SOON! Problem String books: A shared vision for how we could develop the major relationships for each operation, with strings for ALL year
Click here for more information on "Using Quarters" https://www.mathisfigureoutable.com/quarters
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 28, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What message do we want to send to students about compliance? In this episode Pam and Kim talk about the importance of respecting student dignity and separating math from punishment.
Talking Points:
- Senario of compliance
- Reasons we seek compliance from students
- Math is not a punishment or taking it away, a reward
- Pam and Kim reflect on some of their early experiences
- Is it about the math or about the compliance?
- Do your grades reflect compliance?
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 21, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
A huge part of any teacher's life is classroom management, setting expectations, and compliance. In this episode Pam and Kim consider when compliance might or might not be helpful in a math classroom.
Talking Points:
- Sucked down the Math Is Figureoutable vortex
- Would you rather have compliant students? Or have students who question?
- There are times when compliance is important
- Kim and Pam's early experiences with compliance
- Negative consequences for non-compliance aren't always helpful
- Creating a learning atmosphere
- Model your expectations
- Time for reflection not finger wagging
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 14, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Thinking and reasoning is always more powerful than rotely memorizing steps. In this episode Pam and Kim demonstrate how to help students reason about Order of Operations.
Talking Points:
- Nat Banting's "Oops, I Meant"
- Representing a context using the grouping symbols to communicate
- Demonstrate how mathematicians communicate with symbols earl
- Using the equals sign correctly to mean "equal" vs "Do it""
- No more unnecessarily difficult practice
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 7, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Order of operations seems more rote memorizable than figure-out-able, or is it? In this episode Pam and Kim discuss the pitfalls of teaching order of operations as an acronym to memorize, and offer a better alternative.
Talking Points:
- It's about communication rather than a thing to memorize.
- The notation is social knowledge.
- The order is logical mathematical knowledge and therefore figure-out-able!
- Open-middle problems for meaningful practice.
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 31, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Finding a fraction of something can be a tricky concept. In this episode Pam and Kim run through two strings that help reason about using fractions as operators.
Talking Points:
- How are unit fractions related like halves, fourth and eighths?
- Scaling and Over Strategy with unit fractions
- Fractions as operators
- Why is scaling a unit fractions critical? Knowing that three fourths is the same as three 1/4s?
- Knowing non-unit fractions from fractions is a precursor.
- Thinking of fractions only as part-whole is not sufficient.
- A different problem string using the operator meaning of fractions.
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 24, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Does it really matter what we call the whole? In this episode Pam and Kim take a closer look at fraction problems where the unit matters.
Talking Points:
- Kim and the beach
- How can there be 2 possible answers to the question "What is 1/2?"
- Focusing on the unit
- Naming the unit
- What happens when the unit changes?
- Help students focus on the unit, changing the unit, and finding a fractional amount of that new unit
- Even test writers struggle with fractions
- Re-unitizing will support students to reason through fraction multiplication
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 17, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How many people do you know that shy away from fractions? In this episode Pam and Kim discuss why teaching students to use step by step procedures to solve fraction problems actually leaves them not able to think about fractions at all.
Talking Points:
- We love hearing your stories!
- What kind of reasoning do fractions engage?
- What happens when students learn to mimic steps rather than reason about fractions?
- What does reasoning about fractions look like?
- Are greatest common denominators really that important?
See Episode 5, 67, 68 for more about Development of Mathematical Reasoning
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 10, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Minus-minus, plus-plus, or is integer subtraction actually figureoutable? In this episode Pam and Kim use a Problem String to build real understanding of integer subtraction.
Talking Points:
- The importance of having multiple contexts
- Seeing the negative symbol as "opposite of"
- Using distance
- Understanding takes time, but is so worth it!
See Episodes 181-183 for more about Integer operations.
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 3, 2024.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Tracking students and sorting them into 'higher'/'lower' tracks is a topic that we have really, really firm feelings about. In this episode Pam and Kim discuss the unintended consequences of tracking students and offer some ideas to consider.
Talking Points
- Who does tracking benefit, who does it hurt?
- Distaste for the vocabulary used to describe tracks of kids
- Everyone can do more real math than fake math
- From our experience as a teacher
- From our experience as a parent
- From a student's perspective
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 27, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Happy holidays! Pam and Kim invite you to revisit Ep 87, it's super important! How do you navigate teaching math that is figure-out-able if your standards include the teaching of algorithms?
Talking Points:
- All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems.
- Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year.
- Students will approach a standardized test with confidence and less stress if they have been given opportunities to struggle productively all year and become good mathematicians.
- Introduce the algorithm as a study of why the algorithm works for the very end of the year. Introducing the algorithm too early in the year risks giving students the option to turn their brains off.
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Facebook: Pam Harris, author, mathematics education
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 20, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Can integer subtraction feel intuitive without rote memory? In this episode Pam and Kim delve into a Problem String and explore integer subtraction relationships.
Talking Points:
- Integer chips?
- Students reason about subtracting integers
- Distance versus removal
- Problem String subtracting integers in context
- When context is less helpful
- Don't go to rules, stay in reasoning
See Episodes 149 and150 for more about distance vs removal
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 13, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Mimicking rules for integer operations does not help students become doers of Real Math, and frankly doesn't often stick in their long term memory. In this episode Pam and Kim walk through a Problem String that helps students develop an intuitive understanding of integer addition!
Talking Points:
- Exploring the beach as a context
- Equations and number lines in context
- Carefully chosen numbers to avoid distracting cognitive load
- Subtraction symbol or adding a negative? Parentheses or not?
- Let students grapple, then support and help make sense of ambiguity
Check out our social media
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 6, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How can we help students reason about integers? In this episode Pam and Kim discuss fun and natural ways to explore and understand both positive and negative integers.
Talking Points:
- The Pen/Pencil argument continues
- 5th graders can reason about integers
- Games do develp understanding of integers
- Clothes line math with integers
- Exploring four useful contexts for integers
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 29, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How do you label fractions on an open number line? How do you label a fraction of a candy bar? How many cuts do you make to cut a candy bar into fourths? Pam and Kim invite you to revisit episode 138, this time with an ear towards fractions.
Do your students ever get confused about counting obects vs counting distance? In this episode 138 Pam and Kim use a Problem String to help build intuition about everyday subtraction problems.
Talking Points:
- Experience a Problem String to build relationships
- Fencepost Problems are all over the place
- Students can't just pluck numbers out of Fencepost problems
- Cathy Fosnot's replacement unit, "Measuring For the Art Show"
- Other places these kind of problems show up
- Kim explains her strategy
See episode 111 for more about "Measuring for the Art Show"!
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 22, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What does it mean when we say 'fake math' or 'less sophisticated'? Pam and Kim discuss how learning Real Math is empowering and opens a whole new world of understanding.
Talking Points:
- Are squared numbers an important thing to own?
- The Matrix
- It takes experience to understand perspectives
- Martians
- Doing 'fake math' or using a 'less sophisticated' way of thinking does not make the person fake or unsophisticated
- Real math is empowering and can open up a new reality!
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 15, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We can be our own kids' best teachers, even when it comes to gnarly division problems. In this episode Pam and Kim relay their experiences exploring decimal division with their own kids.
Talking Points:
- A tool for holding your thinking - a ratio table
- It's not about how much you can hold in your head
- Help them start with what they know
- Problem Strings are not about answering just the last problem
- It isn't about being able to solve every problem
- It's about owning the major relationships in order to think like a mathematician
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 8, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Recorded live from NCTM! Pam and Kim discuss some of their experiences and takeaways from the 2023 National Council of Teachers of Mathematics conference.
Talking Points:
- Travel stories
- As kids grow, teachers grow as well
- Know your content know your kids to choose Problem Strings for your students
- Tools that focus on answer getting stifle students reasoning
- Using a neutral response to keep students and adults continue their thinking
- We all need to understand the content - teachers and learning
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 1, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Place value is so much more than labeling digits. In this episode Pam and Kim dive into place value and common teaching practices that are necessary, but not enough.
Talking Points:
- A fascination with the macabre
- Typical place value labeling and additional things you can think about to develop place value
- Precise questioning yields deeper place value thinking
- What are Exploding Dots?
- More about our place value system
- Practicing expanded notation is not enough
You can register for the Place Value Mini-Workshop now! Don't miss your opportunity to transform your math teaching: https://www.mathisfigureoutable.com/mini
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 25, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Division is figure-out-able! In this episode Pam and Kim discuss the most sophisticated strategy for division and precursors that students can begin developing in the fourth grade!
Talking Points:
- An Equivalent Ratios Problem String
- Precursor relationships
- Scaling up or Scaling down
- What makes Equivalent Ratios the most sophisticated strategy for division
- 4th grade can begin to reason about division using the "bigger, smaller thing" to reason about division
- 5th grade can begin to reason about equivalence
- Relational thinking
See Ep 64 and 132 for more on equivalent ratios!
Checkout mathisfigureoutable.com/relational-thinking for free exercises to develop the equivalent ratios strategy..
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 18, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Our students can learn to approach math problems like mathematicians! In this episode Pam and Kim look at one of the most sophisticated multiplication strategies that many mathematicians use.
Talking Points:
- Creating an equivalent problem by Doubling and Halving.
- What makes a problem reasonable to solve without a calculator?
- Double/Halve; Triple/Find a Third; Quadruple/Find a fourth
- What makes Doubling and Halving one of the most sophisticated multiplication strategies
- Flexible Factoring - for more information see Ep 153
- Pitfalls of direct teaching and strategy
Check out the Instructional Routine called Relational Thinking at: mathisfigureoutable.com/relational-thinking
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 11, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Some subtraction strategies can only get you so far, but with a little more sophistication complex problems become really nice to think and reason about! In this episode Pam and Kim build and discuss the Constant Difference strategy for subtraction and use it to solve a really gnarly problem.
Talking Points:
- Equivalence strategies are more sophisticated
- Hallmarks of sophisticated stategies
- Modeling Constant Difference
- Relational Thinking Routine
Check out the Instructional Routine called Relational Thinking at: mathisfigureoutable.com/relational-thinking
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 4, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What makes a strategy sophisticated? In this episode Pam and Kim build the most sophisticated strategy and talk about how and why to develop it with students.
Talking Points:
- What are the most sophisticated strategies?
- Strategies that require more simultaneity require more time to develop
- Simultaneous versus sequential
- Representing Give and Take
- We need more than one strategy
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 27, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Kids learn best with support from their parents, and helping with math has never been easier! In this episode, Pam and Kim are excited to share some tips about how to encourage your children as they grow in mathematical thinking and reasoning.
Talking Points:
Wait a little longer
- Resist the urge to tell the right answer
- Ask questions to cement the thinking
- Counting on and back from numbers other than one
- Guess my Number
- Discuss fractions by their unit fractions
- Compare fractions using landmarks
Get all these tips and more at https://www.mathisfigureoutable.com/parenttips
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 20, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
This one's for all you, parents! How can you support your children in becoming mathematicians? In this episode Pam and Kim go over their favorite ways to explore math at home in fun game-like activities.
Talking Points:
Speak about math positively
- Wondering
- Doubling and Halving
- Using 10s to find 9s and using 10s to find 5s
- I Have, You Need
Get the free download: https://www.mathisfigureoutable.com/parenttips
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 13, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Can you reason about what it means for a point to be within a given quadrant? Can your students? In this episode Pam and Kim discuss weather and geography to develop understanding of the quadrants in the cartesian coordinate system.
Talking Points:
- Understanding points relative to their quadrants and the y = x line
- Kim's connection to Alaska
- What makes Australia so unique
- Graphing inequalities is Figure-Out-Able!
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
Workshop registration is open! Learn more here: https://www.mathisfigureoutable.com/workshops
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on September 6, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Workshop registration is open! Learn more here: https://www.mathisfigureoutable.com/workshops
Let's do some guessing! In this episode Pam and Kim develop some functional reasoning by analyzing the relationships between their guesses and reality.
Talking Points:
- Pam's guesses using her pop culture knowledge
- How would you know if you are a good guesser?
- Graphing guesses and actual age as an ordered pair
- Using the data to discuss the meaning of y=x
- The parent function for building all functions
Check out our social media
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
Workshop registration is open! Learn more here: https://www.mathisfigureoutable.com/workshops
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 30, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Workshop registration is open! Learn more here: https://www.mathisfigureoutable.com/workshops
What does it mean for math to be figure-out-able? What will you teach? How? Why? In this episode Pam and Kim discuss their thoughts to changing the "how" and "what" of math education around the world and explore the "why".
Talking Points:
- "What" math we teach should come first
- "How" the math should be embedded in the "what"
- What Pam and Kim think about "Why" make the change?
Check out our social media
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Workshop registration is open! Learn more here: https://www.mathisfigureoutable.com/workshops
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 23, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What role does terminology have in math teaching? How do we want students to approach problems? In this episode Pam and Kim discuss when to teach vocabulary how we can prepare students to tackle problems with confidence.
Talking Points:
- "Just In Case" vs "Just In Time" vocabulary
- Social Knowledge vs Logical Mathematical Knowledge
- Anchor Charts to cinch learning
- Rejecting key words for operations
- Wrong answers are opportunities for good teacher feedback
For more about Anchor Charts check out Episode 123
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Register here for the You Can Reach More Students Math Challenge! Free and live August 23-25, 2023.
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 16, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
There is so much that is good happening in the math teaching community! In this episode Pam and Kim discuss how we can determine how much of which good things to put into our classrooms.
Talking Points:
- Going beyond nixing tricks
- Social versus logical knowledge
- Nixing the tricks is more than explaining the math better
- The dangers of going all in on any good teaching practice
- Number Talks
- Exploding Dots
- Manipulatives
- Keep asking for clarification and refining your craft in order to create mathematicians in your classroom
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 9, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Who does not love a quick, easy routine that gives students useful problem solving relationships? In this episode Pam and Kim revisit I Have, You Need and apply it with different target numbers.
Talking Points:
Kim and Pam play I Have, You Need often with clocks and marathons
It's not about speed
Goal is reducing cognitive load in the midst of solving other problems
Another goal is building fluency
Other important target numbers for early elementary and even middle and high school students
Get the free I Have, You Need download! bit.ly/ihynroutine
See Episode 7 and 121 for more on I Have, You Need
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In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on August 2, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
There's a lot of math jargon in the world and a lot of teaching terms; it can be hard to not talk past each other. In this episode Pam and Kim dig into the definition of Problem Strings and their role in the classroom.
Talking Points:
- Howie Hua
- Problem Strings are NOT strategies to solve A problem
- Problem Strings ARE instructional routines
- Types of Problem Strings
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 26, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What are some important relationships that students can use to do Real Math with fractions? In this episode Pam and Kim discuss some important relationships that can help develop deeper understanding about fractions for fractional equivalence and comparison.
Talking Points:
- A listener's review
- Using benchmark fractions to compare
- Using a number line to compare fractions
- How does understanding unit fractions help compare ugly fractions?
- Why we use symbols to represent complex ideas
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 19, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
What if your students could intuit the relative sizes of fractions? In this episode Pam and Kim think about where fractions go on clothes lines to show how you can help your students understand the meaning of numerators and denominators
Talking points
- A prudent mama's perspective
- Clothes Line Math
- The meaning of numerators and denominators
- Abstracting fraction relations
Take our math perspectives quiz! http://bit.ly/xyzquiz
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 12, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How we teach and what we teach are both really important. In this episode Pam and Kim wrap up their discussion on Peter Liljedahl's book Building Thinking Classroomsand how it meshes with the Math Is Figure-Out-Able movement.
Talking Points:
- Defront the classsroom?
Don't let language hamper the rich task - Consolidations versus math congresses
- Using hints and extensions
- We need the how and the what
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on July 5, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We love when students are thinking and reasoning, and we thing Dr. Peter Liljedahl has some great ideas. In this episode Pam and Kim continue to discuss some of his ideas and how they mesh with the math is figureoutable mentality.
Talking Points:
- Which questions to answer
- Get in, get out
- Approach groups with your own question
- Using neutral responses
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 28, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We love it when students are thinking and reasoning, and it's important to know how best to build and experience sophisticated strategies. In this episode Pam and Kim continue discussing Dr. Peter Liljedahl's work and finetune where it's appropriate to use vertical nonpermanent surfaces, and what other kind of tasks we should be doing whole class with students.
Talking Points:
- Randomized Groups at Vertical Non Permanent Surfaces in random groups are great for Rich Tasks that follow your curriculum
- Problem Strings are best used whole class to build specific strategies, models, and big ideas
See Episode 157 for Pam and Kim's introductory comments about Dr. Liljedahl's work.
Check out Pam's social media (I changed this to "Pam's" since it doesn't include mine)
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 21, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We want our students to be confident problem solvers who can think and reason through complex problems. In this episode, Pam and Kim highlight some of Dr. Peter Liljedahl's work on Building Thinking Classrooms to use student's natural inclinations to help them work better and more collaboratively.
Talking Points:
It's about thinking, not mimicking
- Thinking Tasks not mimicking tasks
- Vertical Non Permanent Surfaces
- Visibly random groups
- It takes time for kids to accept working in random groups
- Pulse of the room: Are student's opting out? What math are groups using?
- The "how " is important, but so is the "what"
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 14, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We've reached our third anniversary of the podcast! There's a lot that's been said, so we thought we'd highlight some of the quintessential Pam Harris topics from previous episodes that you need to transform your math classroom. In this episode Pam and Kim blitz through what makes the Math is Figure-out-able Movement so important and unique. They also list out which episodes you can listen to for more information about these key concepts.
Talking Points:
- The Development of Mathematical Reasoning: Ep 5, 6, 67, 68
- Models vs Strategies: Ep 9
- Algorithms Are Not the Goal: Ep 2, 94-99
- Different Math Perspectives: Ep 24-28
- Problem Strings: Ep 33, 71, 72
- Everyone Learns, Everyone Grows: Ep 39
- Know Your Content, Know Your Kids: Ep 74
- Do, Say, Represent: Ep 128
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on June 7, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Can kids reason about fraction division? In this episode Pam and Kim explore the definition of fractions through a Problem String and show how you can help students build experiences so that fraction division is a natural outcome.
Talking Points:
- Can students reason about 1/25 divided by 4?
- Dividing parts of candy bars Problem String experience
- Discovering the definition of fractions
- Kids can intuit!
See Episodes 142-144 for more about fraction division.
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 31, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
It's exciting to watch our students gain confidence and mathematize with the best of them, but it can be scary knowing that next year their teachers may be disappointed that your students haven't memorized the traditional algorithms. In this episode Pam and Kim discuss how you can communicate expectations to students and teachers alike to embolden your students that math will always be figure-out-able.
Talking Points:
- Your job is for this year, not to prepare for next year
- Help students know math will always be figureoutable
- Introduce next year's teacher to how they can expect your students to approach a problem
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 24, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How sophisticated is your multiplicative reasoning? In this episode Pam and Kim build Flexible Factoring and show how powerful understanding can be!
Talking Points:
We love hearing from listeners!
A Problem String
Develping distributive, associative and commutative properties
Where does Flexible Factoring fit into Multiplicative Reasoning?
Why understanding and owning multiplication facts is more powerful than memorization
For more information about the Development of Mathematical Reasoning, see Episodes 5 and 6.
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 17, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How do you naturally approach math problems? How do you wish you would naturally approach problems? In this episode Pam and Kim discuss how we as teachers and our students can form powerful new habits to become better mathematicians.
Talking Points:
- We all have habits based on our own experiences
- Can we change our old habits?
- Is it easy to change old habits?
- Do you have to know the most efficient strategy when you start messing with a problem?
- Can you change your mind about which strategy you want to use after you have started working with a problem?
- How long does it take a student's numeracy to grow?
- Want to change some of your mathematical habits?
You can register for one of our fantastic online workshops now! The brand new Building Powerful Subtraction workshop is available, as well as all of the workshops from previous years. Don't miss your opportunity to transform your math teaching: https://www.mathisfigureoutable.com/workshops
Want to know which workshop is for you? Take this quiz: https://bit.ly/whichworkshop
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 10, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
How can we help students own subtraction facts? In this episode Pam and Kim describe some basic strategies and then walk us through facilitating two Problem Strings to build subtraction relationships.
Talking Points:
- I Have, You Need - see Episode 7 for more on I Have, You Need
- Patterns in a subtraction chart
- Generalizing about subtracting 9
- Noticing differences of 1 or 2
- Diagonal patterns of Constant Difference
- Subtracting to 10 Problem String
- Using Doubles Problem String
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on May 3, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
We're digging deep into subtraction! In this episode Pam and Kim talk about what they mean by "memorizing" single digit subtraction facts and the relationships that can empower students to own single digit facts and apply the same relationships to more sophisticated numbers as well.
Talking Points:
- The different meanings of "memorize the facts"
- Relying on rote memory of facts in isolation leaves students with no other recourse
- "No timed drills" does not mean no work on facts, but different work
- Remove to 10
- Using Doubles
- Find the Difference
- Remove a Friendly Number Over
- Relationships are built, not rote-memorized
See episode 149 for more about the two meanings of subtraction
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 26, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
There's so much power to understanding subtraction that extends all the way to higher math. In this episode Pam and Kim discuss beginning steps to help students develop an understanding of subtraction, preparing them for success.
Talking Points:
- How does I Have, You Need apply to subtraction?
- Subtracting across zeros is a beast! So what do we do?
- Where subtraction helps in multiplication, division and beyond
- Understanding removal versus difference
- Why is this important for higher math?
- What happens if we force kids into steps?
- What you can do to help your students?
See Episode 150 for more about "Memorizing Subtraction Facts"
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 19, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Establishing a strong understanding of the area model also prepares students for more advanced topics all the way into college! In this episode, Pam and Kim describe how useful the area model is as a foundation for further understanding throughout a student's learning career.
Talking Points:
- Using the area model builds intuition of the distributive property
- Using and understanding of the area model for fraction multiplication
- Paradigm shift for teachers to think about what students know about whole numbers and apply it to fractions
- The area model as a tool, not something that is sketched for every problem
- Area model inspired graphic organizer for polynomial multiplication, polynomial division, and conics
See Episodes 146 and 147 for more discussion of the Area Model
Check out the new t-shirt at https://www.mathisfigureoutable.com/merchandise
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 12, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
The area model can do more than build Spatial Reasoning. It can help make sense of the major multiplication and division strategies! In this episode Pam and Kim use a Problem String to show how reasoning about area can build more sophisticated and efficient multiplicative relationships.
Talking Points:
- Multiplication is about grouping groups
- The area model can help make sense of multiplicative relationships and properties
- Choose and celebrate efficient strategies
- Reasoning about area makes relationships pop so that the strategies are natural outcomes!
See this blog for a picture of Pam's model in this episode: https://www.mathisfigureoutable.com/blog/ep147
See Episodes 146 and 148 for more discussion of the Area Model
Check out the new t-shirt at https://www.mathisfigureoutable.com/merchandise
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on April 5, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
The area model is a great tool to help students develop multiplicative and spatial reasoning, but let's get clear on some things. In this episode Pam and Kim discuss some of the common misconceptions about the area model and show how it can be used help students make connections between area and multiplication.
Talking points:
- What is an area model?
- Common misunderstanding around an area model
- Place Value Partial Products vs Smart Partial Products
- Rote memorizing perspective vs Math-is-figureoutable perespective
- Closed/Discrete versus Open arrays
- Area models build spatial reasoning and connections of products to area and factors to dimensions
- Ratio Tables are better models for cranky computation problems
See Episodes 129-133 for more about Ratio Tables and 147 and 148 for more about the Area Model.
Check out the new t-shirt at https://www.mathisfigureoutable.com/merchandise
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 29, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
There are a lot of small shifts needed in math education, and they can have huge impacts. In this episode Pam and Kim talk about some of these shifts that will be included in the new mini workshop. This workshop will help you address the most important things to get right as a math teacher.
Talking Points:
Algorithms verses strategies
Models verses strategies
Common vocabulary
A few major relationships lead to the major strategies
Problem Strings versus Problem Talks
Major Strategies ebook
Check out the mini workshop https://www.mathisfigureoutable.com/mini
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 22, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Sure, simple fraction division is figure-out-able, but what about gnarly fractions? In this episode Pam and Kim uncover simple relationships that make division of any fractions figure-out-able!
Talking points:
- What happens when the fractions aren't as nice, especially fractions where their denominators are not factors of each other?
- Thinking quotitively
- The connection between division and fractions
- Find common denominators to divide
- Use relative size of the fractions to estimate the quotient
- We don't teach rules for students to mimic, we develop relationships
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 15, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Fraction division does not have to be scary, and it certainly does not have to be memorized. In this episode Pam and Kim show how to reason through non unit fraction division problems.
Talking Points:
- What is a unit fraction?
- What does it mean to think quotitively about division?
- A Problem String building on unit fraction understanding for division of non unit fractions
- How to model this Problem String
- Using whole number relations among fractions
- Fraction division is accessible!
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 8, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
Is fraction division figure-out-able? You bet! In this episode Pam and Kim tackle another listener submitted topic and reason through a fraction division Problem String.
Talking Points:
- A sign of fake math
- An old wound for Pam and Kim
- A listener's question
- Two ways of thinking about division: partitively and quotitively
- A Problem String to develop division of fractions
- Why it helps to develop reasoning early with whole numbers
- Teacher moves to facilitate the string
See Episode 64 for another Problem String and discussion of thinking about quotitive division.
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on March 1, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Want more? Check out the archive of all of our #MathStratChat posts!
As teachers we want to help our students, and often we do that through questioning. In this episode Pam and Kim discuss how maybe there isn't a perfect list of questions, but it's our pattern of questioning that matters.
Talking Points
- We love hearing your suggestions
- Focusing on a list of questions vs a pattern of questioning
- Funneling pattern of questioning vs. Focusing pattern of questioning
- Focusing is more like a conversation rather than a list of questions
- To focus students you need to know your content, know your kids
- Examples through the grade levels
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 22, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Have you ever noticed how many different meanings there are for the word simplify? Even if you limit it to mathematical meanings, there's a lot. In this episode Pam and Kim discuss how we can better communicate with students what we really want them to do when we say 'simplify.'
Talking Points:
- Asking students to 'simplify' can often be a guessing game as to what we really want students to do.
- Why not level the playing field?
- Some meanings of "simplify" can be contradictory.
- There are better ways to ask students what we actually mean for them to do when they see that word "simplify".
See episode 18 "This, Not That" for other examples of unhelpful words sometimes used in math teaching.
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 15, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Happy Valentines Day! We love math, and we love you, our listeners! In this episode Pam and Kim discuss a less familiar addition and subtraction strategy that they're coming to love more and more.
Talking Points:
- A Problem String to build relationships in order to use common factors in addition and subtraction problems
- Why is it not a main strategy?
- Where and why teach it anyway?
Find our free e-book here! https://www.mathisfigureoutable.com/big
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 8, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
Do you ever fall into the "off by one" trap? Do your students ever get confused about counting objects vs counting distance? In this episode Pam and Kim use a Problem String to help build intuition about everyday subtraction problems.
Talking Points:
- Experience a Problem String to build relationships
- Fencepost Problems are all over the place
- Students can't just pluck numbers out of Fencepost problems
- Cathy Fosnot's replacement unit, "Measuring For the Art Show"
- Other places these kind of problems show up
- Kim explains her strategy
See episode 111 for more about "Measuring For the Art Show"!
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on February 1, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
The world is changing, and artificial intelligence is going to replace teachers! ...Or not. In this episode Pam and Kim discuss how teaching Real Math is more important now than ever, and we don't have to be afraid of those pesky robots.
Talking Points:
- How Chat GPT is different from AI like Photomath
- A teacher's paradigm will influnce how much AI will change the way we teach math
- Will the future of AI change the way we think about grading and homework?
- Does the future if AI promote answer getting or deeper understanding?
- Why Real Math is so important
- Teachers are going to need a support system to navigate the change.
Try out Chat GPT here: https://chat.openai.com/chat
Registration for our workshops and Journey is now open! Find what help is best for you at https://www.mathisfigureoutable.com/workshops
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 25, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
When do you offer students help and what kinds of help do you offer? In this episode Pam and Kim discuss the balance of what kinds of help to give students and also where to find just the right help as teachers.
Talking Points:
- Encouragement alone isn't enough help
- Modeling thinking doesn't mean to take over the thinking
- Funneling vs focusing patterns of questioning
- Does your help create mathematicians or learned helplessness?
- Teachers also need just the right amount and kind of help
Registration for our workshops and Journey is now open! Find what help is best for you at https://www.mathisfigureoutable.com/workshops
See also Episode 113 for more discussion about helping students.
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 18, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
What does it take to change our perspectives so we can teach more and more Real Math? In this episode Pam and Kim discuss how they can help YOU when you join the You Can Change Math Class Challenge!
Talking Points:
- What is the Challenge anyway?
- Is the math you do at home different from the math you do in school? (Thank you John SanGiovanni)
- What are the major perspectives and how can I learn more about them?
- How does the perspective of how I was taught affect how I teach?
Register for the challenge here! https://www.mathisfigureoutable.com/change
Get the free ebook here! https://www.mathisfigureoutable.com/big
For more on the perspectives we talked about see episodes 24-28, and take the quiz to learn more about your perspective! https://www.mathisfigureoutable.com/xyz
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 11, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
We have heard from both teachers and leaders that it's a struggle to know what to look for in a Math is Figure-out-able classsroom and how to evaluate it, and help each other better our teaching craft. In this episode Pam and Kim go through the NCTM Effective Teaching practices and discuss and suggest conversations about how those standards look in a Math is Figure-out-able classroom.
Talking Points:
- What does it mean to "establish mathematics goals to focus on learning"?
- What do tasks that "promote reasoning and problem solving" vs direct teaching look like?
- What all is entailed in "connecting matematical representations"?
- Why is "meaningful mathematical discourse" critical and what does it sound like? (listen to Episode 128 for more about Do, Say, Represent)
- What do "purposeful questions" sound like? The difference between funneling vs focusing questions.
- How we tweak "build (procedural) fluency with conceptual understanding"?
- What is "productive struggle"? Do you need time, or help? (listen to Episode 113 for more about productive struggle)
- What do tasks or problems look like that "elicit evidence of student thinking" then "use the thinking" to move the math forward?
Don't forget to join the You Can Change Math Class Challenge! Register at mathisfigureoutable.com/change
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on January 4, 2023.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
It's our wrap up episode on ratio tables. In this episode Pam and Kim answer some frequently asked questions and talk about how we can take ratio tables into higher math and beyond.
Talking Points:
- Why teachers erase and when should students erase?
- Do, Say, Represent: how to help students represent what's going on in their heads
- Ratio tables aren't a gimmick, they make thinking visiable of how mathematicians and other mathy people think for the masses
- Using ratio tables to notice patterns and reason using mathematical relationships in order to write the equation of a line
- Using ratio tables to reason about rational functions and transformations
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 28, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
It's time to talk equivalent ratios and fractions! In this episode Pam and Kim demonstrate how understanding equivalent ratios leads to powerful reasoning about fraction operation, without the need to memorize steps and rules or algorithms.
Talking Points:
- Empowerment is about having choice
- Ratio tables aren't a strategy, they're a model/representation of the strategy or strategies being used
- If you understand fractional equivalence, you don't need rules for fraction operations
- How to add 3/4 and 5/7 thinking and reasoning using a ratio table
- Do non-equivalent ratios go on the same ratio table? How do you handle adding non-equivalent ratios?
Note: for more infomation about the packs and sticks of gum scenario, listen to Episode 131
Check out our social media
Twitter: @PWHarris
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 21, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Have we convinced you to love ratio tables as much as we do yet? In this episode Pam and Kim tackle another model building Problem String to show what a powerful model a ratio table can be.
Talking Points:
- A non-unit ratio Problem String
- Ratios must be equivalent in a ratio table
- Reasoning proportionally can be much cleaner than cross-multiply-and-divide
- Model building strings verses strategy building strings
- Start with reasoning and representing thinking then dive deeper into properties
- What's next? A strategy building string using a ratio table as a model
- Don't forget to post how you represented your ratio table on social media!
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 14, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
We can't get enough of ratio tables! In this episode Pam and Kim go through another division Problem String, highlighting how they model-represent their thinking on ratio tables. They invite listeners to grab a pen or pencil and practice representing their own thinking on a ratio table.
Talking Points:
- Noticings from MathStratChat
- Does context matter?
- Does a ratio table have to be in sequential order?
- Does it matter when to erase during the Problem String?
- Does it matter when to use brackets or arrows?
- Can color help highlight relationships?
- How do you introduce a ratio table?
- A tool to represent thinking that can lead to new thinking
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on December 7, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Why are ratio tables so amazing? In this episode Pam and Kim describe ratio tables and what makes it on the favorite mathematical models short list. Then they show it off with a Problem String.
Talking Points:
- What is a ratio table?
- Can ratio tables be both vertical or horizontal?
- Does the context of a ratio table matter?
- Should you ever erase when using a ratio table?
- What else should students see and use besides a ratio table?
- A Problem String to model on a ratio table
- Some powerful generalizations from the problem string using a ratio table model
- Are we done talking about ratio tables?
Online workshop registration opens in January!
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 30, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
Do your students ever say things like, "I just know" or "I don't know"? What can we do with that? How can we help students have meaningful discussions about their thinking and why is it so important? In this episode, Pam and Kim discuss the challenges of saying and representing our thinking, and how we can help students clarify their thinking in order to be able to discuss their strategies.
Talking Points:
- When students say "I just know" because they just don't know what else to say or do
- We can do more than we can say and say more than we can represent
- Do, Say, Represent
- The importance of knowing your content and knowing your students
- Helping students grapple with and resolve disequilibruim helps clarify and solidify their learning
- Stay tuned for upcoming podcast for more about modeling to make student thinking visible
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 23, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
We're wrapping up our series on the Over strategy. In this episode Pam and Kim reason through a Problem String to develop the Over strategy for division.
Talking Points:
- A Problem String to develop relationships for the Over strategy for division
- Great teacher move that we call "the trail off method" to help students generalize and justify the relationships they are using
- Calling out the relationships vs direct teaching
- Where does the Over strategy fit in the hierarchy for division?
- Advantage of using a ratio table to model Partial Products vs 'lucky 7' or 'magic 7'
- Over strategy is helpful for addition and subtraction, but it is essential for efficient multiplication and division
Be sure to get the BIG download with all of the major strategies! https://www.mathisfigureoutable.com/big
Plus, get the download specifically for building the Over strategy for all four major operations:
https://www.mathisfigureoutable.com/over
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 16, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
We are not over with the Over strategy! This week Pam and Kim dive into the Over strategy for multiplication.
Talking Points:
A new name for the Double and Half strategy?
A Problem String to develop relationships for the Over strategy for multiplication
Where Over strategy for multiplication fits in the hierarchy of multiplicative strategies
Using the Over strategy to help students begin to use more Smart Partial Products
Be sure to get the BIG download with all of the major strategies! https://www.mathisfigureoutable.com/big
Plus, get the download specifically for building the Over strategy for all four major operations:
https://www.mathisfigureoutable.com/over
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 9, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
We just love the over strategy! In this episode Pam and Kim go through a Problem String to develop the over strategy for subtraction.
Talking Points:
- Over subtraction is tricky, without experience
- Numberlines make over subtraction figureoutable!
- Redraw helper problems to help the strategy pop
- Where does over subtraction fit in the hierarchy?
- Plus place value!
Download free examples of the Over Strategy: mathisFigure-Out-Able.com/over
Download the free ebook of major strategies: mathisFigureOutAble.com/big
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on November 2, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
In case you haven't noticed, Kim has a favorite strategy. In this episode Pam and Kim discuss one of the most important strategies and how to use it for addition.
Talking Points:
- Great listener feedback!
- A Problem String
- Where does the Over Strategy fit in the hierarchy of strategies?
- How does the Over Strategy help build place value?
- Modeling is super important
- Where we find the Over strategy day to day
Download free examples of the Over Strategy: mathisFigure-Out-Able.com/over
Download the free ebook of major strategies: mathisFigureOutAble.com/big
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 26, 2022
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
How can we help cement students' learning without memorizing steps? In this episode Pam and Kim share the power of anchor charts and how you can make them with your students.
Talking Points:
- What is an anchor chart?
- Why have students co-create the anchor chart with teacher fascilitation?
- Why is "Do, Say, Represent" critical for student learning?
- What kinds of things go on an anchor chart? Kim suggests 3 things.
- When do you create an anchor chart?
- Where does an anchor chart go?
- When do you refer to an anchor chart?
- How can students use the anchor chart as a tool?
- What do meaningful notes look like for students' notebooks?
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 19, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others' strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
When dealing with word problems it can be tricky for students to decide which operation to use, so we need a way to help them memorize what to do in any given situation... right? In this episode Pam and Kim discuss how reasoning empowers students to skip rotely memorized steps to choosing operations and get straight to problem solving!
Talking Points:
- Word problems feel unfair to students who have only experienced fake math.
- Students with reasoning develop intuition for what relationships a problem requires.
- Rich Tasks and Problem Strings with mini-contexts prepare students to apply their reasoning to real world contexts.
In today’s MathStratChat, Pam and Kim discuss the MathStratChat problem shared on social media on October 12, 2022.
Note: It’s more fun if you try to solve the problem, share it on social media, comment on others' strategies, before you listen to Pam and Kim’s strategies.
Check out #MathStratChat on your favorite social media site and join in the conversation.
When we teach real math, students come up with all sorts of cool strategies! But which ones are the main strategies, and how do we make the distinction? In this episode Pam and Kim take a listener submitted strategy and discuss where and what it's uses are.
Talking Points:
- Main strategies extend to multidigit problems
- Main strategies build sophistication
- Strategies are natural outcomes
What fun rhymes will best help your students learn to round? Just kidding! In this episode Pam and Kim describe their wholistic approach to rounding that helps kids build relationships like place value!
Talking Points
- No rhymes needed
- Using a number line to reason through rounding
- How rounding develops students' place value and other mathematical concepts.
Finding elapsed time can be a tricky concept, but when combined with a number line, we can make it figureoutable! Join Pam and Kim as they discuss using addition strategies to find elapsed time.
Talking Points:
- The birth place of I Have, You Need
- How students might approach elapsed time
- How to help students think about elapsed time more sophisticatedly
Do your students struggle tracking time or reading an analog clock? In this episode Pam and Kim discuss three simple ways you can help your students internalize time and elapsed time.
Talking Points:
- Help students build a feel for benchmark units of time
- Notice and tell what time it is a lot with kids
- Notice aloud how long things take throughout the day
A lot of people feel like when it comes to high school math, it's just not possible to think and reason through things anymore. Not true! In this episode Pam and Kim make the transition from Proportional Reasoning to Functional Reasoning and writing the equation of a line using relationships and what students already know.
Talking Points:
- Is math always Figure-Out-Able?
- How ratio tables prepare students for linear functions
- Example Problem Strings
- Registration for workshops closes this Friday!
Get a workshop while you can: https://www.mathisfigureoutable.com/workshops
What does teaching Real Math look like at your grade level? In the last episode Pam and Kim discussed the One Third/Two Thirds rule to structure math time. In this episode they give specific examples at various grade levels of what it might really look like.
Talking Points:
- 1st Grade - doubling and halving
- 3rd Grade - concepts around 100
- 5th Grade - multiplication and volume
- 7th Grade - rates (see Episode 112 for Unit Rate Problem String)
- Algebra I - exponential functions
- Pre-Calculus - functions
Our workshops are open for registration! Take advantage now to change your math classroom! https://www.mathisfigureoutable.com/workshops
A listener asked how would we structure our math class. In this episode Pam and Kim discuss the approach they'd take to provide their students with the best math education experience possible to learn Real Math and still meet their required standards and scope and sequence.
Talking Points:
- The Two-Third/One-Thirds rule
- Rich Tasks - see Episodes 102 and 103
- Test Prep?!
- Use instructional routines for spiral review
- Tune in to the next episode for examples
Registration for our workshops are open now! Sessions for everyone, K-12! Check them out!
https://www.mathisfigureoutable.com/workshops
The school year is starting! For this exciting time, Pam and Kim want to discuss what starting strategies can help you and your students to build thinking relationships and strategies rather than simply answer getting.
Talking Points:
- Problem Talks are great ways to pre-assess your students
- Partial strategies are a great starting place but we have to help students develop more sophisticated strategies
- The starting strategies for each major operation
- Students need lots of experience developing relationships through Problem Strings and Rich Tasks for strategies to be natural outcomes
Check out our free eBook to learn more about these strategies: https://www.mathisfigureoutable.com/big
And don't miss out on the You Can Change Math Class Challenge! https://www.mathisfigureoutable.com/change
Check out Episodes 10 and 12 of this podcast for more ideas about starting your school year.
How can you make changes in your math classroom to help your students do more Real Math? In this episode Pam and Kim describe some first steps, and bigger steps, you can take to transform your math class.
Talking Points:
- Creating a safe mathematical community conducive for Real Math to happen
- Wait time - "Do you want time or help?"
- Where are you on the continuum to make some or lots of changes?
- Tips on where to start wherever you are on the continuum
- Using Problem Strings, I Have, You Need, MathStratChat and other instructional routines and games
- What you celebrate, answers or thinking, is what students will share
- How to transform your curriculum if you're super gung-ho
Don't miss out on the You Can Change Math Class Challenge! Register today at https://www.mathisfigureoutable.com/change
Learn more about I Have, You Need by listening to episode 7, or visit us at https://www.mathisfigureoutable.com/blog/i-have-you-need
We sure loved discussing the Open Number Line last we, but have you ever hear of the Double Open Number Line? In this episode Pam and Kim discuss how the Double Number Line can be used to develop Proportional Reasoning and help prepare students for Ratio Tables.
Talking Points
- A Problem String to develop the Double Open Number Line
- Comparing it to the Ratio Table
- How the Double Open Number Line can prepare students for fractions, rate, and other concepts.
- The percent bar is a Double Number Line?
Check out our free download on Double Number Lines: https://mathisfigureoutable.com/double
The Open Number Line is not just a powerful tool for computation, but it's an amazing model for developing all sorts of mathematical concepts! In this episode Pam and Kim discuss how to help students develop the Open Number Line in a natural and meaningful way.
Talking Points
- Moving from discrete counting to a continuous model
- Introduce the Number Line through measurement
- Elapsed Time on a Number Line
- The precursor to the coordinate system
Also check out Cathy Fosnot's amazing rich task: https://www.heinemann.com/products/e01010.aspx
Multiplying decimals can be fun! In this episode Pam and Kim tackle several gnarly problems like 0.77 x 2.4, and have a blast doing it.
Talking Points:
- Building reasoning allows students to be flexible and have fun with decimal multiplication
- Kim uses percent and money to solve 0.77 x 2.4 with confidence (no need for a calculator)
- Pam represents her thinking on a ratio table for 0.77 x 2.4
- Different strategies for 0.77 x 0.24?
- What about 7.7 x 0.24?
- Why is thinking and reasoning so important?
Being able to scale comfortably is important for both whole and decimal numbers. And just as there are more sophisticated ways to handle scaling with whole numbers, we can also be more sophisticated scaling decimals! In this episode Pam and Kim describe how we can help students become comfortable with decimal multiplication using their understanding of whole number multiplication and then scaling.
Talking Points:
- Reflecting on the more sophisticated strategy from Ep 106
- Applying knowledge of whole number multiplication to decimals
- It's more about reasoning than shifting the decimal
- Reasoning in small steps builds understanding vs. just counting the decimals
- Reasonableness comes from keeping kids in reasoning land
- Language to focus on and language to avoid
How can we help students make sense of decimal multiplication? In this episode Pam and Kim run through two beginning Problem Strings that will get students feeling comfortable and understanding the world of multiplying decimals.
Talking Points:
- Which models are helpful
- Decimals and money
- Students need to develop a few starting relationships before becoming more sophisticated
- Smart Partial Products with decimals
We've gotten a ton of questions about decimals. In this episode Pam and Kim discuss three different models and why they are great for questioning and building relationships, but may or may not be good for computation.
Talking Points:
- Base Ten Materials
- Exploding Dots by James Tanton
- Money
Most students can scale up by ten as they begin to multiply larger numbers and that is a great starting place for students. In this episode Pam and Kim discuss a more sophisticated way of scaling numbers in multiplication problems.
Talking Points:
- How beginning learners will use multiplying by 10 in double digit multiplication problems.
- How more sophisticated students deal with smaller numbers then scale up.
- How this applies to middle school students.
- How can Five is Half of 10 be used with more sophisticated thinking?
Often people misunderstand what this game we call mathematics is and feel they aren't good enough to play. In this episode Pam and Kim discuss how students need the opportunity to experience and play in the real game of mathematics.
Talking Points:
- Mathematizing is not about speed
- Pam, the basketball player
- It's not about memorizing disconnected rules and procedures.
- Kim, the teacher pleaser
- Experience and opportunities are important so kids have choices
- We need all students in the game of math
- Is there such a thing as a "math gene" or natural talent?
- All students have different talents to bring to the table
- Take the Math Perspective Quiz to find more about your perspective of math class and instruction.
- All students have talents to bring to the table
It's our two year anniversary! We are so grateful you've spent this time with us. In this episode Pam and Kim discuss openly things they've learned and how they've grown during their journey as math teacher educators.
Talking Points:
- It's not 'Pam Math', it's Real Math and developing mathematicians!
- Coaching teachers is about mentoring, not just telling
- The importance of a common vocabulary - Check out Episodes 58 and 101
- Empowering teachers and leaders through Journey and Journey Leader
- Deep dive online workshops for Kindergarten through middle school
- Building Powerful Linear Functions for high school coming soon!
What are some examples of rich tasks that are designed to intrigue and engage students? In this episode Pam and Kim give some specific examples and describe why they are so rich.
Talking Points:
- Relatable to students not just real world
- An eye towards equity
- Lead to the mathematics
- Packed with patterns
- Natural extensions
- Make the math realizable
- Building Powerful Linear Functions coming Fall 2022
See Ep 47: Fractions as Fair Sharing where we explored the Sub Sandwich rich task!
Let's talk rich tasks! On Twitter we enjoyed a great conversation about what makes a rich task rich. We thought we'd comment on some great suggestions from Professor Tad Watanabe, inspired from his mentor Dr. Grayson Weatley.
Talking Points:
- Invite students to make decisions
- Replete with patterns
- Promote discussion and communication
- Tasks should lead somewhere
- Be extendable
- Have an Element of Surprise
- And More!
What comes to mind when someone says the word "strategy"? There are at least four different meanings for the word "strategy" in mathematics teaching. In this episode Pam and Kim parse out the different meanings and discuss how those meanings shape the outcomes of our teaching.
Talking Points:
- Numeracy Strategies
- Problem Solving Strategies
- Teaching Strategies
- Strategies for Teaching
- Why without one type of strategy, the other strategies will fall flat
We love that we've been able to make 100 episodes! We also love that 1 hundred is 10 tens, so let's talk place value! In this episode Pam and Kim discuss why students struggle with place value, and suggest some of their favorite place value activities.
Talking Points:
- Why 'place labeling' is ok, but not enough
- Count Arounds
- Multiple Towers
- Base 10 materials
- Using correct place value language
In the last 5 episodes we've laid out the most important strategies for students to be able to solve for all four operations. So what? In this episode Pam and Kim solve a gnarly problem to demonstrate how mathematizing can empower you and your students, and open up to the world of Real Math.
Talking Points:
- How to use the BIG downloadable e-book
- A gnarly problem solved using Real Math
- It's all about efficiency and developing more sophisticated reasoning
- Partial strategies are a great starting point but not the ending place
- Kudos to Pam's research and thoughtfulness
- Why does Pam seem to focus on computation?
- What believers are saying
- Other ways to learn with Pam
- We can make higher math more accessible
- BONUS: Kim's failed attempt at the standard algorithm
Get the BIG download here! https://mathisfigureoutable.com/big
Division is figure-out-able! In this episode Pam and Kim discuss the four main strategies students need to develop to solve any division problem that's reasonable to solve without a calculator.
Talking Points:
- Pam's personal harmful experience from the long division algorithm
- A precursor strategy: Partial Quotients
- Smart Partial Quotients
- Over-Under
- 5 is Half of 10
- Equivalent Ratios
- Combining strategies
Get the BIG download of all the major strategies for addition, subtraction, multiplication, and division here! https://mathisfigureoutable.com/big
What are the five major strategies for multiplication? In this episode Pam and Kim name and give examples of each of the five major multiplication strategies. If students own these strategies they should be able to solve any multiplication problem that is reasonable to solve without a calculator. They will be able to solve it as efficiently as a traditional algorithm and most of the time more efficiently than the traditional algorithm. But even more important than that, they will be developing Multiplicative Reasoning!
Talking Points:
- Smart Partial Products
- Over/Under
- 5 is Half of 10
- How are these strategies related to the distributive property?
- Doubling/Halving
- How is this strategy related to the associative property?
- Using Quarters & Scaling
- Bonus! Flexible Factoring
Get a download of all the major strategies here: www.mathisfigureoutable.com/big
It's time for subtraction! In this episode Pam and Kim name and give examples of the four main subtraction strategies students need to own to solve any subtraction problem that is reasonable to solve without a calculator.
Talking Points:
- Remove a Friendly Number
- Remove a Friendly Number - Over
- Remove to a Friendly Number
- Constant Difference
- How do students choose which one to use?
Get the download! www.mathisfigureoutable.com/big
What are the major strategies students need to know to solve any addition problem that is reasonable to solve without a calculator? In this episode Pam and Kim list them out, give examples, and some insights into how they choose which strategy to use for any given problem.
Talking Points:
- Splitting by Place Value (a precursor strategy)
- Add a Friendly Number
- Add a Friendly Number - Over
- Get to a Friendly Number
- Give and Take
- When do you use each strategy?
Get our download of all the major strategies here! mathisfigureoutable.com/big
We want students to be real problem solvers, and we know that means much more than helping them get correct answers. But we never want to put students in a position where they are disadvantaged because they don't know the traditional algorithms. We actually want them to have a much deeper and richer understanding of mathematical relationships. In this episode Pam and Kim begin a series exploring the major strategies for each operation that students need so that they can solve ANY problem that's reasonable to solve without a calculator.
Talking Points:
- Pam's journey from learning only step by step procedures to mathematizing
- How this series can take Pam's published books a step further
- How Kim, and many other mathematicians approach problems
- Ownership of the major relationships empowers students with choice
- Honor students thinking, but don't leave students where they are
Get the download!: mathisfigureoutable.com/big
When we feel passionately about the way we teach, we can sometimes inadvertently miscommunicate when speaking with parents. In this episode, Pam and Kim discuss how to appropriately talk about getting correct answers and preparing for high stakes tests so that parents know their children are in good hands.
Talking Points:
- Answers are important!
- What we don't want to communicate to parents
- Preparing students for high stakes tests is important!
- Insight into a test writer's thinking when they write test items
- Helping students mathematize will help them feel more confident and excel on high stakes tests
Partnering with parents can be a blast! In this episode Pam and Kim describe how they organize and run math nights to help parents experience mathematizing and get excited about what their students will be learning.
Talking Points:
- Typical parent math nights vs. our parent math nights
- Opportunity to share grade level or school wide expectations
- Importance of a Q & A for parents
- Help parents experience math the way their students do
- Mathematizing for parents at the "sweet spot" level of math
- Suggestions for finding Problem Strings to use at math nights
- Logistics tips for parent math night
- Advantages of a series of parent nights
How can we proactively partner with and support parents? In this episode Pam and Kim discuss ways they over communicate to parents to keep parents involved and not confused.
Talking Points:
- Newsletters: What is helpful information and tips for parents I can share?
- Parent-teacher conferences: What can I share with parents about math other than just grades?
- Homework assignments: I don't like drill and kill. What kinds of homework are helpful for students and parents?
Parents are so important, and sometimes they get concerned when their child isn't being taught math they way they were expecting. In this episode Pam and Kim discuss hearing parents' concerns and helping them feel heard and then helping them understand the math. We appreciate parents and we are better with them!
Talking Points:
- We want invested parents
- Parents need to be heard, and then they need to understand
- The importance of listening to understand
Kim has a story to tell that Pam hasn't heard yet! Listen in to get a feel of how math can be when students understand that Math is Figure-Out-Able.
Talking Points:
- Pajama Math and exploring relationships in multiplying fractions
- Can you really just multiply straight across with fractions?
- Two ways to reason about 3/5 times 3/9
- Pam and Kim reason multiple ways about 3/4 times 2/5
- Join us in #MathStratChat!
Most of us are probably teaching the way we were taught, to get correct answers to problems. But we aren't actually helping students understand and reason about the math. Which is more important? In this episode Pam and Kim discuss answer getting versus relationship building.
Talking Points:
- Phil Daro's research on patterns of math instruction from across the world
- Student success from answer getting instruction vs instruction that focuses on outcomes from reasoning
- The real purpose of math class
- Now that I know different, how can I do different and help kids reason?
Resources:
Phil Daro video: https://vimeo.com/79916037
Do your standards require you to teach algorithms? What then? In this episode Pam and Kim discuss how they prepare their students for success on high stakes tests without ever teaching a step by step algorithm or process.
Talking Points:
- All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems.
- Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year.
- Students will approach a standardized test with confidence and less stress if they have been given opportunities to struggle productively all year and become good mathematicians.
- Introduce the algorithm as a study of why the algorithm works for the very end of the year. Introducing the algorithm too early in the year risks giving students the option to turn their brains off.
What purpose has and should algorithms have in mathematics education? Are step by step What purpose has and should algorithms have in mathematics education? Are step by step procedures even to be taught at all? In this episode Pam and Kim talk about our role as teachers and what students need to think like mathematicians.
Talking Points:
- One student's perspective
- What are algorithms?
- Why have we taught algorithms in the past?
- Where are algorithms helpful in today's world?
- Do algorithms help students learn to mathematize?
- From another student's perspective
- Learn more in the online workshops
Aren't addition facts cool?! By this point you've learned some amazing relationships and strategies to help your students make real sense of and automatize the single digit addition facts. But sometimes learning and applying are two different things. In this episode Pam and Kim detail how to help your students get out of counting mode and actually apply the relationships they've learned to become fluent with single digit addition facts.
Talking Points:
- Why do some kids keep counting after they've learned these relationships?
- How to help kids break the counting habit and why that is important
- It's not about speed or only the answers, it's about developing more sophisticated thinkers and reasoners
- Deep dive online workshops for teachers
It's time for you to learn about the most important relationship your students need to know to automatize their addition facts: partners of ten. Partners of ten influence strategies for adding bigger numbers as well as strategies for other operations. In this episode Pam and Kim will discuss some of those influences and some games and routines specifically made to provide experience and build partner of ten relationships for all levels and all ages.
Talking Points:
- What are partners of ten?
- Do older students need partners of ten?
- Rich Tasks with 10
- Collect Ten
- I Have, You Need
- Establish partners of ten early in the school year
- Workshop registration is open until Feb 4!
Links:
bit.ly/partnersoftensgames
mathisfigureoutable.com/youneed
mathisfigureoutable.com/workshops
We build addition facts through relationships and fluency through experience. So what important patterns and relationships can help students master or reason with their single digit addition facts rather than rote memorize? How can we teach those patterns and what experiences can help students automatize and become more fluent with addition facts? In this episode Pam and Kim dig deeper into single addition facts and how we as teachers can can empower students to reason like mathematicians.
Talking Points:
- It's not about speed
- Doubles are important
- The Shoe Game
- The Doubles Game (Cathy Fosnot)
- Near doubles
- Ten-and or The teens
Check out the patterns we talked about here:
mathisfigureoutable.com/addrelationships
And don't miss registration for one our deep dive workshops! https://www.mathisfigureoutable.com/workshops
Addition is figure-out-able! In this episode Pam and Kim describe some of the fundamental patterns students should learn as they get familiar and automatize with their single -addition facts. We want students at all levels to have access to their facts so they don't bog down every time they encounter them.
Talking Points
- Connecting the concrete and pictorial experiences to symbolic representation.
- Tips for using flash cards and addition table.
- Noticing patterns can reduce the number of addition facts a student needs to fuss with.
- The role the commutative property plays learning addition facts.
- When is counting ok.
- Learning to trust the commutative property.
- Students need experience, lots of it.
Register for the You Can Change Math Class Challenge here: https://www.mathisfigureoutable.com/change
You can also register for a deep dive workshop today! Go to https://www.mathisfigureoutable.com/workshops to learn more.
So many people get left behind when it comes to higher math, because they never learned mathematize or to think more sophisticatedly and build complex relationships and simultaneity in lower math. Teachers often share that their students lack numbers sense or fluency, specifically lack of memorized basic math facts. That's why in this episode Pam and Kim start a new series on single digit addition fact fluency. Are the facts important? You bet! But how they are taught is even more important to be accessible and equitable for all students.
Talking Points:
- This series is for all grade level teachers!
- Is speed or quick recall important?
- Our goal: rote memorization or number relationships?
Learn more at bit.ly/pharrisinfo.
Don't forget to just the You Can Change Math Class Challenge at https://www.mathisfigureoutable.com/change!
We've come to the end of another year, and we'd thought we'd leave you with some suggestions on goals you can set for your teaching. In this episode Pam and Kim highlight some transformative goals that you probably haven't considered before. How could your math class look next year or next semester?
Talking Points:
- Learners setting goals around mathematical behaviors or practice standards.
- Teacher goals centered around the NCTM mathematics teaching practices.
- Teacher goal to elicit and use evidence of student thinking.
- SMART goals.
- Hey Australia! We appreciate you!
Don't you love the holidays? We sure do! It's such a great excuse to talk math with your family! In this episode Pam and Kim describe some ways (and activities they do) to involve math in their festivities, from formal games like I Have, You Need, Guess My Number, MathStratChat, to simply noticing and wondering.
Talking Points:
- Cooking and Baking
- Spending Holiday Money
- Dinner Games
- Daily Tasks
- Walks
- Car Games
- Notice and Wonder
As we approach Christmas and the holidays, we thought we'd talk about some of our favorite games that we love to gift others! In this episode Pam and Kim share what makes a great mathy game and list a few of their favorites that not only have numbers, but include some with strategy and logic. Also, don't forget to check out some of our Math is Figure-Out-Able merch for your own gift list!
Favorite Games:
- Splendor
- Multi (by joyfulmathematics.com)
- Prime Climb (by mathforlove.com)
- Tiny Polka Dot (by mathforlove.com)
- Qwixx
- Set
- Proof
- Mastermind
- Sequence
- Rack-O
- High Ho Cherry-O
We've got another one of our favorite routines for you today! In this episode Pam and Kim demonstrate the Relational Thinking routine, a routine that helps students understand equivalence and become more comfortable with relational strategies. Thanks to the Cognitively Guided Instruction group for introducing us to this routine!
Talking Points:
- Examples of the routine for all four operations
- What does the equal sign really mean?
- Strategies based on equivalence: Give and Take, Constant Difference, Doubling and Halving, Equivalent Ratio
Resources:
- Find examples of Relational Thinking problems here: https://www.mathisfigureoutable.com/relational-thinking
- Find our Developing Mathematical Reasoning info graphics here: https://www.mathisfigureoutable.com/blog/development-4
There are a lot of great instructional routines out there, and today we want to highlight As Close as it Gets. In this episode Pam and Kim discuss how to use this instructional routine in your classroom and how it can help your students get mathematizing with estimation!
Talking Points:
- A routine to help students learn what Real Math estimation is through reasoning.
- Examples
- Teacher moves to introduce the routine and common pitfalls
- Why do we use the routine?
- Where to find help for your classroom
Learn more about this powerful routine here: https://www.mathisfigureoutable.com/instructionalroutines
Are your students dumb or smart? Fast or slow? Under achiever or advance achiever? Or are they just your students with varying experiences? In this episode, Pam and Kim discuss labels, and the effect they have on you as teachers and your students. They propose a different way to look at your students so that you can provide opportunities and experiences for all students so that they continue to learn and love math.
Talking Points:
- The problem with labels.
- What do we believe about learning?
- Focus on providing experience rather than natural talent or ability.
How can we take what students already know and leverage that to make other mathematical connections? You've probably heard us mention that you should know your content and know your kids, but there's a lot of meaning behind that. In this episode Pam and Kim go in deep on how knowing your content and your kids support effective teaching practices and maximize learning for students.
Talking Points:
- We need to know beyond our standards.
- Why we need to look vertically and horizontally at our standard's landscape?
- How knowing our students can help target their individual zone of proximal development.
We did it! We made it to episode 73! Why is that an important milestone? Just cause it's Kim's favorite number :-). In this episode Pam and Kim take the opportunity to highlight some important milestones in the Math is Figure-Out-Able movement. We're so grateful you're a part of it!
Talking Points:
- Pam and Kim's favorite numbers
- Twitter followers and MathStratChat
- You Can Change Math Class Challenge
- Pam and Kim as colleagues
- Podcast
- Online Workshops
- What's coming up next?
Facilitating a Problem String is tricky business, so Pam and Kim take the time in this episode to provide some do's and don'ts that anyone can learn from.
Talking Points:
- What is a Problem String?
- How long should a Problem String last?
- Can Problem Strings be given in a worksheet or as a bell ringer?
- Does everyone share during the Problem String?
- How do I know which students should share and in what order?
- What if all of my students aren't using the strategy?
- What if I don't understand a student's strategy?
- How do I write Problem Strings?
What makes Problem Strings different from other sequences of problems? In this episode Pam and Kim get into the nitty gritty on how Problem Strings work and what sets them apart.
Talking Points:
- Defining Problem Strings
- The "Why or Purpose" - What sets a Problem String apart from just a list of problems?
- The "How" - How are Problem Strings facilitated differently from a textbook lesson or rich task?
- An example
Find examples of Problem Strings (including video!) at https://www.mathisfigureoutable.com/ps
Problem Strings are meant to build off each other so that the math is always moving forward. That's why we've decided to build off the last episode with another Problem String! In this episode Pam and Kim find the equation of some lines using relationships and develop powerful strategies for more sophisticated thinking.
Talking Points:
- You don't have to have lots of recent experience to notice the patterns.
- Problem Strings to notice patterns and relationships between the x values and the y values.
- How the relationships between the x values and the y values help you think and reason about slope and y intercept.
- Algebra is Figure-Out-Able!!
We've talked a lot about the types of reasoning we need to help students develop, but a lot of teachers believe that there comes a point in higher math where reasoning just won't cut it. In this episode Pam and Kim tackle functional reasoning, and demonstrate that algebra can be so much more than memorized steps.
Talking Points:
- Is using the procedure of finding slope, plugging into a formula, etc the most efficient?
- The importance of working with intuition
- Examples of using patterns that you notice to find the equation of a line without formulas
- Intuitively finding the equation of a line in standard form
In Episode 67 revisited the Development of Mathematical Reasoning (DMR) and we described how students can solve addition problems with Counting Strategies. What about the addition algorithm and multiplication and division problems? In this episode Pam and Kim explore the Development of Mathematical Reasoning even further, and discuss how important it is that we help students become more sophisticated. It's more than just answer getting. And stay tuned to the end for a freebie!
- Examples of solving addition problems with bigger numbers using Additive Reasoning.
- Examples of solving multiplication problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.
- Examples of solving division problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.
- Brand new free infographics of the Development of Mathematical Reasoning.
- Videos of students solving problems using the different types of reasoning to help you use the DMR in your classroom to identify where your students are in their reasoning.
Find the infographics here: https://www.mathisfigureoutable.com/blog/development-4
It's been over a year since Pam and Kim first introduced the DMR (Development of Mathematical Reasoning) and in that time they've refined their ideas even further. In this episode Pam and Kim dive deeper into the development and why it's so important.
Talking Points:
- It's not about answer getting, or students doing it 'their way'.
- Our goal is more sophisticated thinking and reasoning
- Added Statistical Reasoning to DMR
- Where do subtraction and division live on the DMR graphic?
- We don't leave a level of reasoning behind
- Examples of Counting, Additive and Multiplicative Reasoning
- How can you build your own mathematical reasoning?
- Free DMR workshop for anyone at anytime!
Math conferences are powerful ways to improve your teaching. But it's also really easy to go to a conference and accidently miss all the good sessions. In this episode Pam talks about a few powerful leaders in the math education community that she will always go see no matter what they're talking about.
Talking Points:
- Karim Ani
- Peter Liljedahl
- Deborah Ball
- Zaretta Hammond
- Jenny Bay Williams and John SanGiovanni
- Elham Kazeimi
- Cathy Fosnot
- Juli K. Dixon
- Sarah Vanderwerf
- Instructional Routines to find at MathisFigureOutAble.com
JourneyLEADER (learn more at https://www.mathisfigureoutable.com/leader)
Other people to follow: @JBayWilliams, @JohnSanGiovanni,
@ddmeyer, @joboaler, @ekazemi, @ctfosnot, @thestrokeofluck, @saravdwerf
How can we best grow as teachers? Together of course! In this episode Pam and Kim discuss the power of teachers honing their craft through collaborative experiences and conversations. Administrators, leaders and coaches will find this episode particularly helpful.
Talking Points:
- Shared experiences help to communicate and reflect about critical moments and expert teacher moves.
- How coaches, teachers and peers can benefit from coversations about shared experiences to implement action in the classroom.
- How to create shared experiences.
- Introducing JourneyLEADER
You can learn more about our exciting new experience for leaders at mathisfigureoutable.com/leader
Fun with Division: An Important Strategy
There is so much to division! Pam and Kim go through a quick Problem String that builds a less known, but super powerful, division strategy.
Talking Points:
- Reasoning about division with scaling
- Thinking partitively vs quotatively to solve gnarly division problems with whole numbers, fractions, decimals and even polynomials.
Learn more about the Building Powerful Division workshop
Counting strategies can often go overlooked. Learning to count in a way that prepares students for Additive Reasoning is complex. But just how hard can counting be? Wait until you listen to this episode! Pam and Kim discuss how to help young learners increase in their sophistication as they count to add numbers.
Talking Points:
- Counting is more than singing the song.
- Addition requires a strong foundation of Counting Strategies.
- C + M = ?
- Double/triple counting, counting on, Commutative Property for addition.
- Teacher moves to help students become more sophisticated counters.
In this episode Pam and Kim show how three popular models - 100 charts, base ten blocks, and algebra tiles - while powerful for developing reasoning, can limit students' development of more sophisticated thinking as tools for computation.
Talking Points:
- CRA vs tools for thinking
- What are 100 charts, base 10 blocks and algebra tiles?
- 3 limitations for some manipulatives that prevent kids from doing Real Math
- How each not-fav model have the 3 limitations for computing
- Mimicking or Mathematizing?
Continuing their series on modeling, Pam and Kim discuss the advantages and pitfalls of Ten Frames. They emphasize the power of models that can become tools for reasoning, and use Ten Frames as an example of how teachers can focus too much on models that may eventually get it in the way of reasoning.
Talking Points
- What are Ten Frames?
- The 3 limitations to Ten Frames
- It's not just the model, it's how you use the model
- Our preferred model for transitioning from counting to additive reasoning
Let's keep talking about modeling! A lot of you may be familiar with Number Bonds and Tape Diagrams and may be wondering about how they fit in with our modeling framework. In this episode Pam and Kim discuss these models and some of the confusion and misunderstanding surrounding them. They offer suggestions to help teachers advance students from "modeling of the situation" to "modeling to make their thinking visible".
Talking Points:
- What are Number Bonds and Tape Diagrams?
- CGI and direct modeling confusion
- Example of using Number Bonds and Tape Diagrams vs an Open Number Line
- Models that can be tools for thinking for addition, subtraction, multiplication, and division
Are manipulatives sometimes overemphasized? When are they useful, and when can they actually get in the way of the mathematics? What role do they play in our discussion about the modeling framework? Pam and Kim discuss these tricky questions, and discuss the power of contexts and developing models as tools for reasoning.
Talking Points:
- An important modeling framework
- What are manipulatives?
- Gail Burrill - Where's the Math?
- Cathy Fosnot - Do manipulatives embody mathematics?
- Are manipulatives bad?
It's time to talk about one of our foundational ideas for facilitating Real Math! In this episode Pam and Kim detail a modeling framework that helps students to learn to model their own thinking, and then to use models as tools for, or in order to think about, computation. The goal of the framework is for students to be able to reason and solve complex problems on their own with confidence.
Talking Points:
- Model vs. Strategies
- The different meanings for "model"
- In important modeling framework
- An example with sticks of gum and a ratio table
- How students learn to verbalize and model their own thinking
- How this framework differs from CRA
If my experiences as a student are different than my child's experience at school, how can I help them succeed? In this episode for parents, we provide two clear ways you can support your child to be the best math student they can be. Be sure to listen to episodes 55 and 56 for the rest our series for parents.
Talking Points:
- We can all be mathy people
- Parents' attitudes towards math affects your child's attitude towards math
- Importance of student think time
- Importance of parent involvement in math education
See Episodes 34-38 to learn more about best teaching practices for multiplication facts.
Hey parents! Thank you so much for listening to part two of our series for parents. It can be really frustrating to not understand what it is your kid is doing on their homework. What is up with all of the drawing? Where are the algorithms and simple steps? In this episode we'll explain the purpose and goal of why the math on your kid's paper looks different.
Talking Points:
Reasoning about math vs performing memorized steps
- We want our students to be reasoners, not calculators
- Representing students' thinking and reasoning on paper can look messy
- As we understand the possibilities with Real Math, we can encourage and refine teaching so more students are more successful
This episode is for all the parents out there who are invested in helping their children! It can be frustrating to see how math class looks different than it did when we were students. Why is it different anyways? Why would math class have to change? We are so grateful you're taking the time to ask. We'll do our best to provide some answers.
Talking Points:
- Why did the math we were taught in school look the way it did?
- Why do generations of technology dependent students need a different way to learn math?
- Why do students need to understand Real Math for our future?
We love answering your questions! In this episode Pam and Kim answer a question submitted from Rachel Adler. Pam shares her experiences familiarizing her students with data representations, and then Pam and Kim discuss their best advice for first year teachers.
Talking Points:
- Jo Boaler's Data Talks: https://www.youcubed.org/resource/data-talks/
- Integrating data analytics into what you are already teaching
- Solidifying your teaching philosophy and belief system. See episode 12
- The importance of good teacher partners and getting outside of your own classroom
- The importance of good student-teacher relationships
- Starting off the year by setting clear expectations to set the year up for success
- Figure out how you fit as an adult with all students
We loved getting all of your questions! Because there's so many questions, Pam and Kim will have to spend the next couple episodes answering them. In this episode they discuss a question about the relevancy of money strategies, and whether strategies will change over time.
Talking Points:
- Why experience with coins and their relationships is important
- Distinction between teaching strategies and mathematical strategies
- Technology in classrooms as a teaching strategy
Extra resources: Which One Doesn't Belong (https://wodb.ca)
We are so grateful to be celebrating our one year anniversary of the podcast! It's been wonderful to hear all the feedback you've given us as you transform your classrooms. Here's to another year of mathematizing!
Highlights:
- Ep 2: Pam's stance on algorithms
- Ep 9: Defining models and strategies
- Ep 34: Memorizing multiplication facts is not the answer
- Ep 27: The students who need to know why
We've had so much fun talking about fractions! In this episode Pam and Kim do another Problem String to demonstrate the effective use of a clock model.
Talking Points:
- What denominators work well for a clock model?
- Example Problem String with non-unit fractions and mixed numbers
- Should we insist on the most simplified fraction answer?
- Problems that work with both money and a clock model
- Today's students need the experience from learning with a clock model
How important is fractional equivalence? Important enough for another model! These models are fantastic for helping students develop a natural understanding of equivalent fractions. Listen in as Kim and Pam discuss how to use a clock model for denominators uncommon to the money model.
Talking Points:
- Use adding and subtracting fractions to help think and reason about fraction equivalence
- Using the word "over" for fractions is NOT helpful
- Equivalent fraction examples on a clock model
- A real student's math journey
Jordan Using the Clock Model
In this episode Pam and Kim finish up their money Problem String from the last episode. But first, Pam wanted to reflect a little on how she was less than helpful when Kim was struggling to think about nickels. We all learn and grow, and self-reflection is super important!
Talking Points:
- Do you need time, or do you need help? (see episode 40)
- Once kids have an answer, do we force them to find another way?
- For which denominators is thinking about money helpful?
- Ways to think about 2 2/5 minus 9/20
- The reciprocal relationships between fractions and coins can be confusing
- Fractional equivalence is the goal by asking students to add and subtract fractions
It's time to talk about everyone's two favorite things: fractions and money! Fraction equivalence is a super important concept in mathematics, and it is best developed naturally in a familiar context. In this episode Pam and Kim model using coin denominations to reason about fractional equivalence.
Talking Points:
- If you understand fractional equivalence, you don't have to memorize any rules for operators of fractions
- Examples of using the money model to think about fraction equivalence, and bonus, fraction operations as well:
- Using decimals and fraction notation interchangeably
- Kim's uncomfortable relationship with nickels
Let's keep talking fractions! In this episode Pam and Kim discuss an interesting rich task from Cathy Fosnot to help students reason about fractions within the context of sharing fairly. Listen in to learn about the outcomes teachers should look for when teaching fractional sense in a rich contextual problem.
Talking Points:
- Splitting the wholes into unit fractions
- Splitting the leftovers into smaller unit fractions and re-unitizing
- Patterns when comparing same-denominator fractions vs same-numerator fractions
Additional Sources: Field Trips and Fund-Raisers
How young can young learners begin to experience fractions? Younger than you think! In this episode Pam and Kim describe simple ways we can help young students begin to develop fractional understanding. Pay attention to how natural it can be for young learners to learn math!
Talking Points
- Struggles that young learners may experience with "half"
- Simple classroom activities to have students fair shares in early grades as they practice counting
- Experiences and conversations in halving even and odd amounts
- Standards and fractions of an object vs fraction of a set
- Important unit fractions and resources
- Doubling and halving simultaneously
- Simple experiences parents can use to help their kids develop fractional understanding
Additional sources:
- Beads, Shoes and Making Twos
- Games for Early Number Sense
Time to get into fractions! There is so much to learn about teaching fractions and in this episode we wanted to lay some important ground work. All too often we limit students by giving them experience with only one or two of the important ways fractions can be interpreted. When we help students fully understand fractions by using all of the interpretations, their ability to think proportionally skyrockets!
Talking Points
- What is a rational number?
- The 5 Interpretations of Rational Numbers (Credit to Susan Lamon)
- Solving fractions with reasoning!
- Shifting between the 5 interpretations as we solve
- Applying all 5 interpretations to one problem
Though some people think Kim and Pam's voices are hard to tell apart, teaching Real Math has nothing to do with a particular style or even personality type. We believe in seeing the humanity in students and empowering them with mathematical confidence!
Talking Points:
- Pam and Kim's results on the Enneagram Test.
- 2 important things -
- Teaching Real Math is more about beliefs about students and mathematics than personality
- Leverage your beliefs to get support in teaching Real Math.
If there's one thing that often comes up in teachers' conversations, it's standardized tests. And Pam and Kim are not afraid to tackle the tough conversations! In this episode Pam asks Kim about her experience with standardized tests, and how teaching Real Math helped Kim's students to succeed. Also don't forget to send in questions for our special 50th episode! We're so excited!
Talking Points:
- Can students succeed on tests if all they know is Real Math?
- Everyone, in every demographic, can learn more Real Math than fake math.
- How much time do students need to prepare for tests?
- Suggestions for test prep.
- How teachers view the test and their actions speak loudly
- It's all about "know your content, know your kids".
Learn about numberless word problems here: https://bstockus.wordpress.com/numberless-word-problems/
In this final episode in our series on homework, Pam and Kim discuss what types of homework teachers should send out, as well as some important pitfalls to avoid.
Talking Points:
Pen and paper homework
- Games as homework and things to consider
- Computer activities as homework and things to consider
- Communication is critical to honor family time when assigning homework
- Using homework as a teaching tool, not for the sake of work
- Be sure you are sending the right message about mathematics when looking at returned homework.
- How the goal of Real Math helps teachers make decisions about homework
It's part two of our series on homework! Last time we heard Kim's perspective on when and what kinds of homework to give. Now it's Pam's turn. As a teacher for both high school and university classes, Pam gives an insightful look into when homework is necessary, and how we can always allow the humanity of our students to have precedence.
Talking points:
- What does the research say about homework? How does it vary by grade level?
- What is the purpose of homework?
- How much homework should students have?
- What topics should homework cover?
- The role of students' humanity in grades and homework.
Welcome to our first off the cuff episode! Pam and Kim have no notes this time and are happy to tackle the topic of homework. Turns out, they have enough to say that this will be part one of a new series! Listen in as Kim makes a confession, and Pam rats out her kids.
Talking points:
- Some general thoughts about homework.
- When is a topic appropriate to send home for homework?
- Some suggestions for the kinds of homework we should send home
- Parent's role in homework and how can homework be helpful?
In this episode Pam and Kim discuss the secret to helping every student succeed. It's one of their guiding principles, and they can't believe they're only just now sharing it!
Talking Points
- The problem with the traditional approach of teaching to mastery
- How to address the personal needs of students
- How to help all students grow
- What are open tasks?
- What if students aren't getting "it"?
We made it to our final episode in our multiplication facts series! In this episode Pam and Kim share their secret to helping kids narrow in on facts they struggle with. This final episode exemplifies why we believe that through mathematizing students will naturally develop fact fluency.
Talking Points
- What it means to take the long view in multiplication facts
- The importance of really knowing your students
- Clue cards
- Final thoughts on fact fluency
Show links:
- Math-Flips
- Stick and Split
Find the transcript here: https://podcast.mathisfigureoutable.com/1062400/8040345-ep-38-multiplication-facts-the-good-the-bad-and-the-ugly-pt-5
It's time for what you've all been waiting for. GAMES! Sure we don't want kids memorizing songs or rhymes to learn their facts, but in this episode Pam and Kim bring the fun into multiplication. What games are out there that can help students develop multiplicative reasoning? We're glad you asked :-)
Talking Points
- What makes a good math game?
- What makes a poor math game?
- What are the best games today to help students own multiplication facts?
Links
- Live Problem Strings on Facebook Live
- The Product Game (Link includes games for other grade levels as well!)
Last episode Pam and Kim discussed how not to teach multiplication facts. So how should we teach them? This episode we look at multiplication facts through the lens of mathematizing!
Talking Points
- The order that we teach content matters
- The order we teach the facts matters
- The key relationships students need to own facts
- How parents can help their kids own their facts
Free Problem String Download: mathisfigureoutable.com/factsps
What are some great techniques to teach multiplication facts? What are the pitfalls to avoid? In this episode Pam and Kim discuss ways teachers may inadvertently 1) overemphasize speed, 2) introduce shame into their classrooms, and 3) focus on learning facts in isolation. We've all made mistakes, and this episode is about learning and growing for our students.
Talking Points:
- The negative effects of timed multiplication fact tests
- How to avoid using shame as a motivator to learn facts (harder then you think!)
- Why learning facts as isolated ideas is dangerous
Find this episode's transcript here: https://podcast.mathisfigureoutable.com/1062400/7773085-ep-35-multiplication-facts-the-good-the-bad-and-the-ugly-pt-2
In this episode Pam and Kim begin the first of another series: Multiplication Facts! What role can mathematizing and real math play in helping kids master their multiplication facts? Listen in as Pam and Kim outline the differences between 'knowing' and 'memorizing' multiplication facts.
Talking Points:
- Why multiplication facts are important
- The difference between knowing and memorizing facts
- How to get rid of all the stress around multiplication facts
- Is the goal to get through memorizing the facts, or to develop multiplicative reasoning?
We recommend brushing up on episodes 5 & 6 in preparation for this series. Understanding what it means to develop multiplicative reasoning is so important!
Find this episodes transcript here: https://podcast.mathisfigureoutable.com/1062400/7641379-ep-34-multiplication-facts-the-good-the-bad-and-the-ugly-pt-1
In the last two episodes, Pam and Kim did some really cool Problem Strings, but what do they think about Number Talks? Listen in as Pam explains how Number Talks and Problem Strings can go hand in hand for powerful results.
Talking Points:
- Why call 'Number Talks' 'Problem Talks'?
- Short term uses for Problem Talks
- The best use for Problem Talks
- The purpose of Problem Strings
- When to do Problem Talks
- When to do Problem Strings
Want to learn more about this powerful combination? Head to: mathisfigureoutable.com/stringsvtalks
Get this weeks transcript at: https://podcast.mathisfigureoutable.com/1062400/7498621-ep-33-problem-strings-vs-problem-talks
It's time for another Problem String! In this episode Pam and Kim develop one of their favorite multiplication strategies, it's so slick! In doing so they talk more about the importance of letting students discover and develop relationships, as opposed to teaching strategies step by step.
Talking Points
- What makes a good Problem String?
- How do we help kids learn the appropriate uses of alternative strategies?
- What to avoid when facilitating Problem Strings
- Tweet at us your favorite name for this strategy!
In this episode Pam and Kim want to help you develop a cool multiplication strategy. Which multiplication strategy? We aren't going to tell you until the end of the episode : -). We believe in developing strategies as natural outcomes, and then giving it a name. How do we do it? With Problem Strings! Listen in as Pam and Kim go through a Problem String to develop this super handy multiplication strategy.
Talking points:
- Are alternative strategies worth learning?
- What does it mean to do mental math?
- How to make mental math accessible for everyone.
- What is a Problem String?
- The _____ strategy
Don't you just love taking a break to play with numbers? In this week's episode, Pam and Kim share some of the ways that they engage with kids outside of school to get them mathematizing. Parents, ever wondered what can you do for just ten minutes to help your kids build relationships? This episode is perfect for you. Together we can all learn to make math fun!
Talking points:
- Math over the holidays
- Finger Flashing
- Which One Doesn't Belong
- Adding 10, 9, 99, 999 to anything
- How listening and engaging with students informs assessment
Additional resources: https://talkingmathwithkids.com, https://mathbeforebed.com
In this episode Pam and Kim dive deep into their favorite model for multiplication, division and solving proportions: ratio tables! They'll discuss how ratio tables can be a powerful tool to help students develop reasoning from elementary to high school.
Talking Points:
- What are ratio tables?
- How to, and not to, use ratio tables in the classroom
- Using ratio tables to organize data
- Using ratio tables to model thinking
- Using ratio tables for computation
- Example multiplication and division problems
Use this PDF to follow along with Pam and Kim's thinking!
This week Pam and Kim wrap up their discussion on the Perspectives that Impact Math Pedagogy. Understanding the X, Y, and Z perspectives not only helps us understand one another better, but empowers us to choose to take on the real mathematics perspective. Listen in as Pam and Kim discuss the need for mathematics to be experienced, and the power in developing mathematical reasoning.
Talking Points:
- How do each of the perspectives benefit from real math?
- All people can do more real math than fake math
- What pitfalls do each of the perspectives have to avoid when teaching real math?
Take the XYZ quiz here! mathisfigureoutable.com/XYZ
Find this episode's transcript HERE.
We've made it to our last (and maybe favorite) perspective that impacts pedagogy. The Y perspective describes those who struggle with fake math because they deeply desire to know "why". Pam and Kim describe people in their lives who grew up with the Y perspective and discuss their great value to the mathematics community.
Talking Points
- What describes the Y perspective?
- How adults with the Y perspective feel about mathematics
- Why teaching real math is so important
Take the XYZ quiz here! mathisfigureoutable.com/XYZ
This episode is all about the Z perspective. Listen in to hear about the perspective that Pam estimates effects the majority of math educators, it was Pam's perspective too! Pam and Kim parse out the characteristics of the Z perspective and the huge impact it has on teaching today.
Talking Points
- Pam forgot how to subtract
- What is the Z perspective?
- How do Z-perspective students think?
- Pam's first experience with Math Club
- How can understanding the Z perspective empower teachers?
- Take the new XYZ Quiz!
Continuing in the Perspectives Impacting Pedagogy Series, Pam and Kim discuss the X perspective. Did you play with numbers as a kid? Did math make natural sense to you, regardless of how your teacher taught it? You might relate to the X perspective. Listen in to learn how the X perspective influences teachers and students in mathematics.
Talking Points
- What is the X perspective?
- Why X-perspective teachers teach with algorithms
- The 'math-gene' myth
- How X-perspective teachers can choose to teach real math
- Take the new XYZ Quiz!
Read the transcript for this episode at podcast.mathisfigureoutable.com
This episode is part one to a new five part series! Pam and Kim introduce the three main perspectives impacting pedagogy. Understanding these perspectives helps teachers analyze their own teaching have productive conversations regarding math education.
Talking Points:
- The three perspectives impacting pedagogy
- Why math teachers can often talk past each other
- Take the new xyz QUIZ!
Find this episodes transcript HERE
How can we help students feel comfortable with the commutative property? In this episode Pam and Kim go through some addition and multiplication problems to demonstrate how they think and reason using the the commutative property.
Talking Points
- The commutative property in counting
- The commutative property in addition
- Using the commutative property for percentages
Find the transcript HERE
Kim relates a great math experience she had with her son Luke. Luke found a way to mess around with place value in addition that Pam went most of her life not knowing! Listen in as Pam and Kim discuss the importance of learning to manipulate place value as students develop into mathematicians.
Talking Points:
- Introducing the swapping strategy
- What problems fit nicely with the swapping strategy?
- Place labeling vs. Place value
- Send us (@pwharris) your slick swapping strategy solutions to gnarly looking problems!
Transcript: http://podcast.mathisfigureoutable.com/1062400/6371821-ep-22-the-swapping-strategy
Pam and Kim are back at it with percents. They discuss the 3 types of percent problems and how they solve them using relations, not with algorithms. Are percents truly figure-out-able? You bet! Grab a pen and paper for this one as we solve some percent problems!
Talking Points
- The three types of percent problems
- The disadvantages of teaching procedural methods to answer percent problems
- Math is fun when it's figure-out-able!
Pam and Kim are back at it showing that percents too are figure-out-able. In this episode they solve some percentage problems and share their strategies. Listen in as they go through a percentage problem string!
Pam and Kim explore what it means to be flexible with fractions, decimals, and percents. They discuss how we can become more flexible as we deal with rational numbers, and how we can be judicious problem solvers.
Talking Points
- Why kids of today are more familiar with percentages
- Why flexibility matters
- How to become more flexible using different representations of rational numbers
You might want your magnifying glass for this one, cause this episode we're getting a little nitpicky. Pam and Kim discuss common nomenclature/math-slang that can take the reasoning out of mathematics. They offer useful alternatives and illustrate the importance of clear mathematical language
Talking Points:
- How to add Butt-Cheeks
- Why students try 'canceling' everything
- Why reducing 6/8ths to 3/4s might give me more pie...?
- How one got over x.
Math is figure-out-able, but surely there are some parts that are only memorizable, right? In this episode Pam and Kim parse out the difference between social knowledge and logical knowledge. They'll analyze how knowing the difference can affect the types of questions you ask and the role of wait time in teaching.
Talking Points:
- What is the difference between social and logical knowledge?
- What are examples of social knowledge in lower and higher math?
- How should we teach social knowledge?
- How should we teach logical knowledge?
This week's episode is for all you parents and teachers of young children. Pam and Kim discuss ways to make counting figure-out-able! How can we help kids make sense of our number system and master the meaning behind the words we give to numbers? No matter what grade you teach, you're sure to learn something this episode.
Talking Points:
- How different languages name numbers
- How to support young learners to make sense of teens and multi-digit numbers
- Give kids multiple representations of single-digits numbers.
- Pam being creepy at grocery stores
Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/5723239-ep-16-the-language-of-counting
Have you ever tried teaching your students the steps to approaching word problems, but your students still struggled? Pam and Kim discuss a better way to help kids tackle math problems. They explain why if you want the best for your students, the acronyms and problem annotation methods of the past simply won't cut it. Help your students live the problem solving process, and not just memorize it.
Talking Points
- The dangers of teaching "Problem Solving Methods"
- How to engage students in mathematics so that problem solving is a natural outcome
- How to run students through numberless word problems
Resources: Brain Bushart's Numberless Word Problems
Pam and Kim have some fun this episode as they read out a submission from Aaron Houston about his mathy dad. They talk about the kinds of things parents can do with their kids to have fun mathematizing!
Talking Points
- I Have, You Need
- Kids Menus vs Adult Menus
- the Guess my Number game
- How do you think about finding Prime Numbers?
- Math can be fun!
There are so many aspects to teaching, and it gets more complex when we want to discuss teaching math. Pam and Kim define the 5 layers for mathematics teaching. What do math teachers, who want to help their students mathematize, need to focus on?
Talking Points
- Building your own math
- Know the major strategies and models for your content
- Modeling Student Thinking
- Teacher Moves
- Sequencing Tasks
Resources: Journey
As Pam and Kim wrap up their series on how to start the school year right, they encourage staying true to your beliefs as a math teacher. When making decisions in your classroom, there is power in consistency. They discuss how they approach analyzing and implementing other's ideas into their teaching practice, without giving up on their integrity.
Talking Points:
- One meaning for having integrity in your teaching
- How intentional use of worksheets & resources can illustrate your teaching beliefs
- Determine your system of beliefs
Transcript HERE
Join Pam and Kim in part two of their Top 3 Things to Start the Year series. This week its all about building a classroom culture where students and students' thinking are valued. They'll talk about how to implement tasks remotely that build a community of learners. Pam also throws out some great advice for facilitating lessons and tasks remotely. You won't want to miss it!
Talking Points
- Building classroom culture is so important in remote settings
- When classmates respect each other's thinking, more students are enabled to think like mathematicians.
- Designing interactive remote learning
- How to facilitate Problem Strings remotely
- How to facilitate Rich Tasks remotely
Resources
- How Pam uses her iPad to facilitate Problem Strings remotely: https://www.mathisfigureoutable.com/how
- Transcript
As the world prepares for one of the most interesting beginnings to the school year, Pam and Kim are here to help us get it right. They start off this 3 part series by dialing in on the importance of using students names. Find the transcripts HERE.
Talking Points:
- A maternal mathy person
- How Pam learns student names
- Useful tools and tips for using student names in a remote setting
- How to help students use each others names
Resources: Name Tents from Sarah Van Der Werf: https://www.saravanderwerf.com/week-1-day-1-name-tents-with-feedback/
What is the difference between a strategy and a model? Listen as Pam and Kim give clear examples from both elementary and high school content to demonstrate the importance of developing strategy and communicate strategy through models. They provide clear, easy to follow insights so everyone can understand the purpose of models in constructing and communicating strategy.
Talking Points
- Shout-out to Clay! Clay uses powerful additive reasoning when he uses his understanding of place value to add large numbers. Let us know about someone mathy in your life!
- New Problem String videos!
- What is a strategy? What is a model?
- Which is more important, models or strategies?
- Why are models so important in classrooms?
- Can anyone "do" a number line?
Resources
Strategies vs Models Article
Strategy vs Models Card Sorts
Transcript
After last weeks discussion on partners of 10, 100, and 100, Pam and Kim thought of three more habits "mathy people" have in common. Listen in as they discuss:
1. What it means for mathematicians to "Notice and Wonder"
2. Double and halving
3. Creating habits of thinking (as opposed to grabbing for a calculator)
Tune in to next week's episode to hear all about Pam's method of categorizing levels of mathematical thinking, what she calls "The Development of Mathematical Reasoning".
Find this episode's transcript HERE
Talking Points
- The prime numbers in your neighborhood
- The Wonder Game
- Math-Strat-Chat
- Our first shout-out
In this episode Pam and Kim share one of their favorite instructional routines: I Have, You Need. They discuss some of the most common patterns that mathmaticians play with, partners of 10, 100, and 1000. These "partners of ___ " patterns pop up everywhere! You'll never guess where they pop up daily for Pam (hint: its when she's the most worked up).
Try out I Have, You Need with your friends, colleagues, and students! A quick way to build anyone's reasoning abilities and to help us all become better mathematicians.
Download the guide to playing I Have, You Need HEREFind the transcript for this episode HERE
Talking Points:
- We can all be "mathy people"
- What Kim thinks when she hears the number 36
- The routine that made the biggest impact on Pam's college students
- Taking ownership of your students' progression
- I Have, You Need resolves the subtracting across zero horror
- How I Have, You Need applies to middle and high school students
Many people feel that reasoning and numeracy come to an end in highschool. How could we mathematize algebraic concepts? What does it mean, and what does it look like to have functional reasoning? Listen as Pam explains how functional reasoning builds off of proportional reasoning and empowers students to analyze and understand patterns of related value sets. Sounds complicated? Don't worry, Kim does her best to keep Pam on track and grounded.
Talking Points
- How functional reasoning builds on proportional reasoning
- It's not about being able to visualize the graph, it's understanding the relationship between the variables
- How to tell if someone is using functional reasoning
This episode is so important! Pam and Kim describe the Development of Mathematical Reasoning, and how it transforms our understanding of what it means to learn and teach mathematics. They discuss how freeing it feels to know that everyone can develop their reasoning, and how the Development of Mathematical Reasoning empowers teachers to know how best to help their students.
To help you determine where you and your students are in the Development of Mathematical Reasoning, here's a free download! Use the How Do You Reason guide to know how you, your friends, and students are reasoning.
They also announce the new Development of Mathematical Reasoning Workshop! A new free online workshop.So exciting! Be sure to tell all your colleagues about this amazing opportunity to learn how to help anyone develop reasoning.
Talking Points
- What the Development of Mathematical Reasoning looks like
- We don't need calculators, we need reasoners
- One way people get stuck in counting strategies
- The freeing power of progressing in reasoning
- New free online workshop!
Read the transcript here: http://podcast.mathisfigureoutable.com/1062400/4305047-the-development-of-mathematical-reasoning
Who's shaping math education today? Does Pam come up with it all herself? Far from it! In her fourth episode Pam wanted to pay homage to her top 10 influencers as well as share with you all some of her favorite resources for teaching real math. Join her and Kim as they share stories ranging from the excitement of the first graphing calculators to the embarrassment of mispronouncing their hero's name. It's sure to be a good time.
Talking Points
- Who were Pam's early influencers?
- How teacher moves transform Rich Tasks
- Who is shaping math education today?
- Fos-dos and Fos-nots
- Desmos' card sorts and polygraphs: excellent tools for remote teaching.
Pam and Kim continue from Episode 2 to discuss what it means to do and teach real mathematics. When we teach reading, students read. When we teach writing, students write. When we teach math, students mathematize, because we need a verb that describes what mathematicians do when they do what mathematicians do. And when we teach students to do what mathematicians do, they are mathematicians. So teachers are mentoring mathematicians.
Talking Points
- What Pam means when she says Math is Figure-Out-Able
- Mathematicians do not mimic to do math, they use their understanding of mathematical relationships
- What does it mean to mentor students to become mathematicians at their gradelevel?
Find the transcript here:
http://podcast.mathisfigureoutable.com/1062400/3887888-mentoring-mathematicians
What do you think math is, a disconnected set of facts to memorize and rules, procedures to mimic or is it something else entirely? In this episode, Pam and Kim talk about discuss that real math teaching is about listening to students - that you must know your content, and know your kids. Also that math is not about mimicking an algorithm, but rather math is about letting the numbers and the structure dictate the strategy. How would you answer the question, "What is 99 plus anything?" or "What is 99 times anything?" How can you use relationships to solve those problems?
Talking Points:
- What are Algorithms? Why are they not Pam's goal?
- How mathematicians approach problem solving
- What is 99 + anything?
Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/3887876-math-does-not-equal-algorithms
In this debut podcast, mathematics teacher educator, Pam Harris talks with her cohost, Kim Montague, about how they met and the work that they do together now. They set the stage that in this podcast they will talk about real mathematics and about how to teach mathematics. They answer the question, "If not algorithms, then what?"
As Pam and Kim describe their relationship they touch on these principles:
- It is fun to teach math that is figureoutable
- People have had different experiences with math, but everyone can learn to mathematize
- They define what it means to mathematize
- The difference between Real Snacks and Fake Snacks
- Reasoning can be refined and there are strategies which are more elegant than others
- Professional Development should be uplifting and empowering
- This podcast is for everybody!
Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/3614602-math-is-figureoutable