The Build Math Minds podcast is for my fellow Recovering Traditionalists out there. If you don’t know whether or not you are a Recovering Traditionalist, here’s how I define us. We are math educators who used to teach math the traditional way. Flip lesson by lesson in the textbook, directly teaching step-by-step how to solve math problems. But now, we are working to change that to a style of teaching math that is fun and meets our students where they are at, not just teaching what comes next in the textbook. We want to encourage our students to be thinkers, problem solvers, and lovers of mathematics..we are wanting to build our students math minds and not just create calculators. If that is you, then this podcast is for you.
In this cross-posted episode from Math Chat, host Mona Iehl interviews Christina Tondevold about developing number sense in elementary students. Christina shares her journey from a "procedural" math student to becoming a math coach and founder of Build Math Minds.
The conversation explores the eight components of number sense: four early numeracy concepts (subitizing, verbal counting, object counting, and cardinality) and four number relationships (spatial relationships, one/two more or less, benchmarks of 5 and 10, and part-part-whole). Christina explains how these concepts help move students beyond counting to more efficient math strategies.
Practical classroom strategies discussed include using sticky notes to assess students' visual number understanding, implementing subitizing activities, and strategically choosing numbers in word problems to reinforce key number relationships. Both educators emphasize the importance of allowing students to solve problems in ways that make sense to them, rather than forcing procedural approaches.
This episode provides valuable insights for teachers looking to build true mathematical understanding rather than just procedural knowledge in their students.
Check out Mona’s podcast Math Chat
Enroll in The Flexibility Formula Course
In Episode 202: Going Beyond the Task When Building Thinking Classrooms, we reveal the exciting lineup of special guests for our summer book study on 'Mathematics Tasks for the Thinking Classroom Grades K-5' by Peter Liljedahl and Maegan Giroux. Starting July 14th, each week will feature a video with reading prompts followed by live Q&A sessions with experts including first-grade teacher Tammy McMorrow, co-author of the book Maegan Giroux, and Official BTC Consultant Kim Rimbey. Join now at BuildMathMinds.com/bookstudy25 to receive a 20% discount code plus free shipping within the US, and participate in these valuable learning opportunities with educators who are transforming mathematics classrooms.
In Episode 201, I share two exciting summer learning opportunities for fellow Recovering Traditionalists as we prepare to pause the podcast until August. First, enroll in The Flexibility Formula online courses (K-2 or 3-5) to transform how you build math fluency with your students. BuildMathMinds.com/courses
Second, join our free summer book study on "Mathematics Tasks for the Thinking Classroom Grades K-5" by Peter Liljedahl and Maegan Giroux, starting July 14th. Register now at BuildMathMinds.com/bookstudy25 to receive a publisher discount (20% off with free US shipping) and access to exclusive weekly videos featuring insights from myself, Rosalba Serrano, and special guests. We'll explore Part 1 (BTC Practices in Review) and Part 4 (From Page to Practice), focusing on implementing thinking tasks and creating your own curriculum resources. This essential companion to Building Thinking Classrooms will help you prepare for next year's math instruction with practical strategies and ready-to-use templates.
In this milestone 200th episode of The Build Math Minds Podcast, I share the three essential math experiences every classroom needs: Number Routines, Word Problems, and Games. Drawing from research-backed practices in the IES/WWC guides, I explain why these activities are crucial for developing conceptual understanding, procedural fluency, and application in mathematics. Learn how Number Routines make implicit math concepts explicit, how Word Problems should help students understand mathematical structures beyond keywords, and how Games provide engaging practice that builds fluency. To celebrate this 200th episode milestone, I'm offering a free Google file with examples of all three experiences that you can download at BuildMathMinds.com/200. After 200 episodes, these core principles remain unchanged - Routines, Word Problems, and Games help Build Math Minds!
In this episode, I explore the fascinating world of finger use in math and specifically how we represent numbers differently. After noticing that Dan Finkel and I show the number 3 with completely different finger configurations, I dive into why these variations matter for children's mathematical understanding. Through personal stories about my own children's attempts to show the number 5, I highlight how fixed representations can limit children's number sense. Join me to discover why showing quantities in multiple ways—whether using fingers, ten frames, or rekenreks—helps develop deeper mathematical thinking and flexibility. A must-listen for teachers and parents wanting to build stronger number foundations with young learners.
In this episode, Christina Tondevold welcomes special guest Dan Finkel, founder of Math for Love and creator of popular games like Prime Climb and Tiny Polka Dot. Dan shares his three essential principles for effectively implementing mathematical games in the classroom: games should involve meaningful choices, math should be the engine driving the gameplay, and games should be simple to learn and quick to play. Through personal stories and classroom examples, Dan and Christina explore how games transform math from a dreaded chore into an engaging learning experience. The episode concludes with a demonstration of the "31 Game," a simple yet strategic counting game that exemplifies how mathematical play can build number sense, encourage strategic thinking, and create a classroom culture where students aren't afraid to show what they don't know. Perfect for educators looking to reinvigorate their math instruction between standardized testing periods!
Join the Build Math Minds PD site to access the Mini Courses
https://buildmathminds.com/bmm/
Dan’s website Math For Love
https://mathforlove.com/
Dan’s game Prime Climb
https://amzn.to/3Y3jN5y
Dan’s game Tiny Polka Dot
https://amzn.to/44sfRiI
In this final episode of our three-part series on upleveling missing part activities, I share ways to transform two popular math games: Salute and Number Sandwiches. Learn how to modify these traditional games to help your students build a deeper understanding of number relationships through missing part problems. These upleveled versions create opportunities for students to work with equivalent expressions while maintaining the fun and engagement of game-based learning. Perfect for elementary math teachers looking to enhance their daily math lessons with games that challenge students to think more deeply about mathematical relationships.
In this second installment of our three-part series on Missing Part Activities, we explore 'repackaging tasks' - a powerful approach to traditional missing part word problems. While educators are familiar with finding unknown parts in word problems like “Christina has $12, she spends some now she has $7. How much did she spend?”, repackaging tasks push mathematical thinking further by having students redistribute quantities across equivalent expressions. Through practical examples in both multiplication and addition contexts, I demonstrate how these problems help students develop a deeper understanding of equality, number properties, and flexible thinking strategies. Learn how incorporating these enhanced word problems alongside your regular curriculum builds stronger mathematical minds.
Part 1 is Episode 195 - https://www.youtube.com/watch?v=DZZKctj2pns
In this episode, we explore how to elevate your 'Missing Part' math activities beyond the basic type like 5 + __ = 12' into more problems that help students develop a deeper understanding of mathematical equality and build foundational number properties. Get a quick way to implement these enhanced activities in your classroom. Perfect for elementary educators looking to strengthen their students' mathematical thinking without explicitly teaching formal properties. This is the first in a three-part series on upleveling Missing Part activities for more meaningful math instruction.
In this episode, we explore the common misconception about mental math in mathematics education. Featuring insights from Pam Harris' newly published book 'Developing Mathematical Reasoning: Avoiding the Trap of Algorithms,' we discuss why mental math isn't about doing calculations without paper—it's about developing quality thinking strategies.
In this episode, I follow up on last week's introduction to the Lesh Translation Model with an important caution. While I previously shared a template for The Translation Task, today I explore concerns raised by John Mason in the 1987 book "Problems of Representation in the Teaching and Learning of Mathematics." Mason warns that frameworks like the Lesh Model can become "mechanical schemes for generating yet more useless student activity" when implemented without proper attention. I offer two specific ways to prevent this template from becoming routine and mindless. This episode emphasizes the importance of thoughtful implementation over mechanical application of educational frameworks. For more information and to download the Translation Task Template, visit BuildMathMinds.com/193.
In Episode 192, "A Math Task All Teachers Should be Doing," I discuss the Lesh Translation Model, a powerful framework that was frequently featured at the 2025 Virtual Math Summit. This model, which dates back to 1979 but was highlighted in NCTM's 2014 book "Principles to Actions," identifies five different ways to represent mathematical concepts: Manipulatives (objects), Realistic (real-life contexts), Pictorial (drawings), Language (verbal descriptions), and Symbolic (numbers/equations). I explain how these representations are interconnected and how developing multiple representations helps students build a deeper understanding of mathematical concepts. The episode introduces the Translation Task, where students are given one representation of a concept and asked to create the other representations. Grab the free download of the Translation Task template at BuildMathMinds.com/192 to start doing the task immediately with your students to strengthen mathematical understanding through multiple representations.
Highlights from the 2025 Virtual Math Summit Get a look into the 2025 Virtual Math Summit's six live sessions that are transforming mathematics instruction in classrooms across the country. This episode captures the essence of innovative teaching approaches from some of the most influential voices in math education today.
Discover how Peter Liljedahl and Maegan Giroux are revolutionizing classrooms with their "Building Thinking Classrooms" approach, including their counterintuitive advice to create "bad examples" that spark genuine problem-solving. Listen as Pam Harris demonstrates how simple "helper problems" can build powerful number relationships without relying on mindless algorithms.
You'll gain practical insights from Shannon Olson on effectively connecting the five types of mathematical representations, and witness Kim Rimbey's fascinating exploration of how ten frames can develop deep place value understanding across all grade levels. NCTM President Latrenda Knighten shares engaging strategies for incorporating children's literature and instructional routines to enhance mathematical discourse, while Ann Elise Record demonstrates why visual models are far more effective than the misleading "keyword" approach for tackling word problems.
This episode isn't just about theory—it's packed with classroom-tested strategies you can implement immediately to deepen your students' mathematical understanding and confidence.
Show Notes:
Featured Speakers: Building Thinking Classrooms Peter Liljedahl & Maegan Giroux, Pam Harris, Shannon Olson, Kim Rimbey, NCTM President Latrenda Knighten, and Ann Elise Record
Note: March 3rd is the last day to watch the 2025 Virtual Math Summit sessions for free. Extended access is available through BuildMathMinds.com/bmm
Get four powerful strategies for making mathematics engaging and accessible for elementary students from expert presenters at the 2025 Virtual Math Summit. Dr. Raj Shah reveals the psychology of engagement through video game design principles, while Kristin Acosta demonstrates how to use everyday images to spark mathematical discussions. Jeff Gobin shows how digital manipulatives can make abstract concepts concrete, and Tyler Tarver shares research on leveraging educational videos effectively in mathematics instruction. Whether you're looking to increase student participation, reduce math anxiety, or create more engaging lessons, this episode provides practical, research-based strategies you can implement immediately in your classroom. Learn how to meet students where they are while guiding them toward deeper mathematical understanding through visual, digital, and traditional approaches to learning.
Featured Speakers: Dr. Raj Shah, Kristen Acosta, Jeff Gobin, and Tyler Tarver
Discover how to transform your math instruction and make mathematics accessible and engaging for all students. Register for free at VirtualMathSummit.com to watch the full versions of these sessions February 22nd & 23rd.
Register for the Virtual Math Summit: https://virtualmathsummit.com/
Upgrade to have extended access to Virtual Math Summit sessions at VirtualMathSummit.com/upgrade
To get any links mentioned in the episode go to: https://buildmathminds.com/189
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
How can we help our students retain what they learn in mathematics? The latest 2024 NAEP scores show that only 39% of 4th grade students and 28% of 8th grade students are performing at or above the Proficient level in mathematics, suggesting many students aren't retaining fundamental concepts. In this episode, Christina shares research-backed strategies from two Virtual Math Summit presenters, Jen Hunt and Michaela Epstein, that can help combat these concerning trends. Learn about The Forgetting Curve, how working memory impacts math learning, and why practices like math games and spaced practice are scientifically proven to help students retain mathematical concepts. Discover three practical strategies you can implement tomorrow to help your students better retain what they learn in mathematics. Plus, get insights into how dual coding theory and dopamine play crucial roles in mathematical learning and retention. These brain-based strategies can help your students build lasting mathematical understanding.
Featured speakers: Jen Hunt and Michaela Epstein
Register for free at VirtualMathSummit.com to watch these transformative sessions February 22nd & 23rd.
Register for the Virtual Math Summit: https://virtualmathsummit.com/
Upgrade to have extended access to Virtual Math Summit sessions at VirtualMathSummit.com/upgrade
To get any links mentioned in the episode go to: https://buildmathminds.com/188
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
In this episode, get an inside look at three powerful sessions from the 2025 Virtual Math Summit focused on transforming math problem solving in elementary classrooms. Listen to clips from John SanGiovanni sharing a unique routine that shifts focus from answers to understanding, Danielle Moore demonstrating practical strategies for building student independence through CGI instruction, and Christine Riad exploring how classroom culture impacts students' problem-solving confidence. These pre-recorded sessions, along with Ann Elise Record's live session mentioned in episode 186, will give you practical tools to address common struggles students face when solving math problems. Learn how to help students move beyond just asking "Is this addition or subtraction?" to becoming confident mathematical thinkers. Register for free at VirtualMathSummit.com to watch these transformative sessions February 22nd & 23rd.
Register for the Virtual Math Summit: https://virtualmathsummit.com/
Upgrade to have extended access to Virtual Math Summit sessions at VirtualMathSummit.com/upgrade
To get any links mentioned in the episode go to: https://buildmathminds.com/187
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
In this episode, get a sneak peek at the live sessions happening at the 2025 Virtual Math Summit. Learn about sessions from renowned math educators including Pam Harris on moving beyond algorithms, Shannon Olson on connecting mathematical representations, Kim Rimbey's innovative approach to ten-frames, Latrenda Knighten's strategies for mathematical discourse, and Ann Elise Record's deep dive into visualizing problem-solving structures. These live sessions, happening February 22nd-23rd, are designed to give you practical, classroom-ready strategies you can implement immediately. Register for free at VirtualMathSummit.com and learn about options for extended viewing of all sessions at VirtualMathSummit.com/upgrade.
Register for the Virtual Math Summit: https://virtualmathsummit.com/
To get any links mentioned in the episode go to: https://buildmathminds.com/186
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
In Episode 185, we dive into Building Thinking Classrooms (BTC), one of the most transformative approaches in mathematics education. Learn why this popular teaching method is more than just vertical surfaces and random groups - it's about creating environments where students truly think and engage with mathematics. This episode addresses a common misconception about BTC and previews the Peter Liljedahl & Maegan Giroux’s 2025 Virtual Math Summit opening keynote. Plus, get insights from their new book 'Mathematics Tasks for the Thinking Classroom.' Whether you're new to BTC or looking to deepen your practice, this episode gives you some important things to contemplate so you can implement thinking classrooms effectively.
Register for the Virtual Math Summit: https://virtualmathsummit.com/
To get any links mentioned in the episode go to: https://buildmathminds.com/185
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
Transform both your math AND reading instruction with two powerful game-based resources! In this episode, discover how to implement engaging games that provide meaningful practice without the typical hassles of game setup and complicated rules. Learn about Reading Simplified's "Switch It" game for building foundational reading skills, and explore the versatile "Evergreen Games" for math practice that can be adapted for any math concept throughout the year. These games offer the perfect balance of fun and learning, allowing students to get multiple repetitions while actually enjoying the practice!
Key Takeaways:
Request Switch It! from Reading Simplified here: https://readingsimplified.com/switch-it/?utm_source=Affiliate&utm_campaign=BMM
Get the Evergreen Games Template document here: buildmathminds.com/games
Register for the Virtual Math Summit: https://virtualmathsummit.com/
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/184
The Count is an activity from John SanGiovanni's book that turns simple counting into a deep mathematical exploration. In this episode, learn how this routine helps elementary students engage with Math Practice #7 by looking for and making use of mathematical structure. We'll break down how a seemingly simple counting sequence can develop number sense, encourage mathematical thinking, and create a low-pressure environment for pattern recognition.
Key Takeaways:
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/183
Get the special offer to join the Build Math Minds PD site at https://buildmathminds.com/special
Discover how Visual Patterns can transform mathematical thinking in your elementary classroom! Listen in as we explore Fawn Nguyen's powerful activity that engages students in all 8 Standards of Mathematical Practice. Learn how a single activity can help students reason, argue, model, and see the hidden structures in mathematics. This episode is a must-listen for educators looking to make math more engaging, meaningful, and accessible for their students.
Key Takeaways:
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/182
The predictability of mathematics is one of the things I love about math. There are some great activities you can do in your classroom with your students to help them see & USE that predictability. Last week I shared one (Leaping Numbers) and this week I’m sharing another: Finding One and All. This is a great number routine that is similar, yet different, to Number Strings and is a wonderful way to get your students engaged in Math Practice #7: Look For and Make Use of Structure.
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/181
For Build Math Minds Members, log in here to access the done-for-you routine: https://pd.buildmathminds.com/
If you aren’t a member you can join here: https://buildmathminds.com/bmm/
Want a fun, engaging, and mathematically powerful activity to help keep your students engaged in math until the holiday break? In this episode I’m sharing a new activity by one of my favorite creators, Steve Wyborney, Leaping Numbers. This activity is a great way to get your students doing Standard of Math Practice #7: Look For & Make Use of Structure.
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/180
Math tricks or hacks are everywhere, but which ones should you actually use with your students? I came across one this week on social media and thought I’d use it as an example to give you some ideas on how to approach the use of math tricks in your classroom.
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/179
This week’s episode comes from a question that was sent in about helping students who struggle with math problems that are written differently than kids typically see them. These types of “less than” math problems are strange because kids don’t often encounter them in that way even in their own lives. I’m giving you two tips to help students so that these types of problems aren’t so difficult for them.
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/178
Math Misconceptions might just look like mistakes that your students are making, but they are usually slightly different. Mistakes happen when we don’t remember, or remember incorrectly, whereas Misconceptions are rooted in understanding…we believe this is the way it is. Mistakes happen from time to time, and are usually not anything to get too worried about. But Misconceptions stem from a person’s understanding of something and if it isn’t addressed it will forever be misunderstood. In this episode I’m introducing you to our series of short videos we have put together to start a conversation about math misconceptions kids have in the elementary grade.
Watch the Math Misconceptions videos in this Playlist on YouTube:
To get any links mentioned in the episode go to: https://buildmathminds.com/177
In this episode I’m introducing you to a not-yet-released book about the traps of math algorithms, but it’s actually so much more than that. It’s about women supporting women and lifting someone up when you see they are doing good instead of trying to tear them down.
To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to: https://buildmathminds.com/176
Rounding numbers should be way more than just a procedure where we ask students to look to see if the number behind is a 5 or higher. Helping elementary students round should be based upon their number sense. In this last episode of the Rounding Numbers series, I’m giving you an acronym to remember to help your students with rounding numbers: ABR. To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to:
BuildMathMinds.com/175
Rounding numbers should be way more than just a procedure where we ask students to look to see if the number behind is a 5 or higher. Helping elementary students round should be based upon their number sense. In this 2nd episode of the Rounding Numbers series, I’m giving my 2nd tip on how to help your students round with understanding. To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to:
BuildMathMinds.com/174
Rounding numbers should be way more than just a procedure where we ask students to look to see if the number behind is a 5 or higher. Helping elementary students round should be based upon their number sense. In this first episode of the Rounding Numbers series, I’m giving my first tip on how to help your students round with understanding. To see this episode instead of just listen, go to https://www.youtube.com/BuildMathMinds
To get any links mentioned in the episode go to:
BuildMathMinds.com/173
I think we’ve all heard and know about Emotional Eating, but have you ever felt like you’ve done Emotional TEACHING? Not sure it’s a thing, but it kind of feels like it should be. Listen in to my random thoughts and then let me know in the comments over on the YouTube video or the show notes page if you’ve ever done Emotional Teaching? I give an example of Teaching Emotionally in math, but your example could be from any content area.
My kids and I play a lot. Sports, card games, board games, but they all have a preset goal…to win. According to a book I’m reading, true play does NOT have a preset goal. So it got me wondering how much true play my kids, and I, actually do. I’m making it a goal to include more opportunities for us to truly play. In this episode I’m sharing my ideas on what I will be doing this summer to play (and getting my kids to join in) plus I give you the Seven Principles of Self-Active Play they lay out in the book I’m reading. Get any links mentioned in this video at BuildMathMinds.com/170
If you’ve struggled with how to help your elementary students build their math fluency, there is one thing I encourage you to do: Help your students build their flexibility with numbers.
Textbooks try to directly teach strategies to students thinking that is how they will build flexibility, but you spend months doing that and then later in the year they act like they have no idea what you are talking about. That’s when we revert back to just making kids memorize.
In this episode we take a look at my book Fluency Through Flexibility…because fluency doesn’t happen from memorization or teaching a ton of different strategies, it happens when kids build connections & relationships around the numbers so they can use those to help them solve any math problem. Get any links mentioned in this video at BuildMathMinds.com/169
When I first started teaching I don’t think I ONCE used a math manipulative with my students. It was all about learning and memorizing procedures and I didn’t know they needed to actually understand the math. Now, I’m a Recovering Traditionalist and I know that kids need to understand the math, not just DO it, and to help them understand they need to work with math manipulatives.
In this episode, I’m sharing 3 key things to watch out for when working with math manipulatives. We need to be using math manipulatives at any age however we need to make sure we do it properly or they can easily become just like any other rote procedure we tend to teach kids in mathematics. Get any links mentioned in this video at BuildMathMinds.com/168
Growing up I thought doing Mental Math meant doing the algorithm in my head. Times have changed and now many educators have kids solve math in different ways but during Mental Math it’s still only having kids to do math in their head. That’s not exactly what Mental Math should be about. In this episode we explore what doing Mental Math really should be like. Get any links mentioned in this video at BuildMathMinds.com/167
If you’ve ever watched a child during a counting collection and thought “Ugh! Why are you grouping the items like that?!?” Well, there’s probably a reason.
There is a progression kids go through when organizing items they are counting. Now even though this information comes from a book about Early Childhood Education, it still applies to those of you in 3rd-5th as you work to help them group items in ways that lead to multiplicative thinking.
Watch this week’s video about The Progression of Grouping to help you understand why kids might be grouping items a certain way and how to help them. Get any links mentioned in this video at BuildMathMinds.com/166
It is commonly thought that Geometry in the early grades is just about getting kids to name and identify shapes. There are actually 4 big ideas talked about in the Navigating Through Geometry book. One of which is the work around two- and three-dimensional shapes but it is so much more than just naming & identifying shapes. In this episode we take a look at what knowledge kids in PreK-2 should be developing around shapes and the types of experiences you can provide to help them develop it. Get any links mentioned in this video at BuildMathMinds.com/165
There are 4 main strategies children tend to use to solve addition, subtraction, multiplication, and division problems. These math strategies are not tricks. Their foundations are built on number relationships and properties of operations. In the Math Strategy Sessions we have already explored 3 of the strategies and our next session is focused on helping kids use and understand the Inverse Operation Strategy (https://buildmathminds.com/strategy-sessions to register). This is more than just helping kids know Fact Families, it’s about helping them understand the meanings of the operations and the connections between Addition-Subtraction and Multiplication-Division. Helping your students develop the Inverse Operation Strategy will last them the rest of their lives. In this episode I’m sharing the first books I read that highlighted the importance of helping kids develop the strategy. I never learned I could solve a subtraction problem with addition (or division with multiplication) until I was an adult. Kids should be building this understanding way before I did. Get any links mentioned in this video at BuildMathMinds.com/164
There are lots of Problems of Teaching when you are helping young kids learn mathematics. One of the hardest ones is helping your students to be successful learners, constantly trying to manage a large classroom of students who often are not very productive. In the book Teaching Problems and the Problems of Teaching by Dr. Magdalene Lampert, there was a line in the chapter Teaching Students to Be People Who Study in School, that still has me thinking: “...if we view students’ productive or unproductive actions in the classroom as expressions of who they think they are, then classroom management merges with something that might be called ‘academic character education.’” That whole section of the book got me thinking of things you could do in your classroom to help your students be students who study mathematics, which in turn helps them to be successful learners. Listen for my 4 ways to help your students be successful learners of mathematics. Get any links mentioned in this video at BuildMathMinds.com/163
In this video I’m sharing a part of a book that made me go “Hmm, I’ve never really thought about that!” It has to do with just how precise we can actually be when measuring items. One of the Standards of Mathematical Practice is “Attend to Precision” which is about being precise in all mathematical vocabulary and content, but just how precise should we make students be when it comes to measurement? Get any links mentioned in this video at BuildMathMinds.com/162
I love pies, Pecan Pie especially, but I don’t love them during math time. Pies, well circles in general, are an overused visual when it comes to the teaching of fractions. In this video we take a look at visual fraction models that are much better to use and will be helpful to your students as they progress into other mathematical concepts like percentages, ratios, etc. Get any links mentioned in this video at BuildMathMinds.com/161
After the 2024 Virtual Math Summit, there was so much mention of using Sentence Stems I wanted to dig a bit deeper into them. In my research I stumbled upon an old blog post by one of my favorite Math-y people, Sara Van Der Werf. In this podcast episode I’m sharing a piece of her blog post that talks about one tweak you can make to Think/Pair/Share (or Turn & Talk) to help get your students more engaged in the math discussion. Take a listen and go to buildmathminds.com/160 for any links mentioned in the episode.
Cathy Fosnot and Pam Harris are The Queens of Number Strings (or Problem Strings as Pam would call them). I’m way too excited about the fact they are teaming up to do a one-day workshop all about using Problem Strings for Automaticity, Fluency, and Beyond. If you’ve been doing number strings and want to go more in depth on how to use them in your classroom, I highly recommend going to this workshop. Go to https://buildmathminds.com/159 to get links to items mentioned in the episode.
Before the 2024 Virtual Math Summit starts next week, enjoy this preview of a Pre-Summit Session by Rosalba Serrano on Preventing Teacher Burnout. Rosalba shares a ton of information and ideas to help you with burnout but I specifically picked this clip because one of the ideas she shared is one that my family uses a lot: Control the Controllables.
Get registered so you can watch Rosalba’s full session before the summit starts: VirtualMathSummit.com/register.
The 2024 Virtual Math Summit is in two weeks! Here’s a preview of 3 sessions from Jenny Foreman, Loren Thorpe, and myself talking about the challenges and benefits of working on getting your students to think and not just compute during math class. To see the full list of speakers, their presentations, and to get registered go to VirtualMathSummit.com/register. To get any links mentioned in this episode, go to the show notes page at BuildMathMinds.com/157.
The 2024 Virtual Math Summit is this month! Here’s a preview of 3 sessions from Michaela Epstein, Rosalba Serrano, and Nicole Thompson & Jessica Batinovic giving you tips, ideas, and inspiration to make our Number Routines the best they can be for your students. To see the full list of speakers, their presentations, and to get registered go to VirtualMathSummit.com/register. To get any links mentioned in this episode, go to the show notes page at BuildMathMinds.com/156.
The 2024 Virtual Math Summit starts in less than 1 month! Check out this preview of Dr. Jim Ewing’s keynote session about Teaching Math with Newcomers in Mind. To see the full list of speakers, their presentations, and to get registered go to VirtualMathSummit.com/register. To get any links mentioned in this episode, go to the show notes page at BuildMathMinds.com/155.
The 2024 Virtual Math Summit is coming soon. This week’s episode gives you a preview of 4 sessions that focus on helping students build their understanding and fluency of multiplication. Check out this preview of Shannon Olson, Juli Dixon, Thuc-Khahn Park, and Brittany Hege’s sessions. To see the full list of speakers, their presentations, and to get registered go to VirtualMathSummit.com/register. To get any links mentioned in this episode, go to the show notes page at BuildMathMinds.com/154.
The 2024 Virtual Math Summit is just around the corner. This week’s episode gives you a preview of 4 of the sessions. To see the full list of speakers, their presentations, and to get registered go to VirtualMathSummit.com/register. I’m a huge supporter of Student-Centered Classrooms and so for this episode I grabbed some clips to share with you that give you ideas for ways to create that in your math class. Tammy McMorrow, Latrenda Knighten, Ed Nolan, and Mona Iehl each have presentations at this year’s Virtual Math Summit that help bring your students to the center. To get any links mentioned in this episode, go to the show notes page at BuildMathMinds.com/153.
I get asked why I don’t do much training about Time & Measurement. I do have some videos, you can see them in my Playlists at the YouTube channel, but there is a real reason why I don’t talk about those concepts as much as others. So in this video you get my thoughts (based upon what other math educators & researchers have to say) about why we shouldn’t spend a bunch of time teaching time & measurement in math class.
This essential understanding about division is something even adults struggle with: Division is defined by its inverse relationship with multiplication. Our textbooks want us to teach division as its own separate operation but a key to helping students understand and become proficient in division is to teach it in conjunction with multiplication. In this episode I’m sharing an excerpt from one book in the Putting Essential Understandings into Practice series. To get any links mentioned in this episode go to buildmathminds.com/151
Want a quick & easy to implement activity that will show you how much your students know about the math operations and about math story problems? I’ve got it for you in this week’s Build Math Minds podcast. This idea comes from the book Taking Action: Implementing Effective Mathematics Teaching Practices by DeAnn Huinker and Victoria Bill. You can find a link to it and any other resources mentioned at the show notes page buildmathminds.com/150
The two ends of the spectrum when teaching math seem to be “here are the exact ways to solve this problem, follow it exactly,” and “you figure it out, I’m not telling you anything.” Neither of these tend to work. Instead it’s about finding a balance between these. We need to give some guidance, but not too much. We want them to figure out ways to solve problems on their own but we can’t let them flounder.
The book 7 Steps to a Language-Rich, Interactive Classroom by John Seidlitz & Bill Perryman gives educators, as the title says, 7 steps and the first one is: teach students what to say when they don’t know what to say. This also applies when a student doesn’t know where to start with a math problem. So this week’s episode is helping students have Things to Say Instead of IDK.
Join the Build Math Minds PD site: https://buildmathminds.com/bmm
7 Steps to a Language-Rich, Interactive Classroom by John Seidlitz & Bill Perryman
Build Math Minds YouTube channel: https://youtube.com/buildmathminds
It's been an incredible journey over the past two weeks as we've explored nine key strategies to Kickstart your students' number sense. Now, as we reach the end of this Kickstart event, it's essential to understand that the foundations you're laying are seeds of number sense, and their growth will be gradual. These principles we've discussed serve as the blueprint for you to navigate through the upcoming school year:
Do Number Routines and Contextual Problems with a focus on understanding. Watch for your students’ thinking around the number sense concepts. Keep a record of those understandings to help guide the number routines & contextual problems you pick. While you are doing the number routines and contextual problems, make sure the students are doing the talking and you are listening. Use lots of visuals and try to connect the C-R-A models as much as you can. And then practice. Once the understanding is there, kids do need repeated, PURPOSEFUL practice.
That’s your blueprint.
Today, on Day 10, it's time to take this blueprint for building your students' number sense seriously. I've explored concepts, practical strategies, and provided resources to assist you on this path. However, there's more to discover, and if you are ready to explore these ideas further your Day 10 action item is: enroll in my online courses, The Flexibility Formula, tailored for K-2 and 3-5: https://buildmathminds.com/enroll/
The saying "Practice Makes Perfect" often implies that repetition leads to mastery. However, practicing something you do poorly, or incorrectly, doesn't make it perfect; it instead reinforces bad habits. Practice actually makes PERMANENT.
Practice is crucial, but it should follow the establishment of a strong sense of numbers. Day 9’s tip is to find a new way for students to practice math.
Today's audio message discusses two valuable approaches to make practice more enjoyable and connected to your students’ current mathematical needs: using math games and offering students choice during math practice. Listen in to get the details.
Practice is essential for reinforcing knowledge, but let’s do it in a way that is fun, differentiates for your students, and allows for students to reinforce the good mathematical thinking they’ve been building.
Get access to all the resources mentioned when you register for the Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
Day 8 of the Number Sense Kickstart emphasizes a simple, yet sometimes difficult, teaching strategy: Let students solve story problems, don’t give them the steps.
The concept of Cognitively Guided Instruction (CGI) plays a pivotal role here. It acknowledges that students bring their innate mathematical knowledge shaped by everyday experiences with numbers to the table when solving problems. Students often solve problems in different ways than we think they should mathematically…however their strategies are often rooted in the context of the problem so it’s helpful for educators to know the different problem types.
Your task for Day 8 is to select a problem from your textbook, ensure it meets the math content you need for the day, display it, and have your students solve it without offering explicit solution steps. Details on this are in today’s training.
This shift is often difficult for the kids (and you) so, if needed, you can experiment with Numberless Word Problems, an approach developed by Brian Bushart, which gradually introduces numerical information into word problems while promoting critical thinking and mathematical discourse.
As you implement the use of story problems, continue to focus on understanding, identify underlying number concepts, record student insights, actively listen, encourage visual representations, and embrace a variety of models to help kids build connections.
Get access to all the resources mentioned when you register for the Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
In Day 7 of our Number Sense Kickstart we are shifting from the theoretical ideas I’ve shared so far into practical classroom strategies that make it easier to do the theoretical ideas.
Our first practical idea is to do a Number Routine with your students. These structured, brief activities, taking just 5-10 minutes, are a potent tool for meaningful math engagement. Number Routines help students develop the 8 number sense concepts, encouraging them to interact with numbers and share their thinking.
Number Routines create opportunities for deep mathematical understanding and allow teachers to listen more and talk less, gaining insights into student number sense. They can be visual or abstract, but when possible, it's beneficial to incorporate visuals to help your students make connections using the Concrete-Representational-Abstract models.
Listen to the training for today to learn more about Number Routines so you can use one with your students tomorrow.
Get access to all the resources mentioned when you register for the Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
Today we're diving into the Concrete-Representational-Abstract (C-R-A) model of teaching mathematics.
Typically, these stages are presented in isolation, with separate lessons for each. However, the real impact comes when all three are combined in a single lesson. This integration helps students see connections between different problem-solving methods and leads to those "A-HA" moments.
The action item for Day 6 of the Number Sense Kickstart is to seek opportunities to combine C-R-A in your math lessons. Whether in your textbook or your upcoming lesson, aim to integrate all three stages. Learn more about embracing this model to empower students to develop a deep understanding of mathematics.
Get access to all the resources mentioned when you register for the Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
It’s Day 5 of the Number Sense Kickstart and we're focusing on the power of visuals in elementary math education. Just like in reading, where creating mental images enhances comprehension, visuals are essential in math to deepen students' understanding of numbers and mathematical operations. However, sometimes the visuals that are in math textbooks and worksheets you download off the internet don’t actually help students understand the math.
In today’s training we look at ensuring that visuals you use in elementary math lessons help students make sense of the mathematics. There are lots of cases where the visuals being used in the lesson are more of a distraction than helping your students make sense of the math.
Get access to the Math Visuals Decision Tree and the Google Slides of Math Visuals when you register for the Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
This is Day 4 of the Number Sense Kickstart and we are exploring the profound impact of active listening in the classroom.
Did you know that in the typical classroom, teachers do 89% of the talking, while students ask only 11 questions a day, primarily procedural ones? It's time to change this narrative and shift the balance toward student engagement.
We draw inspiration from educator Steven C. Reinhart’s article “Never Say Anything a Kid Can Say For You.” We explore his five techniques that are shared in the article. These techniques will guide you on your path to fostering student empowerment and deep mathematical understanding.
So, are you ready to transform your math classroom? Tune in to learn how to empower your students and truly understand their mathematical thinking. Day 4's tip is simple yet impactful: "Stop Talking & Start Listening."
Find practical strategies and resources on our Kickstart page to kickstart this transformation here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
Most textbooks are focused on answer-getting so their assessments are also focused on just answer-getting. That doesn’t tell you anything about what your students understand, only what they can do. To ensure you are building your students’ understanding of numbers, you need some way to keep track of what they are understanding.
It’s Day 3 of the Number Sense Kickstart and today is all about recording what your students understand about the 8 number sense concepts. If you have taken The Flexibility Formula course, you have detailed information and observation sheets to help you do this. If not, Christina Tondevold gives you a simplified way to record what you are noticing about your students’ number sense. Tune in to listen or even go watch this episode over on the Build Math Minds’ YouTube channel so you can see part of the recording sheet: https://www.youtube.com/buildmathminds
Have you joined the Kickstart yet? Get the 10 Day checklist and the link to all resources mentioned by joining the 10-Day Number Sense Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
Mathematics is so much more than just getting the answers. Answers are important, but that really doesn’t tell you what your students UNDERSTAND about math, it only tells you what they can DO.
If you want to see what your students understand there are 8 number sense concepts that are the root of understanding numbers. It’s Day 2 of our Number Sense Kickstart and in today’s episode Christina Tondevold is detailing each of those 8 number sense concepts. This is the longest video of our Kickstart and if you’ve taken Christina’s online course for teachers, The Flexibility Formula, you already know this information and can skip today’s episode and just do the tip for today: Determine what your students actually need to understand to do the lesson for tomorrow. If you haven’t heard of these 8 number sense concepts before, take a listen.
Download the 10 Day checklist and get the link to all resources mentioned by joining the 10-Day Number Sense Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
Do you have students struggling with their number sense and fluency in elementary mathematics? You aren’t the only one! Over the last few years we’ve seen gaps in students’ understanding get bigger and bigger. So many elementary students are not fluent with math and the underlying issue is their lack of number sense. Textbooks often jump straight into having kids operate with numbers but they have no number sense to be able to understand why the procedures even work. That’s why we’ve created the 10-Day Number Sense Kickstart to help you kickstart your students’ number sense this year.
Over the next two weeks, Christina Tondevold will give you one tip each school day to build your students’ number sense and increase their fluency with mathematics. By the end of this Kickstart, you’ll have a roadmap to keep building it throughout this school year. Today’s episode is Day 1 of the Kickstart.
Download the 10 Day checklist and get the link to all resources mentioned by joining the 10-Day Number Sense Kickstart here: BuildMathMinds.com/10Day-kickstart
If you are looking for a comprehensive online course for elementary educators that will help you better understand and implement the ideas in this Number Sense Kickstart, join The Flexibility Formula Course.
During the 10-Day Kickstart you can get a special gift when you enroll by October 19, 2023. Go to BuildMathMinds.com/enroll to pick the grade level of the course (K-2 or 3-5) and get enrolled.
Here in the United States, it is the end of the school year and teachers are contemplating what work they should send home with students for them to do over the summer. In today's podcast, I get into why I'm not a big fan of general problem packets over the summer and how the phrase "practice makes perfect" is a little inaccurate.
In the last episode of the podcast, I shared the three ideas that make up computational fluency. Flexibility is often the piece that is missing in our fluency instruction, but recently textbooks have tried to incorporate more of it, but in the wrong way. In this week’s podcast, I go over some of the shortcomings in the ways textbook’s teach fluency and what we should really be focusing on when we’re teaching fluency.
The Flexibility Formula courses that I offer have a huge focus on how we can help kids develop number sense, but the main reason to focus on number sense is really to help your students become flexible thinkers; to build their flexibility in mathematics. In episode 144, I talk about how my courses started and the research that inspired them. Come take a listen as I discuss the concepts that make up computational fluency.
Each of you listening to this podcast have different goals for your professional development. You have different things you are wanting to read about to help your students next year have an even better math experience in your classroom. So I’ve compiled a bunch of different lists on Amazon so you can choose from books for specific areas you want to focus on. Come check out Episode #143 where I share my summer reading lists for elementary math teachers for 2022.
Have you ever felt like the thing you’re going through will never end? There is no doubt that hard times can wear us out and make us feel helpless. Then, it can seem like the good times don't last long enough. Whether it's good or bad times, it's important to remember that nothing lasts forever. In this week’s episode, we are talking about how to think about going through the hard times, and the good times by remembering that Nothing Lasts Forever.
Games are one of my favorite ways to have kids practice. They can do 50 problems in 5 minutes and not even realize it. But, one of the biggest complaints I hear about using games in the classroom is that teachers don’t know what the kids are actually doing while playing the game. Are they doing the math or just goofing around?? Come listen to episode 141 where we're talking about getting the most out of math games and go through some recommendations.
As many of you are currently in the thick of standardized testing, it reminds you that testing shouldn’t be like this….but if not this, then what? This week, while sitting in my car waiting for one of the hundred, or so, practices my kids had to finish, I opened up the recent issue of the NCTM journal Mathematics Teacher: Learning & Teaching PK-12. The very first article is about using word problems as a way to assess in mathematics. In episode 140, I go through some of this issue to give you some ideas for some alternatives to math tests. Also, The Build Math Minds PD site membership is open for enrollment!
Should we stop giving tests in math class? This question was recently tweeted by Chris Luzniak and I found the comments under it very thought provoking. So, I thought I'd share some of them with you in today's podcast. Tell me what you think about them in the comments over at buildmathminds/139.
Testing season is upon us and as always, it is stressful. I wish there were easy tips or tricks I could give you to help make it awesome but unfortunately, that doesn’t exist. In episode 138, I give some simple reminders on what to focus on as your student’s go through testing. But the biggest reminder is that your work of helping these kids be mathematicians is more than a test.
This week I finally got a chance to crack open the book Mathematizing Children’s Literature: Sparking Connections, Joy, and Wonder Through Read-Alouds and Discussion by Allison Hintz and Anthony T. Smith. I haven’t even read the whole thing yet because a paragraph from the first page struck me so deeply that I knew I had to share it with you all. In this week’s episode, I share a snippet from that book and get into my own shortcomings using children’s books as learning tools.
Have you ever dove right into something you had no idea how to do? As hard as we try not to, we often ask our students to do just that. When I first started my Recovering Traditionalist journey and implementing more student focused experiences, I thought it would be great but there were definitely some growing pains. In today’s podcast, I’m talking about how the book Introduction to Problem Solving by Susan O’Connell helped me learn how to encourage kids to start problem solving on their own. Come take a listen!
In today’s podcast, I’m sharing an article that presents a visual image I once saw that plays a huge role in how I think about building our understandings of mathematics. I really think about it all the time so I thought it was time to share it with you. That image is the tip of the iceberg. Come take a listen as I get into how the visual representation of the iceberg can help us think about the things underneath the surface that we don’t often consider when we say a kid is struggling to do something.
Pencil or pen? So many educators are adamant that kids MUST use pencils in math class so they can erase their errors. In today’s episode I’m wondering if pens could actually be better. Perhaps there is value in keeping mistakes on the page as our student’s work to get to answers.
In today's episode, I'm wrapping up my series on the Flexibility Formula by looking at Virtual Math Summit sessions from Juliana Matherson, Dr. Hilary Kreisberg, Neily Boyd and Dionne Aminata that address the Experiencing and Equity & Access pillars. These session sneak peeks give us some great tools for serving our students with noteworthy classroom experiences while being sure to include everyone in the instruction regardless of their background. The Virtual Math Summit was on February 26 and 27 and you have until March 8th to watch the sessions. After that, they go into the Build Math Minds PD site for our members to have access to. So make sure you come watch and then join the PD site so you get longer access.
I’ve been doing a series of episodes sharing some summit sessions that address each of The Flexibility Formula. Episode 130 we took a look at Understanding, episode 131 we dove into Observing, and today’s episode we are going to look at the Connecting pillar with Virtual Math Summit presenters Stacey Ellis, Matt Halpern, and Dawn Dibley. Each of them gives us strategies to connect with our students in unique ways that you may not have thought of before. Come take a listen!
The free 2022 Virtual Math Summit is just around the corner on February 26th & 27th. Each session addresses one of the five pillars of the Flexibility Formula. In today's episode, we're going to focus on the Observing pillar by looking at session snippets from Michelle Chu and Kristen Emmel. Michelle talks about making instructional decisions in the moment based on what you're seeing in real time and Kristen talks about using number sense routines to assess students.
If you’ve spent a lot of time with my content or have ever taken one of my PD courses, then you’ve probably run into the Flexibility Formula. The formula is a framework that helps us avoid turning kids into calculators and every session in this year’s Virtual Math Summit addresses at least 1 of the 5 pillars. This week, we’re getting sneak peeks into sessions from Dr. Ange Rogers, Duane Habecker and Shannon McCartney that address the Understanding pillar and help kids understand large numbers.
Sometimes, it can be easy to be pretty focused on things we could do better in our classrooms. But just like we want to do with our students, let's take some time to think about how we can take what we’re already doing and take it further. In today’s episode, I dive into more Virtual Math Summit sneak peeks. This time, from Dina Mendola and me! Dina gets into how we should be thinking about fractions and I talk about one of my favorite topics: subitizing. Registration is still open for the Virtual Math Summit so go get signed up! Yes, it’s still free.
Changing up the strategies we use in our math classrooms can be a really useful way to shake up the status quo, push kids further in their learning, and show us where we can improve as teachers. In this episode, I’m sharing sneak peeks into Virtual Math Summit sessions from Rosalba Serrano, Marian Small, and Shannon Kiebler as they encourage us to do things differently in our math classrooms. The Virtual Math Summit is free for educators so go get signed up at VirtualMathSummit.com/register .
When I was going through school, mimicking the teacher was definitely the norm. For good rule followers, that can be really easy. But is teacher mimicking really our goal as teachers? If we only want students to mimic, then we’re not giving our kids space to think independently, and solve problems in a way that works for their brain. In today’s podcast, I share some sneak peeks from Pam Harris’ and Dr. Doug Clement’s sessions from the upcoming Virtual Math Summit where they share some of their ideas on how we can help our relationships with our students be less robotic when it comes to getting the right answer.
In life, we naturally experience all kinds of highs and lows that stick with us, and influence the way we see the world. In today’s episode, Virtual Math Summit speaker Mike Flynn gives us a sneak peak into one of his presentations where he talks about how the “Pits and Peaks” of life influence our psychology and the way we think about our experiences. More importantly, he tells us about how we can actively use those realizations to help build better experiences for our students inside the classroom.
When it comes to teaching in the classroom, it can be easy to get caught up in the expectations we have for our students. But have you considered the consequences of being hyper focused on expectations? If we look at students through a lens of “we expected you to have THIS and THAT, but you don’t” it starts us off on the wrong foot with how to help the kids. If instead we look at students through a lens of appreciating where they currently are, we are starting on solid ground and can work up from there. Today’s episode goes into details on why focusing on appreciation in our classrooms is so important.
Today, we’re going to wrap up our series on math problems with more than one answer. If you missed part 1 and 2, go check out episodes 121 and 123. Math problems with more than one answer give us the ability to really expand how we ask our students to engage with the problems themselves, and with each other. In particular, they give us an opportunity to allow students to work on Math Practice Standard #3: Construct viable arguments and critique the reasoning of others. Today’s podcast episode explores why that's so important and gives example problems.
A couple weeks ago I talked about how 26 ÷ 6 can have multiple answers. This week, I’m back for part 2 of diving deeper into the idea that math problems can have more than one answer. Specifically, we’re going to look at “Open Middle Math Problems.” Listen in for some great examples of these problems across different grade levels.
Partitive division is typically the natural way that kids think about division and the way that most textbooks start teaching kids division. However, it only gives kids a partial understanding of division. Quotative division problems give kids a deeper understanding of division and help kids focus in on understanding the remainder in the problem. Typically, we think division is only for 3rd grade and up, but division situations come up often for kids in their life and so they naturally experience division very early on. No matter what grade level you teach, this episode will give you a better understanding of teaching division and teaching division with remainders.
We all know that there are many ways to solve any math problem. But have you considered that there are math problems with more than one answer? While I was getting my masters degree, I learned some valuable lessons from that which I wanted to share with you today. Take a listen as I dive into why it's important to open our minds to the idea that math isn’t just about getting one correct answer.
As we get closer to the holidays, our time is ticking to get some great gifts for our loved ones. I’ve found all kinds of reading based gifts but sometimes, the math ones can be a little tougher to find. So, I figured I’d try to help out and share some of my favorite math-based gifts that me and my kids absolutely love. A couple of my choices may even surprise you!
Managing small group work when no other adults are around to assist can be a great challenge. Especially considering the vast differences in mathematical understandings educators are experiencing in the classroom this year. So how can small group work be structured to benefit all kids in the classroom no matter where they are in their understanding? The Build Math Minds Facebook group community delivered a ton of super helpful strategies to help answer that question and I wanted to share some of those in today’s podcast episode.
Thinking is an active and internal process that we should intentionally help our students learn how to share. In order to encourage our kids to share their thinking, we must consider how they (and we) listen, the types of questions we ask as teachers and they ask as students, how ideas are documented, and more. In today’s episode, I get into some amazing ideas about how to get students to share their thinking processes by Making Thinking Visible.
Having your work computer break down on you is one of the worst feelings in the world. Especially, if you forgot to back up all your data. I’ve been absent for a while because that is exactly what happened to me. In this week's episode, I talk about why I’ve been gone for a little bit and why it is of paramount importance to make sure all your digitally stored work is backed up.
I want all kids to have different strategies at their disposal to solve math problems. However, the way our textbooks have us teach them to kids is overwhelming and confuses kids. This episode is a clip from a webinar I did recently about The Missing Piece to Elementary Fact Fluency and part of the issue is that we are directly teaching kids so many strategies when instead we need to help kids develop them on their own.
If you want help with how to do that in your classroom, come join my online PD courses:
The Flexibility Formula K-2nd https://buildmathminds.com/flexibility-formula-prek-2nd/
The Flexibility Formula 3rd-5th https://buildmathminds.com/flexibility-formula-3rd-5th/
In this week’s podcast, we discuss a lot of different topics with Kelly Rogers, a 3rd grade teacher, who shares about building a love of math even during a pandemic. Go here to get links to resources mentioned: buildmathminds.com/115
Recently I did a video over on my vlog about A Big Mistake Educators Make When Building Math Fluency. The mistake is that we directly teach students strategies.
Then I was looking through the book Putting Essential Understanding of Addition and Subtraction into Practice in PreK-Grade 2, I came across a section that described a lot of what I was trying to convey in my video just in a different way.
Now, I know this is from a PreK-Grade 2 book, but if you are an upper elementary teacher, as I read this section, think about how this applies to your situation. Are you teaching multiplication or division in this same way??
Go to buildmathminds.com/114 to get links mentioned in this episode.
In this week’s podcast, I’m sharing the story of the single thought that was running through my head as I sat through Pre-Calculus so that I could get a math endorsement added to my elementary ed teaching license: “how in the heck is this supposed to make me a better 6th grade teacher?!?!?”
The final step towards building your students’ fluency is deciding HOW you are going to implement these ideas into your classroom. I am not going to detail out exactly how you should do that. That’s not what I believe we should do for teachers just like I don’t believe that’s what we should do for our students in math. We should NOT make everyone do it the same way. Every classroom is filled with kids of varying needs and abilities. Every classroom has a teacher with their own teaching style. So what works for one classroom will not always work for everyone else. I understand that having some kind of guideline is important.
Everyone’s situations are different. You may be tied to a textbook or you might be in a district that doesn’t use a textbook and the standards are your only guide. No matter your situation there are three types of activities I recommend trying to incorporate as much as you can.
Go to buildmathminds.com/starterkit to get the Building Elementary Math Fluency Starter Kit to learn more about the Three Types of Activities that Build Math Fluency.
Typically on this podcast I share things that other people have written because I want to encourage you to go learn from the original sources that I have learned from. But today I want to share something I wrote with you.
Fluency is a big focus of mine, so much so that I have full online PD courses that I’ve created for teachers to learn how we build students’ fluency. How we build it is actually through building students’ flexibility...that’s why I called my courses The Flexibility Formula.
To help elementary educators get started down the journey of building fluency by focusing on building students’ flexibility, I created the Building Elementary Math Fluency Starter Kit. I’d like to share a little bit from that starter kit with you today about how Fluency is the By-Product of Flexibility. If you’d like to get the starter kit go to BuildMathMinds.com/starterkit.
Last week, I shared that I was Wondering About The Use of the word AND in Math. For example, how do you say the number 45? Do you say “forty-five” or “forty AND five”? Today, I’m sharing some of the responses I got.
Go to buildmathminds.com/110 to get links to any resources mentioned in this episode.
As a Recovering Traditionalist I want you to know that I don’t have it all figured out and it’s okay that you don’t either. I’m still refining my understanding and teaching and it’s been over 17 years I’ve been working on changing my teaching.
So I’m going to start doing a different type of podcast episode every once in a while. I’m calling them my ‘wonderings.’ So today I’m Wondering About The Use of the word ‘AND’ in Math. buildmathminds.com/109
We are wrapping up the 2021 Virtual Math Summit here. In fact, the day this podcast gets released is the last day of free access to all the sessions. After today they are only available inside the Build Math Minds PD site for members to watch (go here to enroll: https://buildmathminds.com/bmm). One benefit members get is access to a session I did only for BMM members and VIP attendees of the summit, but on today’s podcast you are getting a snippet from that session that I hope inspires you to create more wonder, joy, and beauty in mathematics.
In this week’s episode, we are talking about CGI Math which stands for Cognitively Guided Instruction. Cognitively Guided Instruction helps us learn how to facilitate the development of kids’ math understanding by listening first, then making instructional decisions based upon what you hear.
Go to buildmathminds.com/107 to get links to any resources mentioned in this episode.
This is the last episode of the podcast that I’m giving you a preview of the 2021 Virtual Math Summit because the summit is this week!
Register for the summit here before July 29th: VirtualMathSummit.com/register
Our two presenters featured on this episode will be part of the Speaker Panel Q & As so if you want to participate in those, make sure to register for the VIP access or become a BMM member. Details are on the registration page.
Our two presenter previews this week are about two of my favorite ways to engage kiddos in mathematics: Games & Manipulatives. Get any links I mention in this episode at buildmathminds.com/106
Registration is now open for the 2021 Virtual Math Summit hosted by Build Math Minds: VirtualMathSummit.com/register
In this week’s podcast I’d like to highlight two sessions that are focused on content that 3rd-5th graders are building. Go to buildmathminds.com/105 to get links to any resources mentioned in this episode.
Registration is now open for the 2021 Virtual Math Summit hosted by Build Math Minds: VirtualMathSummit.com/register
This week, I share clips of two sessions from the summit that focus on helping our students build a sense of numbers. Go to buildmathminds.com/104 to get links to any resources mentioned in this episode.
Registration is now open for the 2021 Virtual Math Summit hosted by Build Math Minds: VirtualMathSummit.com/register
To get you excited about the Virtual Math Summit, I thought I’d share a few snippets from sessions to give you a sneak peek over the summer before the summit starts. For this week’s episode, we get to hear from Bettina Atwill, John SanGiovanni, and Donna Boucher. Go to buildmathminds.com/103 for any links mentioned in the episode.
Registration is now open for the 2021 Virtual Math Summit hosted by Build Math Minds: VirtualMathSummit.com/register
For this week’s episode, we are listening to clips from our opening and closing sessions for the 2021 Virtual Math Summit. The sessions by Zaretta Hammond and Pam Seda & Kyndall Brown both have a focus on giving us ways to ensure equity & access in the math classroom. Go to buildmathminds.com/102 for any links mentioned in the episode.
Registration is now open for the 2021 Virtual Math Summit hosted by Build Math Minds: VirtualMathSummit.com/register
For this week’s episode, we get to hear a snippet from Dr. Nicki Newton and Ann Elise Record’s sessions. Go to buildmathminds.com/101 for any links mentioned in the episode.
Registration is now open for the 2021 Virtual Math Summit hosted by Build Math Minds: VirtualMathSummit.com/register
For this week’s episode, we get to hear a snippet from Zak Champagne and Dawn Dibley & Pam Tabor’s sessions. Go to buildmathminds.com/100 for any links mentioned in the episode.
Registration is now open for the 2021 Virtual Math Summit hosted by Build Math Minds: VirtualMathSummit.com/register
To get you excited about the Virtual Math Summit, I thought I’d share a few snippets from sessions to give you a sneak peek over the summer before the summit starts. For this week’s episode, we get to hear from Andre Daughty and Alice Aspinall. Go to buildmathminds.com/99 for any links mentioned in the episode.
Every year, since 2017, I get the pleasure of hosting the Build Math Minds Virtual Math Summit. This year, the free summit for elementary educators will be taking place July 29th and 30th, 2021. Registration is now open here: VirtualMathSummit.com
To get you excited about the Virtual Math Summit, I thought I’d share a few snippets from sessions to give you a sneak peek over the summer before the summit starts. For this week’s episode, I pulled together 3 sessions in which the presenters are all discussing math fluency.
In this week’s episode, I’m giving you my top math education books that I believe every elementary educator should have on their bookshelves.
In a year we thought we’d finally NOT have to worry about standardized testing, educators are in the thick of the testing stressing. In this week’s Build Math Minds podcast, I wanted to share a reminder that This is Only A Test.
Have you ever asked yourself the question, is student enjoyment or student achievement our goal? Yes, we know that it’s both but sometimes there might not be a balance between the two. In this week’s podcast, we’re discussing this topic with Jill Bratton, a second grade teacher, who shares how the thing she’s learned has impacted student learning.
Welcome fellow Recovering Traditionalists to Episode 94. Today we are getting inspiration to make Small Teacher Moves with Vicki Tilson.
You get to listen in on a conversation I had with Vicki Tilson. Vicki has gone through my online courses so I wanted her to share about some of the changes they have made at her school and how it’s impacted student learning of math. One of the things you will hear her mention is the impact of small teacher moves.
Go to buildmathminds.com/94 to get links to everything we mention in this episode.
Welcome fellow Recovering Traditionalists to Episode 93. Today we are looking at Constructing Goals for Student Learning.
Typical lesson plans are focused on what students will be able to do, that’s putting a focus on the performance of your students. When you create learning goals, you are putting a focus on what your students will understand.
This week I’m sharing an article with you. One of the things I really appreciate about this article is how they differentiate between learning goals and performance goals. Go over to buildmathminds.com/93 to get links to resources mentioned in this episode.
In this episode, we are looking at The Power of Counting. Counting is so much more than just memorizing the number names. Have you ever stopped and asked a child why we count? Do they know the purpose of counting? Go over to buildmathminds.com/92.
Welcome fellow Recovering Traditionalists to Episode 91. Today we are taking a look at Teaching Math for Understanding.
In last week’s podcast I briefly mentioned The Flexibility Formula. The Flexibility Formula are the pillars of math instruction that help us be able to build students’ flexibility with mathematics. In this week’s podcast I want to dive a bit into one of the pillars: Understanding. Get any links to resources mentioned in this podcast here: buildmathminds.com/91
Welcome fellow Recovering Traditionalists to Episode 90. Today we are looking at The Missing Piece to Math Fluency.
Back in 2014 I wrote the book Fluency through Flexibility. That book is all about building students flexibility with the numbers 0-20 to help them build their fluency with addition and subtraction within 20. Fast forward a few years to 2016 when I created my first online course called Number Sense 101. It was all about how to build number sense in order to help kids build their fluency in PreK-2 and a few years later I created one for 3rd-5th called Number Sense 201. Well, this last year I redid both of those courses and when I did that I called them The Flexibility Formula.
Back in 2014 when I wrote the book I knew the key to building kids’ fluency was to build their flexibility. When I was redesigning the course I didn’t even think about my old book, however I ended up coming full circle back to the idea that flexibility is the missing piece to building kids’ fluency with math.
Go over to buildmathminds.com/90 to get links mentioned in this episode.
How would the students in your class respond to the following question:
What number would you put in the box to make this a true number sentence?
8 + 4 = ▢ + 5
The majority of elementary kids put ‘12’ in the box. In today’s episode we are talking about the book Thinking Mathematically and what we can learn from it to help our students better understand equality in math.
Welcome fellow Recovering Traditionalists to Episode 88. Today we are looking at Virtual versus Physical Manipulatives.
With distance learning happening for so many right now, during a Build Math Minds Members Q & A session, a member asked if it’s okay to just have kids working with virtual manipulatives or if kids need the physical manipulatives to ensure they are working in the Concrete level.
As I went digging into the research, I found that this is not a new concern. In 2016, Julie Sarama & Douglas Clements wrote a chapter in the book International Perspectives on Teaching and Learning Mathematics with Virtual Manipulatives that can shed some light on this concern that educators are having in 2021. Go over to buildmathminds.com/88 for links mentioned in this episode.
When you see 15-7, do you know that 15-7 is 8 or do you really think in your brain that 7 + 8 would make the 15? Are you using your addition facts to help you with the subtraction facts? A lot of people do, but a lot of people also see them as isolated facts. Sue O’Connell and John SanGiovanni (and many other researchers) have noticed that when kids have addition fluency and they have built the connection between addition and subtraction, they are more fluent with subtraction. I’m sharing a snippet from their book Mastering The Basic Math Facts in Addition and Subtraction. Get a link to the book and other resources mentioned in this episode at buildmathminds.com/87
Welcome fellow Recovering Traditionalists to Episode 86. Today we are looking at Why Subtraction Is So Hard.
The topic of subtraction has come up a lot recently in my life and while I was digging into some research I came across an article by Constance Kamii, Barbara A. Lewis, and Lynn D. Kirkland titled Fluency in subtraction compared with addition. As I was reading through it, I found a section that was thought provoking and I wanted to share with you. All links mentioned in the episode can be found at buildmathminds.com/86
It seems like there is a debate about everything in how we teach math. One of those debates is whether or not kids should do paper-pencil math or mental math. If you’ve been around awhile you can probably guess where I land on this debate….right in the middle, kids need both.
In the book Math: Facing an American Phobia by Marilyn Burns she pretty much sums up my thoughts on pages 10-11. Go over to buildmathminds.com/85 to get the link to purchase the book.
Diagnosing a child with a learning disability should never be done via something you learn in a podcast.
So many people ask me about dyscalculia. I’m not an expert on this, but someone I’m learning from is Ronit Bird.
The research around dyscalculia is still so new, and in the book, she says that estimates say around 4-6% of the population have dyscalculia, which equates to around 1 child in an average classroom.
To help you a bit more to decide if a struggling kiddo has dyscalculia (and should be tested), Ronit gives a list of indicators that I’m sharing in this podcast.
Go over to buildmathminds.com/84 to get the link to purchase the book.
Welcome fellow Recovering Traditionalists to Episode 83. Today we are looking at Inspection-Worthy Mistakes.
When I was in school, math mistakes were met with a big ‘ol red mark and nothing more. Did I learn anything from those red marks? I learned it was a wrong answer. But wrong answers can be a great jumping off point to help students learn so much more than that.
However, you don’t want to stop & do a whole group discussion every time you see a student with a wrong answer, so when should you?
In this week’s podcast, I’m sharing a few ideas from the article Inspection-Worthy Mistakes by Angela T. Barlow, et al.
Get links over at buildmathminds.com/83
Welcome fellow Recovering Traditionalists to Episode 82. Today we are looking at how to have Hands-Down Conversations.
How many of you were expected to raise your hand before you spoke in school? I did. Even my own kids do now in their classrooms. I know this not because I’m in class with them but at the dinner table we will be having a conversation and one of them will raise their hand for a turn to speak.
When I was in the classroom, I had students raise their hands to speak because classroom conversations can get out of hand and unruly very quickly. So I was intrigued when I saw the book Hands Down Speak Out: Listening and Talking Across Literacy and Math K-5 by Kassia Omohundro Wedekind and Christy Hermann Thompson. Go to buildmathminds.com/82 to get links mentioned in this episode and a discount code for the book.
Welcome fellow Recovering Traditionalists to Episode 81. Today we are looking at how to help kids get away from that feeling of “I’m Just Bad at Math!”
The book I’m Just Bad at Math! by Allison Gray is a short chapter book about a girl, Lucy, who wants to be good at math but is struggling. This book is a great read aloud to address the issue that some of your kiddos are thinking they are just bad at math. It can be a great kickoff to a Growth Mindset investigation and how in your classroom you will be helping them change their thinking about their math abilities. I’ll link to the book over at buildmathminds.com/81
Welcome fellow Recovering Traditionalists to Episode 80. Today we are taking a look at The 5 Strands of Mathematical Proficiency.
It’s the time of year that educators start thinking and worrying about the end of the year tests. Yes those are still a ways off but we start to wonder if we are going to have time to prepare students enough with the time we have left.
I want to encourage you to keep these 5 Strands of Mathematical Proficiency in mind. Get all the info here: buildmathminds.com/70
Welcome fellow Recovering Traditionalists to Episode 79. Today is all about How Can I Help?
You may or may not have noticed but I took a break from doing these podcasts. I can blame the craziness of 2020 and navigating this time with 4 young kids but really the reason I wasn’t creating this podcast was because I didn’t think I could be of any help. In this episode, I’m sharing why I’m restarting the podcast and how I can be of help.
Welcome fellow Recovering Traditionalists to Episode 78. Today we are talking about Looking for the CAN DOs in Math.
In today’s episode you get to listen in on a conversation I got to have with an alumni of my online course, Amy Warren. Amy is an elementary special education teacher. We discuss all kinds of topics from looking for the things kids CAN DO to how to do assessments with young kids, even if you are doing virtual school. Go to buildmathminds.com/78 to get links to everything we mention in this episode.
Welcome fellow Recovering Traditionalists to Episode 77. Today we are taking a look at Predicting Later Academic Success.
In this episode, I’m sharing a very research heavy article, but it is worth the read. School Readiness and Later Achievement by Duncan, et al provides such an interesting observation through their meta-analysis of data sets that looked at school readiness (school-entry academic, attention, and socioemotional skills) and later academic success in reading and math. I’m linking up the article over at buildmathminds.com/77
What’s so interesting about the findings from this article is that the strongest predictors of later academic success are school-entry math, reading, and attention skills. And early math skills have the greatest predictive power, followed by reading and then the attention skills.
Welcome fellow Recovering Traditionalists to Episode 76. Today we are taking a look at tips for Creating Images for Subitizing.
The first time I was introduced to Subitizing was in the article Subitizing: What Is It? Why Teach It? By Douglas Clements. The article was published in 1999, but one thing I discovered through that article was even though the term was fairly new, there had been research done around it from as far back as 1912! Still today we have lots of elementary educators who don’t know what Subitizing is, why it’s important, or how to teach it.
If you aren’t sure what Subitizing is, then pause this video and go download the article. I’ll link to it over at buildmathminds.com/76 and then you can come back and listen to the rest of this episode because what I’d like to chat about today is some advice on how to actually create images to use for subitizing activities.
Welcome fellow Recovering Traditionalists to Episode 75. Today we are taking a look at how Counting is a Substitute for Sense Making.
“To encourage counting can actually interfere with the construction of number in that it is a rote process that may be devoid of any mathematical meaning.”
When I read that sentence on page 15 of the book Coming to Know Number by Wheatley & Reynolds, my first instinct was to slam the book shut. My shoulders immediately clenched up and I thought ‘How in the world can they say that!?!? Counting and our number system is the basis for all mathematical ideas.’
In today’s episode I talk about what the book continues on to say and how my shoulders started to relax. Get all the details from today’s episode over at buildmathminds.com/75
Welcome fellow Recovering Traditionalists to Episode 74. Today we are talking about Why Children Have Difficulties with their Math Facts.
Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them by Arthur Baroody is the article that opened my eyes to the true root of student difficulties with mastering their math facts: A Lack of Number Sense.
The reason I fell in love with this article was because I saw myself in it. I saw myself as the learners he talks about and I even saw myself as some of the teachers he talks about. In the article he describes what ‘Conventional Wisdom’ says to help students who are struggling but then opposes that with the “Number Sense View.” He does this for 3 different scenarios related to helping kids learn their facts. Get the link to the article here: buildmathminds.com/74
Welcome fellow Recovering Traditionalists to Episode 73. Today we are talking about Addressing Unfinished Learning.
As we start back to school this year a common concern is how to address the unfinished learning that may have happened during COVID-19. So today I’d like to encourage you to check out two documents put out by the Student Achievement Partners. I’m talking about one of them, Addressing Unfinished Learning, on the podcast today.
Get all the details and links at buildmathminds.com/73
In this week’s podcast, I’m sharing a small part of the book The Distance Learning Playbook, that can help you build teacher-student relationships from a distance. I think this is one of the hardest, yet most impactful, things you can do while teaching from a distance. Get all the details and links at buildmathminds.com/72
Welcome fellow Recovering Traditionalists to Episode 71. Today we are talking about ways to Continue the Learning from the Virtual Math Summit.
The free access to the sessions is over but your opportunity to learn from the summit speakers is not over. So many of them have free resources & trainings available on their sites and many others have written books that have personally changed my teaching. Some of them even have online courses you can take to learn more from them. If you couldn’t participate in this year’s summit or you want to continue the learning you started at the summit, I’m linking to places you can learn more from each presenter over at buildmathminds.com/71. And I’m also sharing the dates for the 2021 Virtual Math Summit.
Welcome fellow Recovering Traditionalists to Episode 70. Today we are Implementing Ideas from the Virtual Math Summit.
This past week was the Virtual Math Summit!!!! I wanted to let you all know that we recently extended the free access period to August 12th due to the storms here in the United States and so many people who are without power. You can watch all the sessions over at the Virtual Math Summit main page buildmathminds.com/vms20, but I’ll also link it up over at the show notes for today’s episode at buildmathminds.com/70.
At the very end of these implementation chats, I asked each educator to share ONE THING that they think is very important to them that it gets implemented this year and in today’s episode I’m going to share the clips of them talking about their ONE THING. Okay, let’s get into it.
Welcome fellow Recovering Traditionalists to Episode 69. Today we are talking about The 2020 Virtual Math Summit.
This week is the Virtual Math Summit!!!! In fact for those of you who are registered you will be sent a link to the pre-conference session that gets released tonight with Sheldon Eakins. If you aren’t registered you better get on over to buildmathminds.com/virtual-math-summit now because time is running out to get FREE access to these amazing math presentations. I’ll also link to the registration over at buildmathminds.com/69.
So to celebrate the 4th annual Virtual Math Summit I thought I’d take a clip from each of the 24 presentations so that you can get a preview of each session.
Welcome fellow Recovering Traditionalists to Episode 68. Today we are talking about What Works Best.
We all know that we can pretty much find research to support any claim you ever want to make about what works when teaching. There’s research to say ability grouping works, there’s research to say it doesn’t. There’s research to say we should use manipulatives, there’s research to say we shouldn’t.
But when I hear that something has an effect-size of _____, it makes me give more pause to consider something.
If you aren’t familiar with effect-sizes, they come from the work of John Hattie that was published in the book Visible Thinking. I’ll link to it over on buildmathminds.com/68 so you can dig into it more. But, to summarize, Hattie did a meta-analysis and combined findings from 80,000 studies to find patterns to help us inform our practice. The effect size is the size of the effect certain things have on student learning.
Welcome fellow Recovering Traditionalists to Episode 67. Today we are talking about Selecting & Sequencing Student Solutions.
I’m so excited that Peg Smith is presenting at the upcoming Build Math Minds Virtual Math Summit! Have you registered yet?? The link to register is over at buildmathminds.com/67 along with all the other resources I’m mentioning in this podcast.
So, Peg is a co-author of multiple books about The 5 Practices.In this podcast I talk about why I’m so excited Peg is presenting at this year’s Build Math Minds Virtual Math Summit and why I can’t wait for you to learn from her. Get all the details at buildmathminds.com/67
Welcome fellow Recovering Traditionalists to Episode 66. Today we are talking about how to Jump-start Math Class with Daily Routines.
I’m so excited that John is coming back this year to the present at the Build Math Minds Virtual Math Summit! John presented back in 2018 on Using Evidence to Find Misconceptions and Do Something About Them so those of you who are members of the Build Math Minds PD site go into the Virtual Math Summit area of the site and click on 2018, you will find John’s session in there.
If you haven’t registered for this year’s Virtual Math Summit make sure you go to buildmathminds.com/virtual-math-summit to get your free registration. John will be sharing some of his favorite number sense routines that are in his new book Daily Routines to Jump-Start Math Class and in today’s podcast I’m sharing a little snippet from that book. buildmathminds.com/66
Welcome fellow Recovering Traditionalists to Episode 65. Today we are talking about Getting Started with Educational Equity.
Today I’m pleased to announce that someone I’ve been learning from about increasing Equity & Access in education has joined the line-up of speakers for the Build Math Minds Virtual Math Summit .
In my previous podcast I encouraged you to learn from Sheldon Eakins and the Leading Equity Center. I’m very excited that Sheldon will now be kicking off the BMM Virtual Math Summit and sharing with us 5 Steps Towards Equity.
So I decided that in today’s podcast I’d share an excerpt from a free resource Sheldon has on his website called Getting Started with Educational Equity: Ten Steps to Get You on The Right Path Towards Leading Equity. You can find it on his main site SheldonEakins.com but I’ll also give the direct link to request that download from him over on the show notes page buildmathminds.com/65.
Welcome fellow Recovering Traditionalists to Episode 64. Today I am talking about Building Our Minds...Not Just In Math.
Just like the opening of this podcast always says, this podcast is about Building Math Minds. In my videos I say we have to “build our math minds, so we can build the math minds of our students.”
Well today is still about building our minds, but it doesn’t pertain to math. If we want to build the minds of our students we first need to build our minds...in all areas.
This past week has been a lot of reflecting and learning about racism. Go to buildmathminds.com/64 for all the links.
Welcome fellow Recovering Traditionalists to Episode 63. Today I am Admitting When I’m Wrong.
Last week over on my vlog TheRecoveringTraditionalist.com, I talked about Teaching After The Coronavirus Shutdown. One of the things I recommended in that video was not using your textbook when you start teaching next year. Anytime I say things about not using a textbook I always get pushback. Yes there is research to show that fidelity to textbooks breeds good test scores, but it also breeds kids who hate math and whole list of things that I could go on and on about.
However, I need to admit that I am wrong because it really isn’t the textbook that I don’t like and that is causing all those things….it’s how we use that textbook. We’ve all seen it. Maybe you’ve even been that teacher. I know I was. I think back to how I taught before I learned about Cognitively Guided Instruction and how kids develop their math understandings. I approached and used my textbook way differently before that than how I used my textbook after
The textbook didn’t change. My knowledge about how to build students’ understanding did and that impacted how I used the activities that were in my textbook.
Get all the resources mentioned in this episode at buildmathminds.com/63
Welcome fellow Recovering Traditionalists to Episode 62. Today I am talking about The 80/20 Rule Applied to Teaching Math.
This week over on my vlog TheRecoveringTraditionalist.com, I talked about Teaching After The Coronavirus Shutdown. Specifically, how to plan for what to teach next year knowing that your students may not have gotten a quarter of the instruction they would have gotten in the grade before yours.
I shared about the document created by Achieve The Core that details out the Major Work of each grade level. The Focus by Grade Level document (or what was originally called the Content Emphases) shows the standard clusters that basically carry more weight in each grade.
At the bottom of each page of the Focus by Grade Level document, in very tiny print, it states:
“At least 65% and up to approximately 85% of class time, with Grades K–2 nearer the upper end of that range, should be devoted to the major work of the grade.”
That statement reminded me of the 80/20 rule, also known as the Pareto Principle. It’s the idea that 80% of the effects come from 20% of the causes.
Get all the resources mentioned in this episode at buildmathminds.com/62
Welcome fellow Recovering Traditionalists to Episode 61. Today we are looking at The Benefits of Inventing Algorithms.
This past weekend I did a webinar each day that thousands of elementary educators attended. It was the same webinar just different days/times to allow for people’s scheduling. If you didn’t get a chance to attend you can still catch the limited-time replay for the next few days at buildmathminds.com/replay. The webinar was all about how to help kids develop their own ways of solving problems and not be reliant upon algorithms or strategies taught by the teacher.
My first glimpse into teaching math in this way was through the research of Thomas Carpenter, Elizabeth Fennema, and Megan Frank-e (1996). Then their book, Children’s Mathematics: Cognitively Guided Instruction came out and gave me even more insight into opening up my teaching through the use of story problems to allow children’s thinking to help guide my instruction.
In today’s podcast I’m reading from that book about the benefits of inventing algorithms.
Get all the resources mentioned in this episode at buildmathminds.com/61
Welcome fellow Recovering Traditionalists to Episode 60. Today is an interview with 3rd grade teacher Cathy Palkovic and a theme of our conversation is about Building Self-Reliance in Math.
In this interview with Cathy we get into all kinds of things from what her distance learning looks like to Math Running Records to how her 3rd graders solved 898x52 without any guidance from her. We discuss how she has helped her students build their self-reliance through things she has learned and one of the things that has helped her along her math teaching journey is my Number Sense course. The registration for the courses are now open from May 1-14 you can go to buildmathminds.com/enroll to join a course but I’ll also link to the course and all the other resources Cathy mentions over at the show notes page buildmathminds.com/60
Welcome fellow Recovering Traditionalists to Episode 59. Today we are looking at The Harmful Effects of Algorithms.
It’s hard to not just teach kids algorithms because honestly, parents are expecting you to teach that to their kids and it’s also difficult if you yourself have only ever solved math problems using algorithms. But true fluency in math doesn’t come just by following rules and procedures it comes from being a flexible thinker. Get all the resources mentioned in this episode at buildmathminds.com/59
Welcome fellow Recovering Traditionalists to Episode 58. Today we are discussing Meaningful Mathematics.
In today’s episode I’d like to read a portion of an article that comes from the National Council of Teachers of Mathematics. Normally I only link to articles on NCTM’s site that you can access for free. This article is not available for free but this article is just too good not to talk about...plus NCTM is doing a free trial of their membership right now. I’ll link to that free trial over at buildmathminds.com/58. When you do the free trial make sure to select the option to receive access to the online archive of the Teaching Children’s Mathematics journal, that’s the journal that this article was published in.
On pages 312-313, William Brownell writes...
Welcome fellow Recovering Traditionalists to Episode 57. Today we are looking at How to Build Math Fluency.
Building kids’ math fluency can impact everything they are going to learn in math. It all starts with understanding what fluency really entails, how to build that fluency when it comes to the basic facts, and what kinds of activities you can be doing to build true fluency for students. That’s what you will get in the Building Math Fluency Starter Kit. I’ll link to it on the show notes page buildmathminds.com/57 or go to buildmathminds.com/fluencykit
I’m going to read a section from the kit for today’s podcast.
Welcome fellow Recovering Traditionalists to Episode 56. Today I’m urging everyone to Stop Teaching.
If I could send any message to everyone in education and all the parents of school-aged kids it would be to Stop Teaching. The only people that doesn’t apply to are high school students (especially Seniors) who need to finish up credits. But for everyone else, Stop Teaching.
Now I know that isn’t possible for everyone out there but I’d like to outline my points and maybe if more people start talking about the current situation in this way we can help convince other people that academics isn’t the most important thing right now. Honestly, this episode is for parents and for education admins who are deciding what’s happening in their district or state. Because it isn’t the teachers saying they want to give kids all this work. It's the admin and those above them telling the teachers what needs to be done and parents requesting things.
Welcome fellow Recovering Traditionalists to Episode 55. Today we are looking at Teaching Math at Home.
Today’s podcast is from a Facebook Live I did recently with Kate Snow from Kate’s Homeschool Math. We wanted to do a video that helps parents and teachers think about what Teaching Math at Home right now looks like.
We talk about it from the perspective of teachers trying to scramble and give good resources to parents and from the perspective of the parent at home trying to help ensure learning continues.
In this video we talk about:
If you want to check out the resources both Kate and I have for teaching math at home head over to buildmathminds.com/55
Welcome fellow Recovering Traditionalists to Episode 54. Today I’m giving you Free Resources. Here at Build Math Minds, I don't have activities that you can give to parents because that's never been what Build Math Minds is about. But I know that that is what you need right now. Get all the info here: buildmathminds.com/54
Welcome fellow Recovering Traditionalists to Episode 53. Today we are looking at why Fluency is NOT Just Fast & Accurate. Over on my vlog I posted a video this week about how fast does not mean children are fluent. As I was doing some research on this I came across a President’s Message by then NCTM President Linda Gojak. Get all the info here: buildmathminds.com/53
Welcome fellow Recovering Traditionalists to Episode 52. Today I’m asking Am I a Broken Record?
Today is episode 52 which means it is the 1 year anniversary of this podcast. Today’s podcast is a bit different than what I normally do. Get all the info here: buildmathminds.com/52
Welcome fellow Recovering Traditionalists to Episode 51. Today we are looking at Choral Counting and Counting Collections.
Inside the Build Math Minds PD site, we do a book study a couple times a year and next week we are starting a book study on the book Choral Counting and Counting Collections by Megan L. Franke, Elham Kazemi, and Angela Chan Turrou.
This book study is for members only but I as I was reading through the book I wanted to share a section from the book to encourage you to go get the book and read through it yourself. Many people think counting activities are just for our young learners but this book shows just how powerful Choral Counting and Counting Collections are throughout all of PreK-5th grade.
The book goes in-depth on each routine but at the end of the book one part caught my attention today and that’s what I want to share with you.
Get all the info here: buildmathminds.com/51
Welcome fellow Recovering Traditionalists to Episode 50 where we discuss Transitioning From Teacher to Math Coach with Peggy Loutzenhiser. Get all the info here: buildmathminds.com/50
Welcome fellow Recovering Traditionalists to Episode 49. Today we are looking at Catalyzing Change.
Changing the way you teach math is hard and it can feel even harder when you think about all the other teachers in your district who aren’t changing their teaching. You think to yourself “Does it even matter? Next year’s teacher doesn’t teach this way so why should I take the time to adjust my teaching” or the ever popular thought of “When my students get to junior high or high school those teachers expect the kids to do____(fill in the blank)____, so I need to prepare them."
Catalyzing Change in High School Mathematics: Initiating Critical Conversations was a book published by NCTM in 2018 in the hopes of starting to change how mathematics is taught in high school. In 2019 DeAnn Huinker wrote an article in Teaching Children Mathematics (also published by NCTM) about how that book has lessons in it that can help catalyze change throughout all the grades. Get all the info here: buildmathminds.com/49
Welcome fellow Recovering Traditionalists to Episode 48. Today we are looking at how Developing a Culture of Questioning Can Be an Agent of Change.
Today I was reading back through the book Agents of Change: How Content Coaching Transforms Teaching & Learning by Lucy West and Antonia (Toni) Cameron. I’m sitting here on my couch bundled up with a blanket and my coffee, fireplace going because it’s freezing outside and the snow is dumping. But just 4 days ago it was 60 degrees outside. It really hit me at that moment how quickly some things change (like the weather) but not in education.
The book Agents of Change is full of ideas on how to build a system within your school or district through Math Coaching that will create sustainable change. However, lots of the ideas within the book are things we can do even if we aren’t a math coach. Get all the info here: buildmathminds.com/48
Welcome fellow Recovering Traditionalists to Episode 47. Today we are looking at how to Innovate Inside the Box.
So I’ve started reading a new book and there is so much goodness in this book it was really hard to decide what part to share with you today.
Innovate Inside the Box: Empowering Learners Through UDL and the Innovator's Mindset by George Couros and Katie Novak is one of those books that makes you think and reflect upon your teaching but it also gives you practical ideas on how to change your teaching. Get all the info here: buildmathminds.com/47
Welcome fellow Recovering Traditionalists to Episode 46. Today we are getting Information & Inspiration from Lori Linsmeyer who encourages us to Get Going Using Math Manipulatives.
Lori was an elementary teacher for 29 years and now does math intervention with a focus of kindergarten through grade 3. In this episode, Lori gives lots of inspiration and information including her thoughts on:
-How We Learned Math Impacts How We Teach Math
-Opening up Math Time Builds Connections
-Using Math Manipulatives
Get all the info here: buildmathminds.com/46
Welcome fellow Recovering Traditionalists to Episode 45. Today we are looking at 13 Rules That Expire.
I’ve been guilty of telling my students tips or rules that I thought were helping them get to an answer quicker, because in the past I used to think my job was to help my students get answers. Now, I see my job of a teacher as helping students make sense and many of those tips had no “sense” behind them. They really were just rules to help my students get an answer.
The article I want to share with you today was published almost 6 years ago but so many of the things mentioned in this article are still being used. I can honestly say I probably would still be doing many of them if I hadn’t read this article - but once we know better, we do better.
13 Rules That Expire by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty forever changed my teaching. Not only do they share the 13 rules but there is also a section about expired math language that we use and they give alternatives to use instead. This article is seriously a MUST READ. To give you a glimpse into the article I’d like to share with you just one of the rules today. Get all the info here: buildmathminds.com/45
Welcome fellow Recovering Traditionalists to Episode 44. Today we are looking at why Making Sense is First and Computation is Second.
I’ve always been bugged by the way textbooks use word problems, but I wasn’t ever able to verbalize what I didn’t like. Then as I was reading the new book Mathematize It! Going Beyond Key Words to Make Sense of Word Problems: Grades 3-5 by Sara Delano Moore, Kimberly Morrow-Leong, and Linda M. Gojak, they put into words what I never was able to.
There is also a book for Grades K-2 for those of you who work with the younger grades.
These books are full of information about the different word problem types, but also about the best way to implement the use of word problems in your classroom. In the last chapter of the book, they describe 8 shifts in instruction that we need to do if we want to build students’ problem-solving skills. One of those is exactly the reason why I don’t like the way textbooks use word problems and so I’d like to share that with you today. Get all the info here: buildmathminds.com/44
Welcome fellow Recovering Traditionalists to Episode 43. Today we are taking a look at Open Middle Math.
This week’s book is from a friend of mine, Robert Kaplinsky. I’ve known Robert for years but I’m not sharing this book just because he is a friend. I only share things that I love and I love Open Middle.
While I’ve known Robert for years and I’ve known about and used Open Middle, I’ve never known the backstory of how they started. So to introduce you to Open Middle problems I thought I’d read a section from Robert’s book, Open Middle Math, that gives the background of Open Middle problems. Get all the info here: buildmathminds.com/43
Welcome fellow Recovering Traditionalists to Episode 42. Today we are Making the Case for Play in the Classroom.
As I’m recording this it’s the holiday season and it’s the time of year when teachers break out all kinds of fun activities and just let the kids play. I mean, how else are you going to survive that last week before break, right!?!?
So with all this play happening, I pulled out the book Exploring Mathematics Through Play in the Early Childhood Classroom by Amy Noelle Parks.
Now, even though this book is full of ideas for the early childhood classroom she makes some great points that apply no matter what grade level you work with.
Get all the info here: buildmathminds.com/42
Welcome fellow Recovering Traditionalists to Episode 41 today we are going to learn how to Help Students Learn to Love Math from BMM member and 1st grade teacher Kelly Sickle.
Kelly is a member of the Build Math Minds PD site and a 1st grade teacher. As you will see in this episode the trainings she has gotten inside of BMM are just a small part of the professional development she has done. Kelly mentions a video about the C-R-A model, I’ll link to that video inside the membership site but I’ll also link to a free video that’s on my vlog. You can find those links at buildmathminds.com/41 and if you are interested in becoming a member of Build Math Minds, I’ll post a link to the waitlist page. We only open up registration once a year to the general public but occasionally we will open it up to people who are on the waitlist. So go to buildmathminds.com/41 to get all the details. Here’s my interview with Kelly.
We don’t have all the kids read the same book in reading, so why do we have all kids work on the same math facts? Now there are definitely times we have them read the same passages so that we can have a common conversation about things, but we also have times that kids are reading books at their level.
We need to do the same for our students when it comes to math. The book Fluency Doesn’t Just Happen is your guide for that. The book is full of what to expect as kids are building their fluency and ideas on how to respect that. What do you actually do in your classroom to allow students to work in their zone of proximal development when it comes to addition and subtraction facts? Get all the info here: buildmathminds.com/40
As I read the article Double Impact: Mathematics and Executive Function, a light bulb came on about why some students are struggling with this new way we are teaching math. If you have kids who are struggling with Executive Functions and then you ask them to do those things while also doing something that has high mathematical demand, they are going to struggle. For example, if students have not worked to develop their cognitive flexibility and then we give them a problem that requires them to do multiple attempts to solve the problem and it also requires some mathematical understandings that aren’t fully developed, they are just going to shut down.
So, as you design or use tasks in your classroom, this article made me realize that we also need to pay attention to the Executive Function demands that the task is placing on them as well. Get all the info here: buildmathminds.com/39
When the standards came out, most teachers went to the grade level standards to find out what they needed to teach for their grade level. Many people skipped the Standards for Mathematical Practice. These are 8 standards that describe how students should interact with mathematics at all grade levels, thus they were not inside each grade level because we should be doing them at all grade levels.
Math Practice #7 is Look for and Make Use of Structure and that is where you can find mention of patterns. One of my favorite books about the Standards for Mathematical Practice is Beyond Answers by Mike Flynn. I love this book because it’s written for primary grades teachers and gives lots of examples of young kids working on these big mathematical practices. It’s so cool to read.
In Chapter 7, Mike talks about Math Practice #7: Look for and Make Use of Structure and he relates it to the movie the Matrix (which I’ll admit I’ve never actually watched).Get all the info here: buildmathminds.com/38
Welcome fellow Recovering Traditionalists to Episode 37. Today we are looking at building Mathematical Argument in the Elementary Classroom.
I love understanding the WHY to anything. I wasn’t always that way. I used to be that good student who would just follow and do whatever my teachers told me to do. It seemed as though teachers would get irritated by those kids who would ask WHY...WHY does this work? WHY do I have to learn this?
The book I’m sharing with you today talks about WHY kids need to investigate the WHY and how to do it in your classroom. But Why Does it Work? Mathematical Arguments in the Elementary Classroom by Susan Jo Russell, Deborah Shifter, Reva Kasman, Virginia Bastable, and Traci Higgins. Get all the info here: buildmathminds.com/37
Welcome fellow Recovering Traditionalists to Episode 36. Today we are looking at how to Encourage Student Perseverance and Authority.
Changing the way we teach mathematics is hard for us as teachers, but sometimes it’s even harder on our students. If you’ve tried to open up your teaching and give students a problem and then just let them solve it anyway they can, then I’m sure you’ve had that feeling that the idea of Productive Struggle sometimes doesn’t seem so productive.
So, today I wanted to share with you an article that you can read on the National Council of Teachers of Mathematics’ website. NCTM publishes a great magazine throughout the year, full of wonderful articles. The article Two Instructional Moves to Promote Student Competence by Jen Munson is from the January 2018 issue. Get all the info here: buildmathminds.com/36
Welcome fellow Recovering Traditionalists to Episode 35. Today we are looking at the Features of Appropriate Math Tasks.
I am 35 episodes in and I cannot believe I haven’t talked about this book yet! Making Sense: Teaching and Learning Mathematics with Understanding by Hiebert et al is one of those books that I have pink highlighter throughout the entire thing.
It was so hard to pick just one passage from this book to share with you today, so I’m sure I’ll share more in future episodes. The whole book gives us a framework for thinking about math classrooms. They highlight 5 dimensions that work together to shape your math classroom, today we are going to look at the first dimension which is The Nature of the Learning Task through this passage from page 8. Get all the info here: buildmathminds.com/35
Welcome fellow Recovering Traditionalists to Episode 34. Today we are looking at Effectively Using Games to Build Mathematical Thinking & Reasoning
Today’s insight comes from Well Played: Building Mathematical Thinking Through Number Games & Puzzles by Linda Dacey, Karen Gartland, and Jayne Bamford Lynch. As you hopefully know, I love Games. I grew up in a game playing family and still love playing games with my own children. So as I was preparing for a video I did recently over on my Vlog, The Recovering Traditionalist, I was reading back through the Well Played books. There is a book for PreK-2 and one for 3-5.
This paragraph from page 6 really made me stop and think about how we use games in the classroom. Get all the info here: buildmathminds.com/34
Welcome fellow Recovering Traditionalists to Episode 33. Today we are talking with Melissa Barone, a middle school teacher, who makes me get emotional as she talks about how to build confidence in students and help them see that their voice matters in math.
In this episode I get to chat with Melissa Barone. Melissa took my Number Sense 201 course that is for 3rd-5th grade teachers, but she’s a middle school teacher. In this interview, she talks about how things she learned from that course (and other places) has helped her transform her math classroom into a place where students are building their confidence in math and seeing that their voice matters in math class.
The number sense courses are now open for 2019 registration and you can get all the info at buildmathminds.com/enroll.
Registration is only open for a short time so depending upon when you listen to this registration might be closed. If so, you can join the waitlist. You can find a link to it and all the resources mentioned in the episode at the show notes page buildmathminds.com/33
Welcome fellow Recovering Traditionalists to Episode 32. Today we get to hear from
Co-teachers in a 3rd grade classroom who discovered they have permission to teach a curriculum they were mandated to use while also meeting the needs of the students they have.
In this episode I get to chat with Jessica Hempel and Christine Farrell. They worked in a district that had a mandated curriculum that had some great parts to it but also some bad parts. Listen in as they talk about how they worked together to figure out how to find a balance between what was mandated and what they saw that their students really needed. Jessica mentions how my Number Sense course gave her permission to do what she knew was right for her students.
If you want to get that “permission” as well, then come join me in the number sense courses. It’s not that you need that permission, what the courses show is the research behind how kids develop mathematical understandings and how number sense is really the root of it all. If you’d like to learn that information along with getting resources to use in your classroom to help build number sense, the courses are now open for 2019 registration and you can get all the info at buildmathminds.com/enroll.
Registration is only open for a short time so depending upon when you listen to this registration might be closed. If so, you can join the waitlist. Again the website is buildmathminds.com/enroll but I’ll also link to it and all the resources mentioned in the episode at the show notes page buildmathminds.com/32
Welcome fellow Recovering Traditionalists to Episode 31 where we are going to get inspiration and information from Christy Crees a 30-plus-year veteran elementary teacher.
In these recent episodes, I’m focusing on having you hear from real teachers out there who have made big changes in how they teach mathematics. All of these teachers have made a choice to put their students at the heart of the learning instead of the textbook. Today we are learning how Christy Crees uses the textbook as a guide but modifies lessons based upon things she has learned about building her students’ number sense.
She does talk about my Number Sense course as part of the learning she’s had. Those courses are now open for 2019 registration you can get all the info at buildmathminds.com/enroll. Registration is only open for a short time so depending upon when you listen to this registration might be closed. If so, you can join the waitlist. Again the website is buildmathminds.com/enroll but I’ll also link to it and all the resources Christy mentions at the show notes page buildmathminds.com/31
Welcome fellow Recovering Traditionalists to Episode 30, where we are going to get inspiration from Jessica Boyer, a 4th Grade Math Specialist.
In this interview, Jessica mentions that her school has no curriculum for her to use. Now I’m not a fan of relying solely on a textbook and I’m a big advocate of teaching without a textbook. Jessica mentions how the extreme end of the spectrum can also be difficult. When you don’t have a textbook to follow you aren’t sure where to go. That’s why I’m a big advocate for learning the learning progressions that kids go through when developing their understanding of mathematics. In this episode she talks about her journey of doing that. Get all the info here: buildmathminds.com/30