Math is Figure-Out-Able!

In Episode 67 revisited the Development of Mathematical Reasoning (DMR) and we described how students can solve addition problems with Counting Strategies. What about the addition algorithm and multiplication and division problems? In this episode Pam and Kim explore the Development of Mathematical Reasoning even further, and discuss how important it is that we help students become more sophistica...

It's been over a year since Pam and Kim first introduced the DMR (Development of Mathematical Reasoning) and in that time they've refined their ideas even further. In this episode Pam and Kim dive deeper into the development and why it's so important.  Talking Points: It's not about answer getting, or students doing it 'their way'.  Our goal is more sophisticated thin...

Math conferences are powerful ways to improve your teaching. But it's also really easy to go to a conference and accidently miss all the good sessions. In this episode Pam talks about a few powerful leaders in the math education community that she will always go see no matter what they're talking about.  Talking Points: Karim Ani Peter Liljedahl Deborah Ball Zaretta Hammond Jenny Bay Wil...

How can we best grow as teachers? Together of course! In this episode Pam and Kim discuss the power of teachers honing their craft through collaborative experiences and conversations. Administrators, leaders and coaches will find this episode particularly helpful. Talking Points: Shared experiences help to communicate and reflect about critical moments and expert teacher moves. How coaches, teache...

Fun with Division: An Important Strategy There is so much to division! Pam and Kim go through a quick Problem String that builds a less known, but super powerful, division strategy.  Talking Points: Reasoning about division with scaling Thinking partitively vs quotitively to solve gnarly division problems with whole numbers, fractions, decimals and even polynomials. See Ep 132 and 176 for more on...

Counting strategies can often go overlooked. Learning to count in a way that prepares students for Additive Reasoning is complex. But just how hard can counting be? Wait until you listen to this episode! Pam and Kim discuss how to help young learners increase in their sophistication as they count to add numbers. Talking Points: Counting is more than singing the song. Addition requires a strong fou...

In this episode Pam and Kim show how three popular models - 100 charts, base ten blocks, and algebra tiles - while powerful for developing reasoning, can limit students' development of more sophisticated thinking as tools for computation.  Talking Points: CRA vs tools for thinking What are 100 charts, base 10 blocks and algebra tiles? 3 limitations for some manipulatives that prevent kids fro...

Continuing their series on models and modeling, Pam and Kim discuss the advantages and pitfalls of Ten Frames. They emphasize the power of models that can become tools for thinking and reasoning. Ten Frames can be an excellent tool for helping kids see the structure of 5 and 10 when counting. But what happens when students need to compute and build Additive Reasoning? Talking Points: What are Ten...

Let's keep talking about modeling! A lot of you may be familiar with Number Bonds and Tape Diagrams and may be wondering about how they fit in with our modeling framework. In this episode Pam and Kim discuss these models and some of the confusion and misunderstanding surrounding them. They offer suggestions to help teachers advance students from "modeling of the situation" to "...

Are manipulatives sometimes overemphasized? When are they useful, and when can they actually get in the way of the mathematics? What role do they play in our discussion about the modeling framework? Pam and Kim discuss these tricky questions, and discuss the power of contexts and developing models as tools for reasoning. Talking Points:  An important modeling framework What are manipulatives? Gail...

It's time to talk about one of our foundational ideas for facilitating Real Math! In this episode Pam and Kim detail a modeling framework that helps students to learn to model their own thinking, and then to use models as tools for, or in order to think about, computation.  The goal of the framework is for students to be able to reason and solve complex problems on their own with confidence....

If my experiences as a student are different than my child's experience at school, how can I help them succeed? In this episode for parents, we provide two clear ways you can support your child to be the best math student they can be. Be sure to listen to episodes 55 and 56 for the rest our series for parents. Talking Points: We can all be mathy people Parents' attitudes towards math aff...

Hey parents! Thank you so much for listening to part two of our series for parents. It can be really frustrating to not understand what it is your kid is doing on their homework. What is up with all of the drawing? Where are the algorithms and simple steps? In this episode we'll explain the purpose and goal of why the math on your kid's paper looks different. Talking Points: Reasoning ab...

This episode is for all the parents out there who are invested in helping their children! It can be frustrating to see how math class looks different than it did when we were students. Why is it different anyways? Why would math class have to change? We are so grateful you're taking the time to ask. We'll do our best to provide some answers.  Talking Points: Why did the math we were taug...

We love answering your questions! In this episode Pam and Kim answer a question submitted from Rachel Adler. Pam shares her experiences familiarizing her students with data representations, and then Pam and Kim discuss their best advice for first year teachers. Talking Points: Jo Boaler's Data Talks: https://www.youcubed.org/resource/data-talks/  Integrating data analytics into what you are a...

We loved getting all of your questions! Because there's so many questions, Pam and Kim will have to spend the next couple episodes answering them. In this episode they discuss a question about the relevancy of money strategies, and whether strategies will change over time.  Talking Points: Why experience with coins and their relationships is important Distinction between teaching strategies a...

We are so grateful to be celebrating our one year anniversary of the podcast! It's been wonderful to hear all the feedback you've given us as you transform your classrooms. Here's to another year of mathematizing! Highlights: Ep 2: Pam's stance on algorithms Ep 9: Defining models and strategies Ep 34: Memorizing multiplication facts is not the answer Ep 27: The students who nee...

We've had so much fun talking about fractions! In this episode Pam and Kim do another Problem String to demonstrate the effective use of a clock model. Talking Points: What denominators work well for a clock model? Example Problem String with non-unit fractions and mixed numbers Should we insist on the most simplified fraction answer? Problems that work with both money and a clock model Today...

How important is fractional equivalence? Important enough for another model! These models are fantastic for helping students develop a natural understanding of equivalent fractions.  Listen in as Kim and Pam discuss how to use a clock model for denominators uncommon to the money model. Talking Points: Use adding and subtracting fractions to help think and reason about fraction equivalence Using th...

In this episode Pam and Kim finish up their money Problem String from the last episode. But first, Pam wanted to reflect a little on how she was less than helpful when Kim was struggling to think about nickels. We all learn and grow, and self-reflection is super important! Talking Points: Do you need time, or do you need help? (see episode 40) Once kids have an answer, do we force them to find ano...

It's time to talk about everyone's two favorite things: fractions and money! Fraction equivalence is a super important concept in mathematics, and it is best developed naturally in a familiar context. In this episode Pam and Kim model using coin denominations to  reason about fractional equivalence.  Talking Points: If you understand fractional equivalence, you don't have to memoriz...

Let's keep talking fractions! In this episode Pam and Kim discuss an interesting rich task from Cathy Fosnot to help students reason about fractions within the context of sharing fairly. Listen in to learn about the outcomes teachers should look for when teaching fractional sense in a rich contextual problem. Talking Points: Splitting the wholes into unit fractions  Splitting the leftovers in...

How young can young learners begin to experience fractions? Younger than you think! In this episode Pam and Kim describe simple ways we can help young students begin to develop fractional understanding. Pay attention to how natural it can be for young learners to learn math! Talking Points Struggles that young learners may experience with "half" Simple classroom activities to have studen...

Time to get into fractions! There is so much to learn about teaching fractions and in this episode we wanted to lay some important ground work.  All too often we limit students by giving them experience with only one or two of the important ways fractions can be interpreted. When we help students fully understand fractions by using all of the interpretations, their ability to think proportionally...

Though some people think Kim and Pam's voices are hard to tell apart, teaching Real Math has nothing to do with a particular style or even personality type. We believe in seeing the humanity in students and empowering them with mathematical confidence! Talking Points: Pam and Kim's results on the Enneagram Test. 2 important things -  Teaching Real Math is more about beliefs about student...