Math is Figure-Out-Able!

It's been over a year since Pam and Kim first introduced the DMR (Development of Mathematical Reasoning) and in that time they've refined their ideas even further. In this episode Pam and Kim dive deeper into the development and why it's so important. Talking Points:It's not about answer getting, or students doing it 'their way'. Our goal is more sophisticated thinking and reasoningAdded Statistical Reasoning to DMRWhere do subtraction and division live on the DMR graphic?We don't leave a level of reasoning behindExamples of Counting, Additive and Multiplicative ReasoningHow can you build your own mathematical reasoning?Free DMR workshop for anyone at anytime!

Math conferences are powerful ways to improve your teaching. But it's also really easy to go to a conference and accidently miss all the good sessions. In this episode Pam talks about a few powerful leaders in the math education community that she will always go see no matter what they're talking about. Talking Points:Karim AniPeter LiljedahlDeborah BallZaretta HammondJenny Bay Williams and John SanGiovanniElham KazeimiCathy FosnotJuli K. DixonSarah VanderwerfInstructional Routines to find at MathisFigureOutAble.comJourneyLEADER (learn more at https://www.mathisfigureoutable.com/leader)Other people to follow: @JBayWilliams, @JohnSanGiovanni, @ddmeyer, @joboaler, @ekazemi, @ctfosnot, @thestrokeofluck, @saravdwerf

How can we best grow as teachers? Together of course! In this episode Pam and Kim discuss the power of teachers honing their craft through collaborative experiences and conversations. Administrators, leaders and coaches will find this episode particularly helpful.Talking Points:Shared experiences help to communicate and reflect about critical moments and expert teacher moves.How coaches, teachers and peers can benefit from coversations about shared experiences to implement action in the classroom.How to create shared experiences.Introducing JourneyLEADERYou can learn more about our exciting new experience for leaders at mathisfigureoutable.com/leader

Fun with Division: An Important StrategyThere 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 scalingThinking partitively vs quotitively to solve gnarly division problems with whole numbers, fractions, decimals and even polynomials.See Ep 132 and 176 for more on equivalent ratios!Learn more about the Building Powerful Division workshopSee Episode 142 for further discussion of quotitive thinking when dividing with fractionsSee Ep 132 and 176 for more on equivalent ratios!See Ep 243 for more information on Integer Division

Counting strategies can often go overlooked. Learning to count in a way that prepares students for Additive Reasoning is complex. But just how hard can counting be? Wait until you listen to this episode! Pam and Kim discuss how to help young learners increase in their sophistication as they count to add numbers.Talking Points:Counting is more than singing the song.Addition requires a strong foundation of Counting Strategies.C + M = ?Double/triple counting, counting on, Commutative Property for addition.Teacher moves to help students become more sophisticated counters.

In this episode Pam and Kim show how three popular models - 100 charts, base ten blocks, and algebra tiles - while powerful for developing reasoning, can limit students' development of more sophisticated thinking as tools for computation. Talking Points:CRA vs tools for thinkingWhat are 100 charts, base 10 blocks and algebra tiles?3 limitations for some manipulatives that prevent kids from doing Real Math How each not-fav model have the 3 limitations for computingMimicking or Mathematizing?

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 Frames?The 3 limitations to Ten FramesIt's not just the model, it's how you use the modelOur 3 preferred models for transitioning from counting to Additive ReasoningSee Episode 5:How Do You Reason to learn more about the Development of Mathematical Reasoning, and how it transforms our understanding of what it means to learn and teach mathematics. 

Let's keep talking about modeling! A lot of you may be familiar with Number Bonds and Tape Diagrams and may be wondering about how they fit in with our modeling framework. In this episode Pam and Kim discuss these models and some of the confusion and misunderstanding surrounding them. They offer suggestions to help teachers advance students from "modeling of the situation" to "modeling to make their thinking visible".Talking Points: What are Number Bonds and Tape Diagrams?CGI and direct modeling confusionExample of using Number Bonds and Tape Diagrams vs an Open Number LineModels that can be tools for thinking for addition, subtraction, multiplication, and division

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

It's time to talk about one of our foundational ideas for facilitating Real Math! In this episode Pam and Kim detail a modeling framework that helps students to learn to model their own thinking, and then to use models as tools for, or in order to think about, computation.  The goal of the framework is for students to be able to reason and solve complex problems on their own with confidence.Talking Points:Model vs. StrategiesThe different meanings for "model"In important modeling frameworkAn example with sticks of gum and a ratio tableHow students learn to verbalize and model their own thinkingHow this framework differs from CRA