Math is Figure-Out-Able!

We've talked a lot about the types of reasoning we need to help students develop, but a lot of teachers believe that there comes a point in higher math where reasoning just won't cut it. In this episode Pam and Kim tackle functional reasoning, and demonstrate that algebra can be so much more than memorized steps.Talking Points:Is using the procedure of finding slope, plugging into a formula, etc the most efficient?The importance of working with intuitionExamples of using patterns that you notice to find the equation of a line without formulasIntuitively finding the equation of a line in standard form

In Episode 67 revisited the Development of Mathematical Reasoning (DMR) and we described how students can solve addition problems with Counting Strategies. What about the addition algorithm and multiplication and division problems? In this episode Pam and Kim explore the Development of Mathematical Reasoning even further, and discuss how important it is that we help students become more sophisticated. It's more than just answer getting. And stay tuned to the end for a freebie!Examples of solving addition problems with bigger numbers using Additive Reasoning.Examples of solving multiplication problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.Examples of solving division problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.Brand new free infographics of the Development of Mathematical Reasoning.Videos of students solving problems using the different types of reasoning to help you use the DMR in your classroom to identify where your students are in their reasoning.Find the infographics here: https://www.mathisfigureoutable.com/blog/development-4

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