Math is Figure-Out-Able!

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

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 peopleParents' attitudes towards math affects your child's attitude towards mathImportance of student think timeImportance of parent involvement in math educationSee Episodes 34-38 to learn more about best teaching practices for multiplication facts. 

Hey parents! Thank you so much for listening to part two of our series for parents. It can be really frustrating to not understand what it is your kid is doing on their homework. What is up with all of the drawing? Where are the algorithms and simple steps? In this episode we'll explain the purpose and goal of why the math on your kid's paper looks different.Talking Points:Reasoning about math vs performing memorized stepsWe want our students to be reasoners, not calculatorsRepresenting students' thinking and reasoning on paper can look messyAs we understand the possibilities with Real Math, we can encourage and refine teaching so more students are more successful

This episode is for all the parents out there who are invested in helping their children! It can be frustrating to see how math class looks different than it did when we were students. Why is it different anyways? Why would math class have to change? We are so grateful you're taking the time to ask. We'll do our best to provide some answers. Talking Points:Why did the math we were taught in school look the way it did?Why do generations of technology dependent students need a different way to learn math?Why do students need to understand Real Math for our future? 

We love answering your questions! In this episode Pam and Kim answer a question submitted from Rachel Adler. Pam shares her experiences familiarizing her students with data representations, and then Pam and Kim discuss their best advice for first year teachers.Talking Points:Jo Boaler's Data Talks: https://www.youcubed.org/resource/data-talks/ Integrating data analytics into what you are already teachingSolidifying your teaching philosophy and belief system. See episode 12The importance of good teacher partners and getting outside of your own classroomThe importance of good student-teacher relationshipsStarting off the year by setting clear expectations to set the year up for successFigure out how you fit as an adult with all students