Math is Figure-Out-Able!

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

Listeners' questions spark an engaging discussion on the evolution of teaching and mathematical strategies. The hosts emphasize the importance of experience with coins to understand decimals and fractions. They advocate for adapting strategies in a digital world, prioritizing meaningful understanding over rote learning. Innovative instructional routines, like 'which one doesn't belong,' are recommended to boost student engagement. Personal anecdotes underscore the benefits of tech integration in math education, highlighting collaboration between teachers and students.

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 algorithmsEp 9: Defining models and strategiesEp 34: Memorizing multiplication facts is not the answerEp 27: The students who need to know why 

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 numbersShould we insist on the most simplified fraction answer?Problems that work with both money and a clock modelToday's students need the experience from learning with a clock model

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 equivalenceUsing the word "over" for fractions is NOT helpfulEquivalent fraction examples on a clock modelA real student's math journeyJordan Using the Clock Model