We've got another one of our favorite routines for you today! In this episode Pam and Kim demonstrate the Relational Thinking routine, a routine that helps students understand equivalence and become more comfortable with relational strategies. Thanks to the Cognitively Guided Instruction group for introducing us to this routine! Talking Points: Examples of the routine for all four operations What does the equal sign really mean? Strategies based on equivalence: Give and Take, Constant Difference...
Dec 07, 2021•20 min•Ep. 77
There are a lot of great instructional routines out there, and today we want to highlight As Close as it Gets. In this episode Pam and Kim discuss how to use this instructional routine in your classroom and how it can help your students get mathematizing with estimation! Talking Points: A routine to help students learn what Real Math estimation is through reasoning. Examples Teacher moves to introduce the routine and common pitfalls Why do we use the routine? Where to find help for your classroo...
Nov 30, 2021•14 min•Ep. 76
Are your students dumb or smart? Fast or slow? Under achiever or advance achiever? Or are they just your students with varying experiences? In this episode, Pam and Kim discuss labels, and the effect they have on you as teachers and your students. They propose a different way to look at your students so that you can provide opportunities and experiences for all students so that they continue to learn and love math. Talking Points: The problem with labels. What do we believe about learning? Focus...
Nov 23, 2021•19 min
How can we take what students already know and leverage that to make other mathematical connections? You've probably heard us mention that you should know your content and know your kids, but there's a lot of meaning behind that. In this episode Pam and Kim go in deep on how knowing your content and your kids support effective teaching practices and maximize learning for students. Talking Points: We need to know beyond our standards. Why we need to look vertically and horizontally at our standar...
Nov 16, 2021•21 min•Ep. 74
We did it! We made it to episode 73! Why is that an important milestone? Just cause it's Kim's favorite number :-). In this episode Pam and Kim take the opportunity to highlight some important milestones in the Math is Figure-Out-Able movement. We're so grateful you're a part of it! Talking Points: Pam and Kim's favorite numbers Twitter followers and MathStratChat You Can Change Math Class Challenge Pam and Kim as colleagues Podcast Online Workshops What's coming up next?...
Nov 09, 2021•18 min
Facilitating a Problem String is tricky business, so Pam and Kim take the time in this episode to provide some do's and don'ts that anyone can learn from. Talking Points: What is a Problem String? How long should a Problem String last? Can Problem Strings be given in a worksheet or as a bell ringer? Does everyone share during the Problem String? How do I know which students should share and in what order? What if all of my students aren't using the strategy? What if I don't understand a student'...
Nov 02, 2021•16 min•Ep. 72
What makes Problem Strings different from other sequences of problems? In this episode Pam and Kim get into the nitty gritty on how Problem Strings work and what sets them apart. Talking Points: Defining Problem Strings The "Why or Purpose" - What sets a Problem String apart from just a list of problems? The "How" - How are Problem Strings facilitated differently from a textbook lesson or rich task? An example If you want to hear more about Problem Strings, check out Episode 163. Find examples o...
Oct 26, 2021•18 min•Ep. 71
Problem Strings are meant to build off each other so that the math is always moving forward. That's why we've decided to build off the last episode with another Problem String! In this episode Pam and Kim find the equation of some lines using relationships and develop powerful strategies for more sophisticated thinking. Talking Points: You don't have to have lots of recent experience to notice the patterns. Problem Strings to notice patterns and relationships between the x values and the y value...
Oct 19, 2021•15 min
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 intuition Examples of using patterns that you no...
Oct 12, 2021•26 min•Ep. 69
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 solvin...
Oct 05, 2021•27 min•Ep. 68
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 reasoning Added Statistical Reasoning to DMR Where do subtraction and division live on the DMR graphic? We don't leave a le...
Sep 28, 2021•26 min•Ep. 67
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 Williams and John SanGiovanni Elham Kazeimi Cathy Fosnot Juli K. Dixon Sarah Vanderwerf Instructional Routines to ...
Sep 21, 2021•22 min•Ep. 66
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 class...
Sep 14, 2021•18 min•Ep. 65
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 equivalent ratios! Learn more about the Building Powerful Division workshop See Episode 142 for furth...
Sep 07, 2021•20 min•Ep. 64
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 ...
Aug 31, 2021•19 min•Ep. 63
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 from doing Real Math How each not-fav model have the 3 limitations for computing Mimicking or Mathematizing?...
Aug 24, 2021•30 min•Ep. 62
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 Frames It's not just the model, it's how you use the model Our 3 pr...
Aug 17, 2021•19 min•Ep. 61
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 modeli...
Aug 10, 2021•22 min•Ep. 60
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 Burrill - Where's the Math? Cathy Fosnot - Do manipulatives embody mathematics? Are manipulatives ba...
Aug 03, 2021•16 min•Ep. 59
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. Strategies The different meanings for "model" In important modeling framework An...
Jul 27, 2021•20 min•Ep. 58
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 affects your child's attitude towards math Importance of student think time Importance of parent involvement in m...
Jul 20, 2021•12 min•Ep. 57
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 steps We want our students to be reasoners, not calculators Representing stud...
Jul 13, 2021•12 min•Ep. 56
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 l...
Jul 06, 2021•14 min•Ep. 55
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 teaching Solidifying your teaching philosophy and belief system. See episode 12 The importance of g...
Jun 29, 2021•23 min•Ep. 53
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 and mathematical strategies Technology in classrooms as a teaching strategy Extra resources: Which One Does...
Jun 22, 2021•17 min•Ep. 53
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 need to know why
Jun 15, 2021•22 min•Ep. 52
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's students need the experience from learning with a clock model...
Jun 08, 2021•21 min•Ep. 51
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 the word "over" for fractions is NOT helpful Equivalent fraction examples on a clock model A real stude...
Jun 01, 2021•22 min•Ep. 50
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 another way? For which denominators is thinking about money helpful? Ways to think about 2 2/5 minus 9/...
May 25, 2021•18 min•Ep. 49
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 memorize any rules for operators of fractions Examples of using the money model to think about fraction equivalence, and bon...
May 18, 2021•25 min•Ep. 48
