DiscoverMath is Figure-Out-Able with Pam Harris
Math is Figure-Out-Able with Pam Harris
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Math is Figure-Out-Able with Pam Harris

Author: Pam Harris

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Math teacher educator Pam Harris and her cohost Kim Montague answer the question: If not algorithms, then what?Join them for ~15 minutes every Tuesday as they cast their vision for mathematics education and give actionable items to help teachers teach math that is Figure-Out-Able.
23 Episodes
How can we help students feel comfortable with the commutative property? In this episode Pam and Kim go through some addition and multiplication problems to demonstrate how they think and reason using the the commutative property. 
Kim relates a great math experience she had with her son Luke. Luke found a way to mess around with place value in addition that Pam went most of her life not knowing! Listen in as Pam and Kim discuss the importance of learning to manipulate place value as students develop into mathematicians.Talking Points:Introducing the swapping strategyWhat problems fit nicely with the swapping strategy?Place labeling vs. Place valueSend us (@pwharris) your slick swapping strategy solutions to gnarly looking problems! Transcript:
Pam and Kim are back at it with percents. They discuss the 3 types of percent problems and how they solve them using relations, not with algorithms.  Are percents truly figure-out-able? You bet! Grab a pen and paper for this one as we solve some percent problems!Talking PointsThe three types of percent problemsThe disadvantages of teaching procedural methods to answer percent problemsMath is fun when it's figure-out-able!
Pam and Kim are back at it showing that percents too are figure-out-able. In this episode they solve some percentage problems and share their strategies. Listen in as they go through a percentage problem string!
Pam and Kim explore what it means to be flexible with fractions, decimals, and percents. They discuss how we can become more flexible as we deal with rational numbers, and how we can be judicious problem solvers. Talking PointsWhy kids of today are more familiar with percentagesWhy flexibility mattersHow to become more flexible using different representations of rational numbers
Ep 18: This, not that

Ep 18: This, not that


You might want your magnifying glass for this one, cause this episode we're getting a little nitpicky. Pam and Kim discuss common nomenclature/math-slang that can take the reasoning out of mathematics. They offer useful alternatives and illustrate the importance of clear mathematical languageTalking Points:How to add Butt-CheeksWhy students try 'canceling' everythingWhy reducing 6/8ths to 3/4s might give me more pie...?How one got over x.
Math is figure-out-able, but surely there are some parts that are only memorizable, right? In this episode Pam and Kim parse out the difference between social knowledge and logical knowledge. They'll analyze how knowing the difference can affect the types of questions you ask and the role of wait time in teaching.Talking Points:What is the difference between social and logical knowledge?What are examples of social knowledge in lower and higher math?How should we teach social knowledge?How should we teach logical knowledge?
This week's episode is for all you parents and teachers of young children. Pam and Kim discuss ways to make counting figure-out-able! How can we help kids make sense of our number system and master the meaning behind the words we give to numbers? No matter what grade you teach, you're sure to learn something this episode.Talking Points:How different languages name numbersHow to support young learners to make sense of teens and multi-digit numbersGive kids multiple representations of single-digits numbers.Pam being creepy at grocery storesFind the transcript here:
Have you ever tried teaching your students the steps to approaching word problems, but your students still struggled? Pam and Kim discuss a better way to help kids tackle math problems. They explain why if you want the best for your students, the acronyms and problem annotation methods of the past simply won't cut it. Help your students live the problem solving process, and not just memorize it. Talking PointsThe dangers of teaching "Problem Solving Methods"How to engage students in mathematics so that problem solving is a natural outcomeHow to run students through numberless word problemsResources: Brain Bushart's Numberless Word Problems
Pam and Kim have some fun this episode as they read out a submission from Aaron Houston about his mathy dad. They talk about the kinds of things parents can do with their kids to have fun mathematizing! Talking PointsI Have, You NeedKids Menus vs Adult Menusthe Guess my Number gameHow do you think about finding Prime Numbers?Math can be fun!
There are so many aspects to teaching, and it gets more complex when we want to discuss teaching math. Pam and Kim define the 5 layers for mathematics teaching. What do math teachers, who want to help their students mathematize, need to focus on? Talking PointsBuilding your own mathKnow the major strategies and models for your contentModeling Student ThinkingTeacher MovesSequencing TasksResources: Journey
As Pam and Kim wrap up their series on how to start the school year right, they encourage staying true to your beliefs as a math teacher. When making decisions in your classroom, there is power in consistency. They discuss how they approach analyzing and implementing other's ideas into their teaching practice, without giving up on their integrity.Talking Points:One meaning for having integrity in your teachingHow intentional use of worksheets & resources can illustrate your teaching beliefsDetermine your system of beliefs Transcript HERE
Join Pam and Kim in part two of their Top 3 Things to Start the Year series. This week its all about building a classroom culture where students and students' thinking are valued. They'll talk about how to implement tasks remotely that build a community of learners. Pam also throws out some great advice for facilitating lessons and tasks remotely. You won't want to miss it!Talking PointsBuilding classroom culture is so important in remote settingsWhen classmates respect each other's thinking, more students are enabled to think like mathematicians. Designing interactive remote learningHow to facilitate Problem Strings remotelyHow to facilitate Rich Tasks remotelyResourcesHow Pam uses her iPad to facilitate Problem Strings remotely:
As the world prepares for one of the most interesting beginnings to the school year, Pam and Kim are here to help us get it right. They start off this 3 part series by dialing in on the importance of using students names. Find the transcripts HERE.Talking Points:A maternal mathy personHow Pam learns student namesUseful tools and tips for using student names in a remote settingHow to help students use each others namesResources: Name Tents from Sarah Van Der Werf:
Strategies and Models

Strategies and Models


What is the difference between a strategy and a model? Listen as Pam and Kim give clear examples from both elementary and high school content to demonstrate the importance of developing strategy and communicate strategy through models. They provide clear, easy to follow insights so everyone can understand the purpose of models in constructing and communicating strategy.Talking PointsShout-out to Clay! Clay uses powerful additive reasoning when he uses his understanding of place value to add large numbers. Let us know about someone mathy in your life!New Problem String videos!What is a strategy? What is a model?Which is more important, models or strategies?Why are models so important in classrooms?Can anyone "do" a number line?ResourcesStrategies vs Models ArticleStrategy vs Models Card SortsTranscript
After last weeks discussion on partners of 10, 100, and 100, Pam and Kim thought of three more habits "mathy people" have in common. Listen in as they discuss:1. What it means for mathematicians to "Notice and Wonder"2. Double and halving3. Creating habits of thinking (as opposed to grabbing for a calculator)Tune in to next week's episode to hear all about Pam's method of categorizing levels of mathematical thinking, what she calls "The Development of Mathematical Reasoning".Find this episode's transcript HERETalking PointsThe prime numbers in your neighborhoodThe Wonder GameMath-Strat-ChatOur first shout-out
In this episode Pam and Kim share one of their favorite instructional routines: I Have, You Need. They discuss some of the most common patterns that mathmaticians play with, partners of 10, 100, and 1000. These "partners of ___ " patterns pop up everywhere! You'll never guess where they pop up daily for Pam (hint: its when she's the most worked up). Try out I Have, You Need with your friends, colleagues, and students! A quick way to build anyone's reasoning abilities and to help us all become better mathematicians.Download the guide to playing I Have, You Need HEREFind the transcript for this episode HERETalking Points:  We can all be "mathy people"What Kim thinks when she hears the number 36The routine that made the biggest impact on Pam's college studentsTaking ownership of your students' progressionI Have, You Need resolves the subtracting across zero horrorHow I Have, You Need applies to middle and high school students
Many people feel that reasoning and numeracy come to an end in highschool. How could we mathematize algebraic concepts? What does it mean, and what does it look like to have functional reasoning? Listen as Pam explains how functional reasoning builds off of proportional reasoning and empowers students to analyze and understand patterns of related value sets. Sounds complicated? Don't worry, Kim does her best to keep Pam on track and grounded. Talking PointsHow functional reasoning builds on proportional reasoningIt's not about being able to visualize the graph, it's understanding the relationship between the variablesHow to tell if someone is using functional reasoning
This episode is so important! Pam and Kim describe the Development of Mathematical Reasoning, and how it transforms our understanding of what it means to learn and teach mathematics. They discuss how freeing it feels to know that everyone can develop their reasoning, and how the Development of Mathematical Reasoning empowers teachers to know how best to help their students. To help you determine where you and your students are in the Development of Mathematical Reasoning, here's a free download! Use the How Do You Reason guide to know how you, your friends, and students are reasoning. They also announce the new Development of Mathematical Reasoning Workshop! A new free online workshop. So exciting! Be sure to tell all your colleagues about this amazing opportunity to learn how to help anyone develop reasoning. Talking PointsWhat the Development of Mathematical Reasoning looks likeWe don't need calculators, we need reasonersOne way people get stuck in counting strategiesThe freeing power of progressing in reasoningNew free online workshop!Read the transcript here:
Top Ten Influencers

Top Ten Influencers


Who's shaping math education today? Does Pam come up with it all herself? Far from it! In her fourth episode Pam wanted to pay homage to her top 10 influencers as well as share with you all some of her favorite resources for teaching real math. Join her and Kim as they share stories ranging from the excitement of the first graphing calculators to the embarrassment of mispronouncing their hero's name. It's sure to be a good time. Talking PointsWho were Pam's early influencers?How teacher moves transform Rich TasksWho is shaping math education today?Fos-dos and Fos-notsDesmos' card sorts and polygraphs: excellent tools for remote teaching.
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