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 FigureOutAble. See www.MathisFigureOutAble.com for more great resources!
Ep 120: Rounding
What fun rhymes will best help your students learn to round? Just kidding! In this episode Pam and Kim describe their wholistic approach to rounding that helps kids build relationships like place value!Talking PointsNo rhymes neededUsing a number line to reason through roundingHow rounding develops students' place value and other mathematical concepts.

18:48  10/04/2022  
Ep 119: Elapsed Time on a Number Line
Finding elapsed time can be a tricky concept, but when combined with a number line, we can make it figureoutable! Join Pam and Kim as they discuss using addition strategies to find elapsed time.Talking Points:The birth place of I Have, You NeedHow students might approach elapsed timeHow to help students think about elapsed time more sophisticatedly

19:15  09/27/2022  
Ep 118: Time and Elapsed Time
Do your students struggle tracking time or reading an analog clock? In this episode Pam and Kim discuss three simple ways you can help your students internalize time and elapsed time.Talking Points:Help students build a feel for benchmark units of timeNotice and tell what time it is a lot with kidsNotice aloud how long things take throughout the day

17:58  09/20/2022  
Ep 117: Math is Figureoutable, Even In High School
A lot of people feel like when it comes to high school math, it's just not possible to think and reason through things anymore. Not true! In this episode Pam and Kim make the transition from Proportional Reasoning to Functional Reasoning and writing the equation of a line using relationships and what students already know.Talking Points:Is math always FigureOutAble?How ratio tables prepare students for linear functionsExample Problem StringsRegistration for workshops closes this Friday!Get a workshop while you can: https://www.mathisfigureoutable.com/workshops

19:36  09/13/2022  
Ep 116: Structuring Your Math Class Examples
What does teaching Real Math look like at your grade level? In the last episode Pam and Kim discussed the One Third/Two Thirds rule to structure math time. In this episode they give specific examples at various grade levels of what it might really look like.Talking Points:1st Grade  doubling and halving3rd Grade  concepts around 1005th Grade  multiplication and volume7th Grade  rates (see Episode 112 for Unit Rate Problem String)Algebra I  exponential functionsPreCalculus  functionsOur workshops are open for registration! Take advantage now to change your math classroom! https://www.mathisfigureoutable.com/workshops

35:13  09/06/2022  
Ep 115: Structuring Your Math Class
A listener asked how would we structure our math class. In this episode Pam and Kim discuss the approach they'd take to provide their students with the best math education experience possible to learn Real Math and still meet their required standards and scope and sequence.Talking Points:The TwoThird/OneThirds ruleRich Tasks  see Episodes 102 and 103Test Prep?!Use instructional routines for spiral reviewTune in to the next episode for examplesRegistration for our workshops are open now! Sessions for everyone, K12! Check them out!https://www.mathisfigureoutable.com/workshops

18:32  08/30/2022  
Ep 114: Moving Students Forward Pt 2
The school year is starting! For this exciting time, Pam and Kim want to discuss what starting strategies can help you and your students to build thinking relationships and strategies rather than simply answer getting.Talking Points:Problem Talks are great ways to preassess your studentsPartial strategies are a great starting place but we have to help students develop more sophisticated strategiesThe starting strategies for each major operationStudents need lots of experience developing relationships through Problem Strings and Rich Tasks for strategies to be natural outcomesCheck out our free eBook to learn more about these strategies: https://www.mathisfigureoutable.com/bigAnd don't miss out on the You Can Change Math Class Challenge! https://www.mathisfigureoutable.com/changeCheck out Episodes 10 and 12 of this podcast for more ideas about starting your school year.

25:35  08/23/2022  
Ep 113: Moving Students Forward Pt 1
How can you make changes in your math classroom to help your students do more Real Math? In this episode Pam and Kim describe some first steps, and bigger steps, you can take to transform your math class. Talking Points: Creating a safe mathematical community conducive for Real Math to happen Wait time  "Do you want time or help?"Where are you on the continuum to make some or lots of changes?Tips on where to start wherever you are on the continuum Using Problem Strings, I Have, You Need, MathStratChat and other instructional routines and gamesWhat you celebrate, answers or thinking, is what students will shareHow to transform your curriculum if you're super gungho Don't miss out on the You Can Change Math Class Challenge! Register today at https://www.mathisfigureoutable.com/changeLearn more about I Have, You Need by listening to episode 7, or visit us at https://www.mathisfigureoutable.com/blog/ihaveyouneed

22:00  08/16/2022  
Ep 112: The Double Open Number Line Model
We sure loved discussing the open number line model last week, but have you ever heard of the double open number line? In this episode Pam and Kim discuss how the double open number line can be used to develop Proportional Reasoning and to think and reason about rates.Talking Points:A Problem String to reason about unit rates and model on a double open number lineWhen could an double open number line be helpful in middle school and high school?When is a ratio table more versatile than a double open number line?What other concepts can a double open number line be helpful for students?The percent bar is a double open number line?Check out our free download on Double Number Lines: https://mathisfigureoutable.com/double

30:04  08/09/2022  
Ep 111: The Open Number Line Model
The open number line is not just a powerful tool for computation, but it's an amazing model for developing all sorts of mathematical concepts! In this episode Pam and Kim discuss how to help students develop the open number line in a natural and meaningful way.Talking Points:What is an open number line vs a closed number line?Are number lines, closed or open, discrete models and why does it matter?Why shift to a measurement model vs a discrete model?What are some common errors students make when we use the traditional way of teaching measurement?We suggest a rich task by Cathy Fosnot to help students develop an understanding of the open number line through measurementWhat can you model on an open number line? Elapsed time, addition and subtraction of whole numbers and integers and moreIs an open number line helpful for higher math concepts?Check out Cathy Fosnot's amazing rich task: https://www.heinemann.com/products/e01010.aspx

24:38  08/02/2022  
Ep 110: Thinking Through Decimal Multiplication
Multiplying decimals can be fun! In this episode Pam and Kim tackle several gnarly problems like 0.77 x 2.4, and have a blast doing it. Talking Points: Building reasoning allows students to be flexible and have fun with decimal multiplication Kim uses percent and money to solve 0.77 x 2.4 with confidence (no need for a calculator) Pam represents her thinking on a ratio table for 0.77 x 2.4 Different strategies for 0.77 x 0.24? What about 7.7 x 0.24? Why is thinking and reasoning so important?

14:45  07/26/2022  
Ep 109: Multiplying By One Tenth
Being able to scale comfortably is important for both whole and decimal numbers. And just as there are more sophisticated ways to handle scaling with whole numbers, we can also be more sophisticated scaling decimals! In this episode Pam and Kim describe how we can help students become comfortable with decimal multiplication using their understanding of whole number multiplication and then scaling.Talking Points:Reflecting on the more sophisticated strategy from Ep 106Applying knowledge of whole number multiplication to decimalsIt's more about reasoning than shifting the decimalReasoning in small steps builds understanding vs. just counting the decimalsReasonableness comes from keeping kids in reasoning landLanguage to focus on and language to avoid

16:48  07/19/2022  
Ep 108: Beginning Decimal Multiplication
How can we help students make sense of decimal multiplication? In this episode Pam and Kim run through two beginning Problem Strings that will get students feeling comfortable and understanding the world of multiplying decimals.Talking Points:Which models are helpful Decimals and moneyStudents need to develop a few starting relationships before becoming more sophisticatedSmart Partial Products with decimals

23:27  07/12/2022  
Ep 107: All About Decimals
We've gotten a ton of questions about decimals. In this episode Pam and Kim discuss three different models and why they are great for questioning and building relationships, but may or may not be good for computation.Talking Points:Base Ten Materials Exploding Dots by James TantonMoney

18:11  07/05/2022  
Ep 106: Multiplying by Ten
Most students can scale up by ten as they begin to multiply larger numbers and that is a great starting place for students. In this episode Pam and Kim discuss a more sophisticated way of scaling numbers in multiplication problems. Talking Points:How beginning learners will use multiplying by 10 in double digit multiplication problems.How more sophisticated students deal with smaller numbers then scale up.How this applies to middle school students.How can Five is Half of 10 be used with more sophisticated thinking?

17:45  06/28/2022  
Ep 105: Let the Students Play
Often people misunderstand what this game we call mathematics is and feel they aren't good enough to play. In this episode Pam and Kim discuss how students need the opportunity to experience and play in the real game of mathematics.Talking Points:Mathematizing is not about speedPam, the basketball playerIt's not about memorizing disconnected rules and procedures.Kim, the teacher pleaser Experience and opportunities are important so kids have choicesWe need all students in the game of mathIs there such a thing as a "math gene" or natural talent?All students have different talents to bring to the tableTake the Math Perspective Quiz to find more about your perspective of math class and instruction.All students have talents to bring to the table

22:21  06/21/2022  
Ep 104: Things We Have Learned
It's our two year anniversary! We are so grateful you've spent this time with us. In this episode Pam and Kim discuss openly things they've learned and how they've grown during their journey as math teacher educators.Talking Points:It's not 'Pam Math', it's Real Math and developing mathematicians!Coaching teachers is about mentoring, not just tellingThe importance of a common vocabulary  Check out Episodes 58 and 101Empowering teachers and leaders through Journey and Journey LeaderDeep dive online workshops for Kindergarten through middle schoolBuilding Powerful Linear Functions for high school coming soon!

24:32  06/14/2022  
Ep 103: Rich Tasks, Investigations, 3Act Tasks, Pt 2
What are some examples of rich tasks that are designed to intrigue and engage students? In this episode Pam and Kim give some specific examples and describe why they are so rich.Talking Points:Relatable to students not just real worldAn eye towards equityLead to the mathematicsPacked with patternsNatural extensionsMake the math realizableBuilding Powerful Linear Functions coming Fall 2022See Ep 47: Fractions as Fair Sharing where we explored the Sub Sandwich rich task!

21:33  06/07/2022  
Ep 102: Rich Tasks, Investigations, 3Act Tasks, Pt 1
Let's talk rich tasks! On Twitter we enjoyed a great conversation about what makes a rich task rich. We thought we'd comment on some great suggestions from Professor Tad Watanabe, inspired from his mentor Dr. Grayson Weatley.Talking Points:Invite students to make decisionsReplete with patternsPromote discussion and communicationTasks should lead somewhereBe extendableHave an Element of SurpriseAnd More!

17:15  05/31/2022  
Ep 101: Strategies!
What comes to mind when someone says the word "strategy"? There are at least four different meanings for the word "strategy" in mathematics teaching. In this episode Pam and Kim parse out the different meanings and discuss how those meanings shape the outcomes of our teaching.Talking Points:Numeracy StrategiesProblem Solving StrategiesTeaching StrategiesStrategies for TeachingWhy without one type of strategy, the other strategies will fall flat

12:51  05/24/2022  
Ep 100: Celebrating Place Value
We love that we've been able to make 100 episodes! We also love that 1 hundred is 10 tens, so let's talk place value! In this episode Pam and Kim discuss why students struggle with place value, and suggest some of their favorite place value activities.Talking Points:Why 'place labeling' is ok, but not enoughCount AroundsMultiple TowersBase 10 materialsUsing correct place value language

29:54  05/17/2022  
Ep 99: If Not Algorithms, Then What? Finale!
In the last 5 episodes we've laid out the most important strategies for students to be able to solve for all four operations. So what? In this episode Pam and Kim solve a gnarly problem to demonstrate how mathematizing can empower you and your students, and open up to the world of Real Math.Talking Points:How to use the BIG downloadable ebookA gnarly problem solved using Real MathIt's all about efficiency and developing more sophisticated reasoningPartial strategies are a great starting point but not the ending placeKudos to Pam's research and thoughtfulnessWhy does Pam seem to focus on computation?What believers are sayingOther ways to learn with PamWe can make higher math more accessibleBONUS: Kim's failed attempt at the standard algorithmGet the BIG download here! https://mathisfigureoutable.com/big

29:19  05/10/2022  
Ep 98: If Not the Division Algorithm, Then What?
Division is figureoutable! In this episode Pam and Kim discuss the four main strategies students need to develop to solve any division problem that's reasonable to solve without a calculator. Talking Points:Pam's personal harmful experience from the long division algorithmA precursor strategy: Partial QuotientsSmart Partial QuotientsOverUnder5 is Half of 10Equivalent RatiosCombining strategiesGet the BIG download of all the major strategies for addition, subtraction, multiplication, and division here! https://mathisfigureoutable.com/big

29:33  05/03/2022  
Ep 97: If Not the Multiplication Algorithm, Then What?
What are the five major strategies for multiplication? In this episode Pam and Kim name and give examples of each of the five major multiplication strategies. If students own these strategies they should be able to solve any multiplication problem that is reasonable to solve without a calculator. They will be able to solve it as efficiently as a traditional algorithm and most of the time more efficiently than the traditional algorithm. But even more important than that, they will be developing Multiplicative Reasoning! Talking Points:Smart Partial ProductsOver/Under5 is Half of 10How are these strategies related to the distributive property?Doubling/HalvingHow is this strategy related to the associative property?Using Quarters & Scaling Bonus! Flexible FactoringGet a download of all the major strategies here: www.mathisfigureoutable.com/big

25:10  04/26/2022  
Ep 96: If Not the Subtraction Algorithm, Then What?
It's time for subtraction! In this episode Pam and Kim name and give examples of the four main subtraction strategies students need to own to solve any subtraction problem that is reasonable to solve without a calculator.Talking Points:Remove a Friendly NumberRemove a Friendly Number  OverRemove to a Friendly NumberConstant DifferenceHow do students choose which one to use?Get the download! www.mathisfigureoutable.com/big

18:27  04/19/2022  
Ep 95: If Not the Addition Algorithm, Then What?
What are the major strategies students need to know to solve any addition problem that is reasonable to solve without a calculator? In this episode Pam and Kim list them out, give examples, and some insights into how they choose which strategy to use for any given problem. Talking Points: Splitting by Place Value (a precursor strategy)Add a Friendly Number Add a Friendly Number  Over Get to a Friendly Number Give and Take When do you use each strategy?Get our download of all the major strategies here! mathisfigureoutable.com/big

23:09  04/12/2022  
Ep 94: If Not Algorithms, Then What?
We want students to be real problem solvers, and we know that means much more than helping them get correct answers. But we never want to put students in a position where they are disadvantaged because they don't know the traditional algorithms. We actually want them to have a much deeper and richer understanding of mathematical relationships. In this episode Pam and Kim begin a series exploring the major strategies for each operation that students need so that they can solve ANY problem that's reasonable to solve without a calculator. Talking Points:Pam's journey from learning only step by step procedures to mathematizingHow this series can take Pam's published books a step furtherHow Kim, and many other mathematicians approach problemsOwnership of the major relationships empowers students with choiceHonor students thinking, but don't leave students where they areGet the download!: mathisfigureoutable.com/big

19:49  04/05/2022  
Ep 93: Partnering With Parents: Do Correct Answers Matter?
When we feel passionately about the way we teach, we can sometimes inadvertently miscommunicate when speaking with parents. In this episode, Pam and Kim discuss how to appropriately talk about getting correct answers and preparing for high stakes tests so that parents know their children are in good hands.Talking Points:Answers are important!What we don't want to communicate to parentsPreparing students for high stakes tests is important!Insight into a test writer's thinking when they write test itemsHelping students mathematize will help them feel more confident and excel on high stakes tests

19:47  03/28/2022  
Ep 92: Partnering With Parents: Math Night!
Partnering with parents can be a blast! In this episode Pam and Kim describe how they organize and run math nights to help parents experience mathematizing and get excited about what their students will be learning.Talking Points:Typical parent math nights vs. our parent math nightsOpportunity to share grade level or school wide expectationsImportance of a Q & A for parentsHelp parents experience math the way their students doMathematizing for parents at the "sweet spot" level of mathSuggestions for finding Problem Strings to use at math nightsLogistics tips for parent math nightAdvantages of a series of parent nights

19:07  03/22/2022  
Ep 91: Partnering With Parents: Over Communicate
How can we proactively partner with and support parents? In this episode Pam and Kim discuss ways they over communicate to parents to keep parents involved and not confused. Talking Points: Newsletters: What is helpful information and tips for parents I can share?Parentteacher conferences: What can I share with parents about math other than just grades?Homework assignments: I don't like drill and kill. What kinds of homework are helpful for students and parents?

20:01  03/15/2022 