Math is Figure-Out-Able with Pam Harris
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.
Available episodes
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1 day ago
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 Strategies
* Problem Solving Strategies
* Teaching Strategies
* Strategies for Teaching
* Why without one type of strategy, the other strategies will fall flat
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May 17, 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 enough
* Count Arounds
* Multiple Towers
* Base 10 materials
* Using correct place value language
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May 10, 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 e-book
* A gnarly problem solved using Real Math
* It's all about efficiency and developing more sophisticated reasoning
* Partial strategies are a great starting point but not the ending place
* Kudos to Pam's research and thoughtfulness
* Why does Pam seem to focus on computation?
* What believers are saying
* Other ways to learn with Pam
* We can make higher math more accessible
* BONUS: Kim's failed attempt at the standard algorithm
Get the BIG download here! https://mathisfigureoutable.com/big
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May 3, 2022
Ep 98: If Not the Division Algorithm, Then What?
Division is figure-out-able! 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 algorithm
* A precursor strategy: Partial Quotients
* Smart Partial Quotients
* Over-Under
* 5 is Half of 10
* Equivalent Ratios
* Combining strategies
Get the BIG download of all the major strategies for addition, subtraction, multiplication, and division here! https://mathisfigureoutable.com/big
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Apr 26, 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 Products
* Over/Under
* 5 is Half of 10
* How are these strategies related to the distributive property?
* Doubling/Halving
* How is this strategy related to the associative property?
* Using Quarters & Scaling
* Bonus! Flexible Factoring
Get a download of all the major strategies here: www.mathisfigureoutable.com/big
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Apr 19, 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 Number
* Remove a Friendly Number - Over
* Remove to a Friendly Number
* Constant Difference
* How do students choose which one to use?
Get the download! www.mathisfigureoutable.com/big
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Apr 12, 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
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Apr 5, 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 mathematizing
* How this series can take Pam's published books a step further
* How Kim, and many other mathematicians approach problems
* Ownership of the major relationships empowers students with choice
* Honor students thinking, but don't leave students where they are
Get the download!: mathisfigureoutable.com/big
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Mar 28, 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 parents
* Preparing students for high stakes tests is important!
* Insight into a test writer's thinking when they write test items
* Helping students mathematize will help them feel more confident and excel on high stakes tests
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Mar 22, 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 nights
* Opportunity to share grade level or school wide expectations
* Importance of a Q & A for parents
* Help parents experience math the way their students do
* Mathematizing for parents at the "sweet spot" level of math
* Suggestions for finding Problem Strings to use at math nights
* Logistics tips for parent math night
* Advantages of a series of parent nights
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Mar 15, 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?
* Parent-teacher 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?
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Mar 8, 2022
Ep 90: Partnering With Parents-Listening
Parents are so important, and sometimes they get concerned when their child isn't being taught math they way they were expecting. In this episode Pam and Kim discuss hearing parents' concerns and helping them feel heard and then helping them understand the math. We appreciate parents and we are better with them!
Talking Points:
* We want invested parents
* Parents need to be heard, and then they need to understand
* The importance of listening to understand
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Mar 1, 2022
Ep 89: Playing With Fraction Multiplication
Kim has a story to tell that Pam hasn't heard yet! Listen in to get a feel of how math can be when students understand that Math is Figure-Out-Able.
Talking Points:
* Pajama Math and exploring relationships in multiplying fractions
* Can you really just multiply straight across with fractions?
* Two ways to reason about 3/5 times 3/9
* Pam and Kim reason multiple ways about 3/4 times 2/5
* Join us in #MathStratChat!
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Feb 22, 2022
Ep 88: Getting Correct Answers or Building Relationships?
Most of us are probably teaching the way we were taught, to get correct answers to problems. But we aren't actually helping students understand and reason about the math. Which is more important? In this episode Pam and Kim discuss answer getting versus relationship building.
Talking Points:
* Phil Daro's research on patterns of math instruction from across the world
* Student success from answer getting instruction vs instruction that focuses on outcomes from reasoning
* The real purpose of math class
* Now that I know different, how can I do different and help kids reason?
Resources:
Phil Daro video: https://vimeo.com/79916037
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Feb 15, 2022
Ep 87: But I'm Required to Teach Algorithms
Do your standards require you to teach algorithms? What then? In this episode Pam and Kim discuss how they prepare their students for success on high stakes tests without ever teaching a step by step algorithm or process.* *
Talking Points:
* All year long invest your time wisely helping kids learn to reason, increasing their sophistication of relationships and solving more difficult problems.
* Students can and will perform well on standardized tests if they have been thinking and reasoning, experiencing new situations all year.
* Students will approach a standardized test with confidence and less stress if they have been given opportunities to struggle productively all year and become good mathematicians.
* Introduce the algorithm as a study of why the algorithm works for the very end of the year. Introducing the algorithm too early in the year risks giving students the option to turn their brains off.
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Feb 8, 2022
Ep 86: Are Algorithms Necessary?
What purpose has and should algorithms have in mathematics education? Are step by step What purpose has and should algorithms have in mathematics education? Are step by step procedures even to be taught at all? In this episode Pam and Kim talk about our role as teachers and what students need to think like mathematicians.
Talking Points:
* One student's perspective
* What are algorithms?
* Why have we taught algorithms in the past?
* Where are algorithms helpful in today's world?
* Do algorithms help students learn to mathematize?
* From another student's perspective
* Learn more in the online workshops
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Feb 1, 2022
Ep 85: Single Digit Addition Facts Finale
Aren't addition facts cool?! By this point you've learned some amazing relationships and strategies to help your students make real sense of and automatize the single digit addition facts. But sometimes learning and applying are two different things. In this episode Pam and Kim detail how to help your students get out of counting mode and actually apply the relationships they've learned to become fluent with single digit addition facts.
Talking Points:
* Why do some kids keep counting after they've learned these relationships?
* How to help kids break the counting habit and why that is important
* It's not about speed or only the answers, it's about developing more sophisticated thinkers and reasoners
* Deep dive online workshops for teachers
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Jan 25, 2022
Ep 84: Single Addition Facts, Part 4
It's time for you to learn about the most important relationship your students need to know to automatize their addition facts: partners of ten. Partners of ten influence strategies for adding bigger numbers as well as strategies for other operations. In this episode Pam and Kim will discuss some of those influences and some games and routines specifically made to provide experience and build partner of ten relationships for all levels and all ages.
Talking Points:
* What are partners of ten?
* Do older students need partners of ten?
* Rich Tasks with 10
* Collect Ten
* I Have, You Need
* Establish partners of ten early in the school year
* Workshop registration is open until Feb 4!
Links:
bit.ly/partnersoftensgames
mathisfigureoutable.com/youneed
mathisfigureoutable.com/workshops
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Jan 18, 2022
Ep 83: Single Digit Addition Facts Pt 3
We build addition facts through relationships and fluency through experience. So what important patterns and relationships can help students master or reason with their single digit addition facts rather than rote memorize? How can we teach those patterns and what experiences can help students automatize and become more fluent with addition facts? In this episode Pam and Kim dig deeper into single addition facts and how we as teachers can can empower students to reason like mathematicians.
Talking Points:
* It's not about speed
* Doubles are important
* The Shoe Game
* The Doubles Game (Cathy Fosnot)
* Near doubles
* Ten-and or The teens
Check out the patterns we talked about here:
mathisfigureoutable.com/addrelationships
And don't miss registration for one our deep dive workshops! https://www.mathisfigureoutable.com/workshops
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Jan 11, 2022
Ep 82: Single Digit Addition Facts, Pt 2
Addition is figure-out-able! In this episode Pam and Kim describe some of the fundamental patterns students should learn as they get familiar and automatize with their single -addition facts. We want students at all levels to have access to their facts so they don't bog down every time they encounter them.
Talking Points
* Connecting the concrete and pictorial experiences to symbolic representation.
* Tips for using flash cards and addition table.
* Noticing patterns can reduce the number of addition facts a student needs to fuss with.
* The role the commutative property plays learning addition facts.
* When is counting ok.
* Learning to trust the commutative property.
* Students need experience, lots of it.
Register for the You Can Change Math Class Challenge here: https://www.mathisfigureoutable.com/change
You can also register for a deep dive workshop today! Go to https://www.mathisfigureoutable.com/workshops to learn more.
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Jan 4, 2022
Ep 81: Single Digit Addition Facts Pt 1
So many people get left behind when it comes to higher math, because they never learned mathematize or to think more sophisticatedly and build complex relationships and simultaneity in lower math. Teachers often share that their students lack numbers sense or fluency, specifically lack of memorized basic math facts. That's why in this episode Pam and Kim start a new series on single digit addition fact fluency. Are the facts important? You bet! But how they are taught is even more important to be accessible and equitable for all students.
Talking Points:
* This series is for all grade level teachers!
* Is speed or quick recall important?
* Our goal: rote memorization or number relationships?
Learn more at bit.ly/pharrisinfo.
Don't forget to just the You Can Change Math Class Challenge at https://www.mathisfigureoutable.com/change!
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Dec 28, 2021
Ep 80: Resolutions Anyone?
We've come to the end of another year, and we'd thought we'd leave you with some suggestions on goals you can set for your teaching. In this episode Pam and Kim highlight some transformative goals that you probably haven't considered before. How could your math class look next year or next semester?
Talking Points:
* Learners setting goals around mathematical behaviors or practice standards.
* Teacher goals centered around the NCTM mathematics teaching practices.
* Teacher goal to elicit and use evidence of student thinking.
* SMART goals.
* Hey Australia! We appreciate you!
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Dec 21, 2021
Ep 79: Talking Math With Your Kids For The Holidays
Don't you love the holidays? We sure do! It's such a great excuse to talk math with your family! In this episode Pam and Kim describe some ways (and activities they do) to involve math in their festivities, from formal games like I Have, You Need, Guess My Number, MathStratChat, to simply noticing and wondering.
Talking Points:
* Cooking and Baking
* Spending Holiday Money
* Dinner Games
* Daily Tasks
* Walks
* Car Games
* Notice and Wonder
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Dec 14, 2021
Ep 78: Gift Giving Ideas - Mathy Games for All Ages
As we approach Christmas and the holidays, we thought we'd talk about some of our favorite games that we love to gift others! In this episode Pam and Kim share what makes a great mathy game and list a few of their favorites that not only have numbers, but include some with strategy and logic. Also, don't forget to check out some of our Math is Figure-Out-Able merch for your own gift list!
Favorite Games:
* Splendor
* Multi (by joyfulmathematics.com)
* Prime Climb (by mathforlove.com)
* Tiny Polka Dot (by mathforlove.com)
* Qwixx
* Set
* Proof
* Mastermind
* Sequence
* Rack-O
* High Ho Cherry-O
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Dec 7, 2021
Ep 77: The 'Relational Thinking' Instructional Routine
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, Doubling and Halving, Equivalent Ratio
Resources:
* Find examples of Relational Thinking problems here: https://www.mathisfigureoutable.com/relational-thinking
* Find our Developing Mathematical Reasoning info graphics here: https://www.mathisfigureoutable.com/blog/development-4
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Nov 30, 2021
Ep 76: The 'As Close As It Gets' Instructional Routine
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 classroom
Learn more about this powerful routine here: https://www.mathisfigureoutable.com/instructionalroutines
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Nov 23, 2021
Ep 75: Stop Labeling Students
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 on providing experience rather than natural talent or ability.
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Nov 16, 2021
Ep 74: Know Your Content, Know Your Kids
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 standard's landscape?
* How knowing our students can help target their individual zone of proximal development.
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Nov 9, 2021
Ep 73: Some Favorite Numbers - Milestones for Math is Figure-Out-Able
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?
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Nov 2, 2021
Ep 72: The Do's and Don'ts of Problem Strings
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's strategy?
* How do I write Problem Strings?
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Oct 26, 2021
Ep 71: What are Problem Strings Anyways?
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
Find examples of Problem Strings (including video!) at https://www.mathisfigureoutable.com/ps
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Oct 19, 2021
Ep 70: Equations of Lines Pt 2
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 values.
* How the relationships between the x values and the y values help you think and reason about slope and y intercept.
* Algebra is Figure-Out-Able!!
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Oct 12, 2021
Ep 69: Equations of Lines Pt 1
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 notice to find the equation of a line without formulas
* Intuitively finding the equation of a line in standard form
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Oct 5, 2021
Ep 68: Revisiting the Development of Mathematical Reasoning Pt 2
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 solving addition problems with bigger numbers using Additive Reasoning.
* Examples of solving multiplication problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.
* Examples of solving division problems with Counting Strategies, Additive Reasoning and Multiplicative Reasoning.
* Brand new free infographics of the Development of Mathematical Reasoning.
* Videos of students solving problems using the different types of reasoning to help you use the DMR in your…
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Sep 28, 2021
Ep 67: Revisiting the Development of Mathematical Reasoning
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 level of reasoning behind
* Examples of Counting, Additive and Multiplicative Reasoning
* How can you build your own mathematical reasoning?
* Free DMR workshop for anyone at anytime!
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Sep 21, 2021
Ep 66: Shout Out to Leaders of the Mathematics Education Community!
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 find at MathisFigureOutAble.com
JourneyLEADER (learn more at https://www.mathisfigureoutable.com/leader)
Other people to follow: @JBayWilliams, @JohnSanGiovanni,
@ddmeyer, @joboaler, @ekazemi, @ctfosnot, @thestrokeofluck, @saravdwerf
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Sep 14, 2021
Ep 65: Collaborative Coaching through Shared Experiences
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 classroom.
* How to create shared experiences.
* Introducing JourneyLEADER
You can learn more about our exciting new experience for leaders at mathisfigureoutable.com/leader
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Sep 7, 2021
Ep 64: Fun with Division: An Important Strategy
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 quotatively to solve gnarly division problems with whole numbers, fractions, decimals and even polynomials.
Learn more about the Building Powerful Division workshop
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Aug 31, 2021
Ep 63: Counting is More Than A, B, C
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.
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Aug 24, 2021
Ep 62: Models That Aren't Our Fav
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?
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Aug 17, 2021
Ep 61: Ten Frames
Continuing their series on modeling, Pam and Kim discuss the advantages and pitfalls of Ten Frames. They emphasize the power of models that can become tools for reasoning, and use Ten Frames as an example of how teachers can focus too much on models that may eventually get it in the way of 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 preferred model for transitioning from counting to additive reasoning
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Aug 10, 2021
Ep 60: Number Bonds and Tape Diagrams
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 confusion
* Example of using Number Bonds and Tape Diagrams vs an Open Number Line
* Models that can be tools for thinking for addition, subtraction, multiplication, and division
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Aug 3, 2021
Ep 59: Why Not Manipulatives?
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 bad?
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Jul 27, 2021
Ep 58: Introducing the Modeling Framework
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 example with sticks of gum and a ratio table
* How students learn to verbalize and model their own thinking
* How this framework differs from CRA
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Jul 20, 2021
Ep 57: For Parents: How Can I Help My Kid?
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 math education
See Episodes 34-38 to learn more about best teaching practices for multiplication facts.
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Jul 13, 2021
Ep 56: For Parents: Why Does "New Math" Look Different?
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 students' thinking and reasoning on paper can look messy
* As we understand the possibilities with Real Math, we can encourage and refine teaching so more students are more successful
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Jul 6, 2021
Ep 55: For Parents: Why All the "New Math"?
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?
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Jun 29, 2021
Ep 54: Q&A Part 2, Data Analytics and Advice for First Year Teachers
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 good teacher partners and getting outside of your own classroom
* The importance of good student-teacher relationships
* Starting off the year by setting clear expectations to set the year up for success
* Figure out how you fit as an adult with all students
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Jun 22, 2021
Ep 53: Q&A Part 1, Do Strategies Change Over Time?
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 Doesn't Belong (https://wodb.ca)
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Jun 15, 2021
Ep 52: One Year Anniversary Highlight Reel
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
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Jun 8, 2021
Ep 51: Fractions, a Clock Model Pt 2
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
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Jun 1, 2021
Ep 50: Fractions, 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 equivalence
* Using the word "over" for fractions is NOT helpful
* Equivalent fraction examples on a clock model
* A real student's math journey
Jordan Using the Clock Model
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May 25, 2021
Ep 49: Fractions, A Money Model Pt 2
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 9/20
* The reciprocal relationships between fractions and coins can be confusing
* Fractional equivalence is the goal by asking students to add and subtract fractions
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May 18, 2021
Ep 48: Fractions, A Money Model
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 bonus, fraction operations as well:
* Using decimals and fraction notation interchangeably
* Kim's uncomfortable relationship with nickels
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May 11, 2021
Ep 47: Fractions as Fair Sharing
Let's keep talking fractions! In this episode Pam and Kim discuss an interesting rich task from Cathy Fosnot to help students reason about fractions within the context of sharing fairly. Listen in to learn about the outcomes teachers should look for when teaching fractional sense in a rich contextual problem.
Talking Points:
* Splitting the wholes into unit fractions
* Splitting the leftovers into smaller unit fractions and re-unitizing
* Patterns when comparing same-denominator fractions vs same-numerator fractions
Additional Sources: Field Trips and Fund-Raisers
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May 4, 2021
Ep 46: Fractions for Young Learners
How young can young learners begin to experience fractions? Younger than you think! In this episode Pam and Kim describe simple ways we can help young students begin to develop fractional understanding. Pay attention to how natural it can be for young learners to learn math!
Talking Points
* Struggles that young learners may experience with "half"
* Simple classroom activities to have students fair shares in early grades as they practice counting
* Experiences and conversations in halving even and odd amounts
* Standards and fractions of an object vs fraction of a set
* Important unit fractions and resources
* Doubling and halving simultaneously
* Simple experiences parents can use to help their kids develop fractional understanding
Additional sources:
* Beads, Shoes and Making Twos
* Games for Early Number Sense
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Apr 27, 2021
Ep 45: 5 Interpretations of Rational Numbers
Time to get into fractions! There is so much to learn about teaching fractions and in this episode we wanted to lay some important ground work. All too often we limit students by giving them experience with only one or two of the important ways fractions can be interpreted. When we help students fully understand fractions by using all of the interpretations, their ability to think proportionally skyrockets!
Talking Points
* What is a rational number?
* The 5 Interpretations of Rational Numbers (Credit to Susan Lamon)
* Solving fractions with reasoning!
* Shifting between the 5 interpretations as we solve
* Applying all 5 interpretations to one problem
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Apr 20, 2021
Ep 44: Is it About Personality?
Though some people think Kim and Pam's voices are hard to tell apart, teaching Real Math has nothing to do with a particular style or even personality type. We believe in seeing the humanity in students and empowering them with mathematical confidence!
Talking Points:
* Pam and Kim's results on the Enneagram Test.
* 2 important things -
* Teaching Real Math is more about beliefs about students and mathematics than personality
* Leverage your beliefs to get support in teaching Real Math.
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Apr 13, 2021
Ep 43: Standardized Tests
If there's one thing that often comes up in teachers' conversations, it's standardized tests. And Pam and Kim are not afraid to tackle the tough conversations! In this episode Pam asks Kim about her experience with standardized tests, and how teaching Real Math helped Kim's students to succeed. Also don't forget to send in questions for our special 50th episode! We're so excited!
Talking Points:
* Can students succeed on tests if all they know is Real Math?
* Everyone, in every demographic, can learn more Real Math than fake math.
* How much time do students need to prepare for tests?
* Suggestions for test prep.
* How teachers view the test and their actions speak loudly
* It's all about "know your content, know your kids".
Learn about numberless word problems here: https://bstockus.wordpress.com/numberless-word-problems/
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Apr 6, 2021
Ep 42: Homework Pt 3
In this final episode in our series on homework, Pam and Kim discuss what types of homework teachers should send out, as well as some important pitfalls to avoid.
Talking Points:
Pen and paper homework
* Games as homework and things to consider
* Computer activities as homework and things to consider
* Communication is critical to honor family time when assigning homework
* Using homework as a teaching tool, not for the sake of work
* Be sure you are sending the right message about mathematics when looking at returned homework.
* How the goal of Real Math helps teachers make decisions about homework
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Mar 30, 2021
Ep 41: Homework Pt 2
It's part two of our series on homework! Last time we heard Kim's perspective on when and what kinds of homework to give. Now it's Pam's turn. As a teacher for both high school and university classes, Pam gives an insightful look into when homework is necessary, and how we can always allow the humanity of our students to have precedence.
Talking points:
* What does the research say about homework? How does it vary by grade level?
* What is the purpose of homework?
* How much homework should students have?
* What topics should homework cover?
* The role of students' humanity in grades and homework.
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Mar 23, 2021
Ep 40: Homework Pt 1
Welcome to our first off the cuff episode! Pam and Kim have no notes this time and are happy to tackle the topic of homework. Turns out, they have enough to say that this will be part one of a new series! Listen in as Kim makes a confession, and Pam rats out her kids.
Talking points:
* Some general thoughts about homework.
* When is a topic appropriate to send home for homework?
* Some suggestions for the kinds of homework we should send home
* Parent's role in homework and how can homework be helpful?
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Mar 16, 2021
Ep 39: Everybody Learns, Everybody Grows
In this episode Pam and Kim discuss the secret to helping every student succeed. It's one of their guiding principles, and they can't believe they're only just now sharing it!
Talking Points
* The problem with the traditional approach of teaching to mastery
* How to address the personal needs of students
* How to help all students grow
* What are open tasks?
* What if students aren't getting "it"?
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Mar 9, 2021
Ep 38: Multiplication Facts: The Good, the Bad, and the Ugly Pt 5
We made it to our final episode in our multiplication facts series! In this episode Pam and Kim share their secret to helping kids narrow in on facts they struggle with. This final episode exemplifies why we believe that through mathematizing students will naturally develop fact fluency.
Talking Points
* What it means to take the long view in multiplication facts
* The importance of really knowing your students
* Clue cards
* Final thoughts on fact fluency
Show links:
* Math-Flips
* Stick and Split
Find the transcript here: https://podcast.mathisfigureoutable.com/1062400/8040345-ep-38-multiplication-facts-the-good-the-bad-and-the-ugly-pt-5
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Mar 2, 2021
Ep 37: Multiplication Facts: The Good, the Bad, and the Ugly Pt 4
It's time for what you've all been waiting for. GAMES! Sure we don't want kids memorizing songs or rhymes to learn their facts, but in this episode Pam and Kim bring the fun into multiplication. What games are out there that can help students develop multiplicative reasoning? We're glad you asked :-)
Talking Points
* What makes a good math game?
* What makes a poor math game?
* What are the best games today to help students own multiplication facts?
Links
* Live Problem Strings on Facebook Live
* The Product Game (Link includes games for other grade levels as well!)
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Feb 23, 2021
Ep 36: Multiplication Facts: The Good, the Bad, and the Ugly Pt 3
Last episode Pam and Kim discussed how not to teach multiplication facts. So how should we teach them? This episode we look at multiplication facts through the lens of mathematizing!
Talking Points
* The order that we teach content matters
* The order we teach the facts matters
* The key relationships students need to own facts
* How parents can help their kids own their facts
Free Problem String Download: mathisfigureoutable.com/factsps
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Feb 16, 2021
Ep 35: Multiplication Facts: The Good, the Bad, and the Ugly Pt 2
What are some great techniques to teach multiplication facts? What are the pitfalls to avoid? In this episode Pam and Kim discuss ways teachers may inadvertently 1) overemphasize speed, 2) introduce shame into their classrooms, and 3) focus on learning facts in isolation. We've all made mistakes, and this episode is about learning and growing for our students.
Talking Points:
* The negative effects of timed multiplication fact tests
* How to avoid using shame as a motivator to learn facts (harder then you think!)
* Why learning facts as isolated ideas is dangerous
Find this episode's transcript here: https://podcast.mathisfigureoutable.com/1062400/7773085-ep-35-multiplication-facts-the-good-the-bad-and-the-ugly-pt-2
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Feb 9, 2021
Ep 34: Multiplication Facts: The Good, the Bad, and the Ugly Pt 1
In this episode Pam and Kim begin the first of another series: Multiplication Facts! What role can mathematizing and real math play in helping kids master their multiplication facts? Listen in as Pam and Kim outline the differences between 'knowing' and 'memorizing' multiplication facts.
Talking Points:
* Why multiplication facts are important
* The difference between knowing and memorizing facts
* How to get rid of all the stress around multiplication facts
* Is the goal to get through memorizing the facts, or to develop multiplicative reasoning?
We recommend brushing up on episodes 5 & 6 in preparation for this series. Understanding what it means to develop multiplicative reasoning is so important!
Find this episodes transcript here: https://podcast.mathisfigureoutable.com/1062400/7641379-ep-34-multiplication-facts-the-good-the-bad-and-the-ugly-pt-1
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Feb 2, 2021
Ep 33: Problem Strings vs Problem Talks
In the last two episodes, Pam and Kim did some really cool Problem Strings, but what do they think about Number Talks? Listen in as Pam explains how Number Talks and Problem Strings can go hand in hand for powerful results.
Talking Points:
* Why call 'Number Talks' 'Problem Talks'?
* Short term uses for Problem Talks
* The best use for Problem Talks
* The purpose of Problem Strings
* When to do Problem Talks
* When to do Problem Strings
Want to learn more about this powerful combination? Head to: mathisfigureoutable.com/stringsvtalks
Get this weeks transcript at: https://podcast.mathisfigureoutable.com/1062400/7498621-ep-33-problem-strings-vs-problem-talks
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Jan 26, 2021
Ep 32: Another Cool Multiplication Strategy
It's time for another Problem String! In this episode Pam and Kim develop one of their favorite multiplication strategies, it's so slick! In doing so they talk more about the importance of letting students discover and develop relationships, as opposed to teaching strategies step by step.
Talking Points
* What makes a good Problem String?
* How do we help kids learn the appropriate uses of alternative strategies?
* What to avoid when facilitating Problem Strings
* Tweet at us your favorite name for this strategy!
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Jan 19, 2021
Ep: 31: A Cool Multiplication Strategy
In this episode Pam and Kim want to help you develop a cool multiplication strategy. Which multiplication strategy? We aren't going to tell you until the end of the episode : -). We believe in developing strategies as natural outcomes, and then giving it a name. How do we do it? With Problem Strings! Listen in as Pam and Kim go through a Problem String to develop this super handy multiplication strategy.
Talking points:
* Are alternative strategies worth learning?
* What does it mean to do mental math?
* How to make mental math accessible for everyone.
* What is a Problem String?
* The _____ strategy
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Jan 12, 2021
Ep 30: Ten Minute Math
Don't you just love taking a break to play with numbers? In this week's episode, Pam and Kim share some of the ways that they engage with kids outside of school to get them mathematizing. Parents, ever wondered what can you do for just ten minutes to help your kids build relationships? This episode is perfect for you. Together we can all learn to make math fun!
Talking points:
* Math over the holidays
* Finger Flashing
* Which One Doesn't Belong
* Adding 10, 9, 99, 999 to anything
* How listening and engaging with students informs assessment
Additional resources: https://talkingmathwithkids.com, https://mathbeforebed.com
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Jan 5, 2021
Ep 29: Ratio Tables!
In this episode Pam and Kim dive deep into their favorite model for multiplication, division and solving proportions: ratio tables! They'll discuss how ratio tables can be a powerful tool to help students develop reasoning from elementary to high school.
Talking Points:
* What are ratio tables?
* How to, and not to, use ratio tables in the classroom
* Using ratio tables to organize data
* Using ratio tables to model thinking
* Using ratio tables for computation
* Example multiplication and division problems
Use this PDF to follow along with Pam and Kim's thinking!
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Dec 29, 2020
Ep 28: Real Mathematics Perspective
This week Pam and Kim wrap up their discussion on the Perspectives that Impact Math Pedagogy. Understanding the X, Y, and Z perspectives not only helps us understand one another better, but empowers us to choose to take on the real mathematics perspective. Listen in as Pam and Kim discuss the need for mathematics to be experienced, and the power in developing mathematical reasoning.
Talking Points:
* How do each of the perspectives benefit from real math?
* All people can do more real math than fake math
* What pitfalls do each of the perspectives have to avoid when teaching real math?
Take the XYZ quiz here! mathisfigureoutable.com/XYZ
Find this episode's transcript HERE.
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Dec 22, 2020
Ep 27: The Y Perspective
We've made it to our last (and maybe favorite) perspective that impacts pedagogy. The Y perspective describes those who struggle with fake math because they deeply desire to know "why". Pam and Kim describe people in their lives who grew up with the Y perspective and discuss their great value to the mathematics community.
Talking Points
* What describes the Y perspective?
* How adults with the Y perspective feel about mathematics
* Why teaching real math is so important
Take the XYZ quiz here! mathisfigureoutable.com/XYZ
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Dec 15, 2020
Ep 26: The Z Perspective
This episode is all about the Z perspective. Listen in to hear about the perspective that Pam estimates effects the majority of math educators, it was Pam's perspective too! Pam and Kim parse out the characteristics of the Z perspective and the huge impact it has on teaching today.
Talking Points
* Pam forgot how to subtract
* What is the Z perspective?
* How do Z-perspective students think?
* Pam's first experience with Math Club
* How can understanding the Z perspective empower teachers?
* Take the new XYZ Quiz!
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Dec 8, 2020
Ep 25: The X Perspective
Continuing in the Perspectives Impacting Pedagogy Series, Pam and Kim discuss the X perspective. Did you play with numbers as a kid? Did math make natural sense to you, regardless of how your teacher taught it? You might relate to the X perspective. Listen in to learn how the X perspective influences teachers and students in mathematics.
Talking Points
* What is the X perspective?
* Why X-perspective teachers teach with algorithms
* The 'math-gene' myth
* How X-perspective teachers can choose to teach real math
* Take the new XYZ Quiz!
Read the transcript for this episode at podcast.mathisfigureoutable.com
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Dec 1, 2020
Ep 24: Perspectives Impacting Pedagogy
This episode is part one to a new five part series! Pam and Kim introduce the three main perspectives impacting pedagogy. Understanding these perspectives helps teachers analyze their own teaching have productive conversations regarding math education.
Talking Points:
* The three perspectives impacting pedagogy
* Why math teachers can often talk past each other
* Take the new xyz QUIZ!
Find this episodes transcript HERE
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Nov 24, 2020
Ep 23: The Commutative Property
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.
Talking Points
* The commutative property in counting
* The commutative property in addition
* Using the commutative property for percentages
Find the transcript HERE
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Nov 17, 2020
Ep 22: The Swapping Strategy
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 strategy
* What problems fit nicely with the swapping strategy?
* Place labeling vs. Place value
* Send us (@pwharris) your slick swapping strategy solutions to gnarly looking problems!
Transcript: http://podcast.mathisfigureoutable.com/1062400/6371821-ep-22-the-swapping-strategy
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Nov 10, 2020
Ep 21: Playing with Percents Pt 2
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 Points
* The three types of percent problems
* The disadvantages of teaching procedural methods to answer percent problems
* Math is fun when it's figure-out-able!
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Nov 3, 2020
Ep 20: Playing with Percents Pt 1
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!
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Oct 27, 2020
Ep 19: Fractions, Decimals, Percents
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 Points
* Why kids of today are more familiar with percentages
* Why flexibility matters
* How to become more flexible using different representations of rational numbers
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Oct 20, 2020
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 language
Talking Points:
* How to add Butt-Cheeks
* Why students try 'canceling' everything
* Why reducing 6/8ths to 3/4s might give me more pie...?
* How one got over x.
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Oct 13, 2020
Ep 17: Social vs Logical Knowledge
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?
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Oct 6, 2020
Ep 16: The Language of Counting
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 numbers
* How to support young learners to make sense of teens and multi-digit numbers
* Give kids multiple representations of single-digits numbers.
* Pam being creepy at grocery stores
Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/5723239-ep-16-the-language-of-counting
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Sep 29, 2020
Ep. 15: Problem Solving with a Twist
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 Points
* The dangers of teaching "Problem Solving Methods"
* How to engage students in mathematics so that problem solving is a natural outcome
* How to run students through numberless word problems
Resources: Brain Bushart's Numberless Word Problems
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Sep 22, 2020
Ep 14: Guess My Number
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 Points
* I Have, You Need
* Kids Menus vs Adult Menus
* the Guess my Number game
* How do you think about finding Prime Numbers?
* Math can be fun!
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Sep 15, 2020
Ep 13: The Layers to Mathematics for Teaching
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 Points
* Building your own math
* Know the major strategies and models for your content
* Modeling Student Thinking
* Teacher Moves
* Sequencing Tasks
Resources: Journey
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Sep 8, 2020
Ep 12: Top 3 Things to Start the Year: Know Your Beliefs
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 teaching
* How intentional use of worksheets & resources can illustrate your teaching beliefs
* Determine your system of beliefs
Transcript *HERE*
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Sep 1, 2020
Ep 11: Top 3 Things to Start the Year: Building Culture Remotely
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 Points
* Building classroom culture is so important in remote settings
* When classmates respect each other's thinking, more students are enabled to think like mathematicians.
* Designing interactive remote learning
* How to facilitate Problem Strings remotely
* How to facilitate Rich Tasks remotely
Resources
* How Pam uses her iPad to facilitate Problem Strings remotely: https://www.mathisfigureoutable.com/how
* Transcript
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Aug 25, 2020
Ep 10: Top 3 Things to Start the Year: Student Names
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 person
* How Pam learns student names
* Useful tools and tips for using student names in a remote setting
* How to help students use each others names
Resources: Name Tents from Sarah Van Der Werf: https://www.saravanderwerf.com/week-1-day-1-name-tents-with-feedback/
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Aug 18, 2020
Ep 9: 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 Points
* Shout-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?
*Resources*
Strategies vs Models Article
Strategy vs Models Card Sorts
Transcript
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Aug 11, 2020
Ep 8: More Cool Things Mathy People Do
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 halving
3. 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 *HERE*
Talking Points
* The prime numbers in your neighborhood
* The Wonder Game
* Math-Strat-Chat
* Our first shout-out
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Aug 4, 2020
Ep 7: I Have, You Need
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 *HERE**
*Find the transcript for this episode *HERE*
Talking Points:
* We can all be "mathy people"
* What Kim thinks when she hears the number 36
* The routine that made the biggest impact on Pam's college students
* Taking ownership of your students' progression
* I Have, You Need resolves the subtracting across zero horror
* How I Have, You Need applies to middle and high school students
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Jul 28, 2020
Ep 6: The Development of Mathematical Reasoning Pt 2: Functional Reasoning
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 Points
* How functional reasoning builds on proportional reasoning
* It's not about being able to visualize the graph, it's understanding the relationship between the variables
* How to tell if someone is using functional reasoning
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Jul 21, 2020
Ep 5: The Development of Mathematical 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 Points
* What the Development of Mathematical Reasoning looks like
* We don't need calculators, we need reasoners
* One way people get stuck in counting str…
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Jul 14, 2020
Ep 4: 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 Points
* Who were Pam's early influencers?
* How teacher moves transform Rich Tasks
* Who is shaping math education today?
* Fos-dos and Fos-nots
* Desmos' card sorts and polygraphs: excellent tools for remote teaching.
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Jul 7, 2020
Ep 3: Mentoring Mathematicians
Pam and Kim continue from Episode 2 to discuss what it means to do and teach real mathematics. When we teach reading, students read. When we teach writing, students write. When we teach math, students mathematize, because we need a verb that describes what mathematicians do when they do what mathematicians do. And when we teach students to do what mathematicians do, they are mathematicians. So teachers are mentoring mathematicians.
Talking Points
* What Pam means when she says Math is Figure-Out-Able
* Mathematicians do not mimic to do math, they use their understanding of mathematical relationships
* What does it mean to mentor students to become mathematicians at their gradelevel?
Find the transcript here:
http://podcast.mathisfigureoutable.com/1062400/3887888-mentoring-mathematicians
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Jun 30, 2020
Ep 2: Math Does Not Equal Algorithms!
What do you think math is, a disconnected set of facts to memorize and rules, procedures to mimic or is it something else entirely? In this episode, Pam and Kim talk about discuss that real math teaching is about listening to students - that you must know your content, and know your kids. Also that math is not about mimicking an algorithm, but rather math is about letting the numbers and the structure dictate the strategy. How would you answer the question, "What is 99 plus anything?" or "What is 99 times anything?" How can you use relationships to solve those problems?
Talking Points:
* What are Algorithms? Why are they not Pam's goal?
* How mathematicians approach problem solving
* What is 99 + anything?
Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/3887876-math-does-not-equal-algorithms
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Jun 16, 2020
Ep 1: Math is Figureoutable
In this debut podcast, mathematics teacher educator, Pam Harris talks with her cohost, Kim Montague, about how they met and the work that they do together now. They set the stage that in this podcast they will talk about real mathematics and about how to teach mathematics. They answer the question, "If not algorithms, then what?"
As Pam and Kim describe their relationship they touch on these principles:
* It is fun to teach math that is figureoutable
* People have had different experiences with math, but everyone can learn to mathematize
* They define what it means to mathematize
* The difference between Real Snacks and Fake Snacks
* Reasoning can be refined and there are strategies which are more elegant than others
* Professional Development should be uplifting and empowering
* This podcast is for everybody!
Find the transcript here: http://podcast.mathisfigureoutable.com/1062400/3614602-math-is-figureoutable
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