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-nume...
May 11, 2021•24 min•Ep. 47
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...
May 04, 2021•30 min•Ep. 46
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 (Cred...
Apr 27, 2021•26 min•Ep. 45
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....
Apr 20, 2021•14 min
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 lear...
Apr 13, 2021•22 min
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 lookin...
Apr 06, 2021•20 min•Ep. 42
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 h...
Mar 30, 2021•22 min•Ep. 41
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?...
Mar 23, 2021•23 min•Ep. 40
In this episode Pam and Kim discuss why a traditional teaching approach is not effective and propose an alternate way of teaching to help every student learn and grow. It's one of their guiding principles, and they can't believe they're only just now sharing it! All students struggle at some point and all students need a challenge, so this is a great listen for everyone! Talking points: What is the traditional way of teaching? The outcomes of the traditional approach of teaching to mastery How t...
Mar 16, 2021•21 min•Ep. 39
We made it to our final episode in our multiplication facts series! In this episode Pam and Kim share ideas about helping kids narrow in on facts they struggle with after many opportunities and experiences with multiplication. This final episode exemplifies why we believe that taking the long view and building relationships and Multiplicative Reasoning all year can help students' fact fluency with just a little nudge. Talking Points: What it means to take the long view in multiplication facts Wh...
Mar 09, 2021•22 min•Ep. 38
It's time for what you've all been waiting for. GAMES! Sure we don't want kids memorizing songs or rhymes to build their facts, but in this episode Pam and Kim bring the fun into multiplication. What games are out there that can help students build their facts and Multiplicative Reasoning at the same time? We're glad you asked :-) Talking Points: Teacher and parent attitude is important Students' job is to figure out the math facts not rote memorize or skip count or sing a song Students need thi...
Mar 02, 2021•21 min•Ep. 37
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 using Problem Strings! Talking Points: The order that we teach math content matters to give students the best experience with multiplication throughout the year The sequence we teach the multiplication facts matters Example Problem Strings to build multiplicative relationships The key relationships students need to o...
Feb 23, 2021•21 min•Ep. 36
When choosing tasks 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: What the research says about the negative effects of timed activities such as multiplication fact tests Shame is not a motivator to ...
Feb 16, 2021•19 min•Ep. 35
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 'rote memorizing' multiplication facts. Talking Points: Multiplication facts are important The problem is not the facts but the stress from rote memorizing facts The difference between knowing and rote memorizing facts What the standards say abou...
Feb 09, 2021•16 min•Ep. 34
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 goals for Problem Talks The major purpose of Problem Talks MathStratChat as a Problem Talk The purpose of Problem Strings What is a Problem String? When to do a Problem Talk or a Problem String How much time ...
Feb 02, 2021•23 min•Ep. 33
It's time for another Problem String! In this episode Pam and Kim highlight one of their favorite multiplication strategies. It's so slick! In doing so they continue the conversation about the importance of letting students discover and develop relationships, as opposed to teaching strategies step by step. Talking Points: A Problem String for the ____ strategy Modeling the strategy on an area model Can you also triple, quadruple, etc.? Bonus! A problem with decimals Really cool decimal relations...
Jan 26, 2021•25 min•Ep. 32
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 efficient multiplication strategy. Talking points: What does it mean to do mental math? We can purposefully help people rea...
Jan 19, 2021•27 min•Ep. 31
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 of all ages 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: Finger Flash game I Have, You Need routine Alligator Song and counting backwards Age games MathStratChat Whi...
Jan 12, 2021•27 min•Ep. 30
In this episode Pam and Kim dive deep into their favorite model for multiplication, division, and solving proportions: ratio tables! They'll discuss 3 ways ratio tables can be a powerful tool to help students mathematize from 3rd grade to high school. Talking Points: What are ratio tables? How to, and not to, use ratio tables in the classroom Three ways 3-5 grade can use a ratio table: -to organize data -to model multiplicative thinking -for multiplication and division computation But do 3-5 gra...
Jan 05, 2021•25 min•Ep. 29
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: Your perspective may not be the same for everyone around you The ultimate goal is Real Math- all p...
Dec 29, 2020•23 min•Ep. 28
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? Pam and Kim's personal experiences with the Y perspective How adults and learners with the Y perspective feel about mathematic...
Dec 22, 2020•23 min•Ep. 27
This episode is all about the Z perspective. Listen in to hear about the perspective that This episode is all about the Z perspective. Listen in to hear about the perspective that Pam estimates influences 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 exper...
Dec 15, 2020•18 min•Ep. 26
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 Kim's experience growing up with the X perspective Pam's experiences...
Dec 08, 2020•22 min•Ep. 25
This episode is part one to a new five part series! Pam and Kim introduce the three main perspectives that influence the way we teach math. Understanding these perspectives helps teachers analyze their past perspective so they can make choices and have productive conversations regarding changing and improving math education for all students. Talking Points: The three perspectives impacting our pedagogy Is there one perspective that is the best? How our perspective affects conversations about mat...
Dec 01, 2020•15 min•Ep. 24
How can we help students feel comfortable with using 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 when a student is counting on to add The commutative property in addition of larger numbers Using models to represent the commutative property Using the commutative property for percentages It's not just about naming the p...
Nov 24, 2020•18 min•Ep. 23
Pam went most of her life not knowing about this really cool thing! Listen in as Kim relates a great math experience she had with her son, Luke, while they were messing around with addition. Pam and Kim discuss the importance and kinds of place value experiences we provide for students as we mentor them as mathematicians. Talking Points: Introducing the Swapping strategy What problems fit nicely with the Swapping strategy? Place labeling vs. Place value Necessary but not sufficient Tweet us (@pw...
Nov 17, 2020•14 min•Ep. 22
Are percents truly figure-out-able? You bet! Grab a pen and paper for this one as Pam and Kim discuss the 3 types of percent problems and how they solve them using relations, not with algorithms. Talking Points: What Journey members are emailing about The three types of percent problems Pam and Kim share their thinking as they solve all three types of percent problems Two traditional ways of teaching percents and how they rob students of resoning fluently Math is fun when it's figure-out-able!...
Nov 10, 2020•23 min•Ep. 21
So are percents really figure-out-able too? In this episode Pam and Kim do a Problem String and share their strategies to solve some percent problems. Listen in as they play with percents! Talking Points: Can we make math fun? Benchmarks that kids need to know around percents Percent Problem String
Nov 03, 2020•14 min
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 to help us be more judicious problem solvers. Talking Points: Why kids of today are more familiar with percentages Using benchmark fractions, decimals and percentages How students might mess with gnarly fractions, decimals and percents Why flexibility matters How to become more flexible using different representations of rational n...
Oct 27, 2020•20 min•Ep. 19
You might want your magnifying glass for this one, because in this episode we're getting a little nitpicky. Pam and Kim discuss common and often traditional nomenclature/math-slang that can take the reasoning out of mathematics. They offer useful alternatives and illustrate the importance of using clear mathematical language so students have less opportunites for misunderstaning the mathematics. Talking Points: Adding a zero No 'Butt-Cheeks' in math 'Canceling' can means many different things Wi...
Oct 20, 2020•19 min•Ep. 18
