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 reason and mathematize mentally.
• How mathematicians solve computational problems, Ann Dowker's research
• What is a Problem String?
• A multiplication Problem String example
• Another multiplication Problem String example with decimals!
• The big reveal: The _____ strategy

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 
• Which One Doesn't Belong
• Adding 10 and 9; 100 and 99; 1,000 and 999 to anything
• Listening and engaging with students is so important

Additional resources: https://talkingmathwithkids.com, https://mathbeforebed.com

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 grade solve unit rate problems?
• Where do non-unit rates show up?
• Examples of using a ratio table to solve multiplication and division problems

Use this PDF to follow along with Pam and Kim's thinking!

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 people can do more Real Math than fake math
• Real Math offers something for all perspectives
• Where to start teaching Real Math
• What do you do with students that all have different perspectives
• How to lean into the frustrations of students for each perspective
• How leaders can work with teachers with the different perspectives
• How can we all communicate better?

Take the XYZ quiz here! mathisfigureoutable.com/XYZ

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 mathematics
• Two things that people with the Y perspective need to understand
• Why teaching Real Math is so important 

Take the XYZ quiz here! mathisfigureoutable.com/XYZ

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 experience with Math Club
• What people with the Z perspective need to understand
• How can understanding the Z perspective empower teachers?
• Take the new XYZ Quiz!

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 with her son and collegues with the X perspective
• The 'math-gene' myth held by the X perspective
• 3 things teachers and students with the X perspective need to understand.
• Take the new XYZ Quiz!

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 math teaching
• Take the new XYZ QUIZ!

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 property

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 (@pwharris, @kimmontague) your slick swapping strategy solutions to gnarly looking problems!