Concrete vs abstract representations

Anna asks about representations; John and Barbara discuss when to use concrete manipulatives and when to abstract.

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Episode notes

In this episode, Anna is joined by two familiar guests, mathematician and founder of JUMP Math, Dr. John Mighton, and learning expert and bestselling author Dr. Barbara Oakley. They discuss their new Coursera course, Making Math Click: Understanding Math Without Fear, what learning science reveals about how students learn math, and why practice and worked examples play such a critical role in building math confidence.

They discuss schemas, give some cautionary advice about using manipulatives and concrete-pictorial-abstract approaches, and explain why moving quickly from concrete to abstract matters. They describe what’s at stake when math education fails, what’s lost when students don’t develop foundational skills, and what it will take to help more learners succeed in math.

This is a practical, engaging, and insightful episode for teachers, parents, university students, and anyone who has ever felt they weren’t a math person.

This episode is also available in video at www.youtube.com/@chalktalk-stokke

Making Math Click: Understand Math Without Fear: Free course with certificate: https://www.coursera.org/learn/math-click?action=showPartnerSupportedAccess

TIMESTAMPS

[00:00:22] Introduction
[00:05:40] How Barbara’s background shaped her approach to math
[00:07:00] John’s experience with math from a young age
[00:09:21] John and Barbara’s Coursera course
[00:11:07] Who is their course for?
[00:15:45] Is the course beneficial for teachers?
[00:21:54] What math and Sylvia Plath’s writing have in common
[00:23:51] Building schemas in math
[00:26:46] Getting good at math leads to liking math
[00:31:08] Kaminsky’s research on manipulatives vs. abstract representations
[00:33:39] Fading from concrete to abstract
[00:40:30] Barbara’s article in the Seattle Times
[00:42:30] Real world consequences of innumeracy
[00:49:13] Learning math takes practice and patience
[00:51:38] Societal loss from kids not learning math
[00:57:13] Failed constructivist approaches
[01:00:50] Barbara’s and John’s recommendations for system improvements
[01:05:42] Final thoughts