Podcast #45

In this episode Professor Steven Strogatz joins us from the Cornell Math Department. He is a world-renowned mathematician, known primarily for his work in non-linear dynamics and chaos theory, and he is the award-winning author of Sync, The Calculus of Friendship, and The Joy of x. He also happens to be one of the best teachers at Cornell. During our a wide-ranging conversation, Steve talks with us about helping students discover for themselves the joys and frustrations of mathematical thinking.

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Show Notes

0:00 Intro

0:42 Welcome Steven!

1:20 No such thing as an original idea; Kids these days don’t get all our jokes

2:43 Math: Curiosity, Discovery, and Creativity vs. Pain, Misery, and Boredom

5:00 Most math taught to students dates from before 1700

6:00 Many students have such a bad attitude about math by the time they reach college that it’s not hard to convince them that it’s better than they think

6:46 Students giving their teachers a hard time (following in Gauss’s footsteps)

10:00 How to inspire students with lecture. How important is lecturing? Getting students to fall in love with a subject so they go off and learn on their own

13:00 What is a successful teacher? Inspiring students to teach themselves

15:25 Why good teaching isn’t just what we see in the movies . Some students love stories. Others love applications. Others logical purity. Others like the competition. We need to serve all of them.

17:56 How can we customize our teaching for individual students? Asking students to write their mathematical autobiography.

20:00 Mathematical Explorations: Teaching math to students that thought they were done in high school.

21:56 Inquiry-based learning: No lecturing and no answers to questions—Students have to figure things out themselves through activities.

24:31 Doing math with paper shapes, scissors, and puzzles.

26:30 Having a discussion after the activity

28:30 Embodied learning: Teaching symmetry and group theory by having students walk around and wave their hands

32:00 It’s perfectly okay to be stumped. If you’re a cold fish teaching Socratic style, they’re going to want to do to you what they did to Socrates.

33:00 What’s the same about teaching screen writing and math: Creativity

34:30 Are we trying to teach skills or something more? Getting a little touchy feely.

36:00 Intrinsic motivation vs. extrinsic motivation.

37:50 Millionaires and Billionaires are not the same—Teaching numeracy by putting things into your own terms.

41:05 Surgically removing misconceptions before teaching new models

42:04 Creating math by making aesthetic choices; e.g., 0! = 1 and multiplying two negative numbers to get a positive number.

46:03 Creativity vs. analysis—Maybe it’s not so black and white. Creative analysis and analytical creativity. 3 interesting proofs of Cauchy’s Theorem.

51:24 Edward brings Piaget into the mix: Sensory/motor vs. concrete vs. symbols/abstractions

52:27 The creative side of teaching: An amazing exposition on eigenvalues and eigenvectors that incorporates a physical explanation, an application, and a financial motivation

57:46 Still making mistakes, Steve has a hard time assigning grades when students spend the semester cutting triangles out of paper: the pros and cons of portfolio grading

1:02:27 The pros and cons of peer evaluation