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.
0:00 ⏯ Intro
0:42 ⏯ Welcome Steven!
- The Calculus of Friendship: What a Teacher and a Student Learned about Life while Corresponding about Math
- Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life
- The Joy of x: A Guided Tour of Math, from One to Infinity
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
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