Teaching

Where Proof, Evidence, and Imagination Intersect — Quanta Magazine

My latest column for Quanta Magazine explores the role that evidence plays in mathematics, a field better known for its reliance on logical proof.

For example, do you know the next term in this sequence?

1, 2, 4, 8, 16

You might be surprised!

“Mathematics has a long history of defying expectations and forcing us to expand our imaginations. That’s one reason mathematicians strive for proof, not just evidence. It’s proof that establishes mathematical truth. All available evidence might point to 32 as the next number in our sequence, but without a proof, we can’t be certain.

Some simple examples involving high school math show how evidence can lead us toward proof in mathematics, but can also lead us astray if we aren’t careful. You can learn more by reading the article at Quanta Magazine, which is freely available here.

By MrHonner, ago

Critical Issues in Mathematics Education at MSRI

Next week I’m heading to the Mathematical Sciences Research Institute (MSRI) in Berkeley, CA to participate in the 2019 Critical Issues in Mathematics Education (CIME) conference.

CIME brings together academics, researchers, industry partners, and teachers to discuss important issues in education. The theme of this year’s conference is mathematical modeling in K-16 education. Here’s a summary of the goals from the conference website.

The CIME workshop on MM will bring together mathematicians, teacher educators, K-12 teachers, faculty and people in STEM disciplines. As partners we can address ways to realize mathematical modeling in the K-12 classrooms, teacher preparation, and lower and upper division coursework at universities. The content and pedagogy associated with teaching mathematical modeling needs special attention due to the nature of modeling as a process and as a body of content knowledge.

I’m proud to be representing K-12 teachers as well as Math for America at this year’s CIME, where I will be presenting as part of the conference’s opening panel along with Jo Boaler, Ricardo Cortez, and Maria Hernandez.

A full schedule and list of speakers is available at the CIME conference website.

UPDATE: The full video of our panel discussion can be seen here.

By MrHonner, ago

Unscrambling the Hidden Secrets of Superpermutations — Quanta Magazine

My latest column for Quanta Magazine brings the exciting story of superpermutations down to the level of high school counting.

A superpermutation is a string of symbols in which each permutation, or arrangement, of those symbols appears in some order. Imagine, for example, you are trying to thwart the evil plans of a mad scientist and must key in a secret passcode:

Suddenly, inspiration strikes. If you punch in 123451, you’re actually trying two codes: 12345 and 23451. Even better, entering 1234512 will succeed if the code is 12345, 23451 or 34512.

You do some quick calculations. Instead of keying in 600 digits to cover all the possibilities, you now only have to enter 153 digits. You have just enough time — and it works! You’ve saved the day. It’s a good thing you read about “superpermutations” in Quanta.

Finding minimal length superpermutations is a open research problem in mathematics, but recent developments have come from the most unlikely of places! Find our more by reading the article, which is freely available here.

By MrHonner, ago

STEM Up Your Classroom — Free Webinar

On January 24th I will be participating in a free webinar titled “How to STEM Up Your Classroom” with the NSTA/NCTM National STEM Teacher Ambassadors.

The webinar will feature a number of different perspectives on STEM in the classroom. The teacher ambassadors hail from different states and territories across the country, and work in a variety of settings: high school, K-6, administration, district intervention, policy, and more.

It’s a wonderful group of dedicated teachers with a wealth of expertise to share, and it should be a fun 90 minutes. You can learn more about the free webinar, and register, here.

UPDATE: The full video of the webinar can be found here.

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By MrHonner, ago

MfA Workshop — The Problem with Pentagons

This week I’ll be running a workshop, “The Problem with Pentagons”, for Math for America teachers.

The workshop focuses on the classification of pentagonal tilings of the plane. Although humans have been tiling with polygons for hundreds of years, the answer to the question “Which pentagons can tile the plane?” was only recently answered!

The surprising story of pentagonal tilings spans cultures, centuries, and disciplines. In addition to some beautiful geometry, the story is also filled with lots of twists and turns that illustrate the many ways in which mathematics happens. It’s a wonderful opportunity to bring living, breathing mathematics to our students, and I’m looking forward to discussing the many classroom connections with MfA teachers.

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By MrHonner, ago
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