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.
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.
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.
I’m excited to be heading back to the North Carolina School of Science and Mathematics (NCSSM) for their annual Teaching Contemporary Mathematics (TCM) conference.
I’ll be presenting Building Bridges through Computing, in which I’ll talk about how mathematical computing projects in Python and Scratch can build bridges between theory and practice, the procedural and the abstract, and the simple and the impossible! My talk will focus on Pre Calculus and Calculus topics, and include projects like solving systems of equations, estimating roots, and elementary numerical methods.
Estimating Intersections in Python
I presented at TCM in 2016 on Mathematical Simulations in Scratch and really enjoyed my visit. The conference is focused on big ideas and brings in lots of inspired teachers, and NCSSM is a unique school with incredible programs and exceptional teachers.
TCM 2019 runs January 24-26. You can find out more information here.
Another year in the books! And another busy one. Here’s a quick look back at my 2018: A year full of interesting professional opportunities and challenges.
In June of this year I was named an inaugural winner of the MfA Muller Award for Professional Influence in Education. This generous award recognizes Math for America Master Teachers who influence the teaching professional in exceptional ways. Here I am with Pete Muller (who created the award), Math for America founder Jim Simons, and the inaugural science teacher awardee, Seth Guiñals-Kupperman.
That same month I was named a National STEM Teacher Ambassador as part of a joint program between the National Science Teachers Association (NSTA) and the National Council of Teachers of Mathematics (NCTM). Ambassadors were selected among previous PAEMST awardees, and received training in policy and advocacy. As part of my work as teacher ambassador, I wrote “There’s More to Math than Drills“, an op-ed for NSTA that responds to a call for more drilling in math classrooms.
I also wrote a math lesson on economic mobility for the New York Times Leaning Network that uses a wonderful interactive infographic built from a landmark study of income data from 20 million Americans.
I had some unique and amazing speaking opportunities this past year. I appeared on the My Favorite Theorem podcast, where I talked about why I love Varignon’s Theorem both as a mathematician and as a teacher. And through Math for America, I participated in a Story Collider event where I told the story of my ever-changing relationship with mathematics.
All this, of course, on top of a full year of teaching, instructional coaching, creating new courses, and a brief stint as department chair! I’m thankful to have enjoyed a productive and fulfilling 2018, and I look forward to more in the new year.
