Teaching

Workshop — Learning to Love Row Reduction

I’m running a workshop for teachers tonight titled Learning to Love Row Reduction.

If a math teacher has done anything with matrices, they’ve probably row-reduced one. Row reduction is often experienced as mindless symbol manipulation, but in fact it is an incredible and surprising process that is deeply connected to the fundamental ideas of linear algebra. A little row reduction takes you a very long way! My goal in this workshop is to show teachers just how far it can take us.

This is part of an ongoing series of workshops I’m running on Linear Algebra, that have their origins in the tremendous amount I’m learning by teaching this course at the high school level. I’ll be offering the workshop through Math for America, where I’ve given talks and offered workshops on linear algebra, computing, and many other topics.

2022 — Year in Review

In keeping up with (what is now a 10-year!) tradition, here’s a brief review of my professional year.

Without question my biggest professional accomplishment of 2022 was the publication of my book, Painless Statistics. People are buying it and even saying nice things about it! From start to finish it was an incredible learning process, and I now know what is meant by the saying “It is better to have written a book than to write one.”

I was happy to resume giving talks and workshop again in person in 2022. In the spring I returned to Queen’s College to speak to soon-to-be math teachers about making math by design. And after two years of remote-only teacher workshops, I was thrilled to return to the Math for America offices for The Geometry of Linear Algebra. It’s been exciting to learn so much linear algebra as I teach it, and I already have new workshops and talks scheduled for 2023.

On top of publishing Painless Statistics, it was another busy year of writing. As usual my column for Quanta Magazine provided a year full of the best kind of mathematical challenges, and I had a blast writing about brownie bake-offs and geometric dissections, different kinds of infinities, and Wordle, among other things. And I reviewed Ben Orlin’s book Math Games with Bad Drawings for the American Mathematical Monthly.

Above all, it was just nice to have a professional year that seemed to be trending toward normal.

For the first time in 5 years my school year planning can begin with "Everything I need to do this year can be done as I did it last year". A welcome change!
— Patrick Honner (@MrHonner) August 5, 2022

Here’s to an even more normal 2023!

Teaching

2022 in Tweets

Here’s a tweet-per-month review of my 2022. Enjoy!

January

End of Week Checklist:

☑️ Computed Fourier Series in Calculus
☑️ Expressed symmetries as equations in Geometry
☑️ Researched a dozen different applications in Linear Algebra

Oh, and
☑️ Final exams
☑️ Final projects
☑️ Final grades
☑️ Covered a 1st period 9th grade PE class
— Patrick Honner (@MrHonner) January 28, 2022

February

Here's how a student integrated xcos(x) today. Her technique is pretty brilliant! I've never considered doing something like this before. pic.twitter.com/ZtiGbse5Z5
— Patrick Honner (@MrHonner) February 3, 2022

March

This morning I had a moment of finally understanding a mathematical idea that I've been thinking about for at least the past five years. Math is like that sometimes.
— Patrick Honner (@MrHonner) March 6, 2022

April

Me: <egregiously violating algebraic rules in erroneously simplifying exponential expression>
Student, politely, after raising hand: "Can you explain the laws of exponents you used here? I'm not familiar with them."
— Patrick Honner (@MrHonner) April 7, 2022

May

I always introduce non-separable differential equations by asking students to solve y' = x + y, which they generally aren't equipped to do. Occasionally students intuit an answer, but a student did this today, which I've never seen before. Brilliant!#math #mathchat #APCalc pic.twitter.com/xFI2n8DuUq
— Patrick Honner (@MrHonner) May 6, 2022

June

"For some reason, once you starting thinking about Calculus, you can never go back."

-Student reflection
— Patrick Honner (@MrHonner) June 14, 2022

July

I maintained a pretty stoic demeanor my first year of teaching but one notable exception was the day a student told me they preferred the Slope-Intercourse form of a line.
— Patrick Honner (@MrHonner) August 1, 2022

August

For the first time in 5 years my school year planning can begin with "Everything I need to do this year can be done as I did it last year". A welcome change!
— Patrick Honner (@MrHonner) August 5, 2022

September

A short thread on one of my favorite Pre-Calculus topics: Tangent Lines!

Given a polynomial P(x), divide by (x – a)² and write in quotient-remainder form. By the division algorithm, the remainder has lower degree than the divisor. This means the remainder is linear. pic.twitter.com/YLNzxHI40z
— Patrick Honner (@MrHonner) September 28, 2022

October

I am a mathematician. I also routinely count on my fingers to compute Friday's date when making my calendars.
— Patrick Honner (@MrHonner) October 9, 2022

November

Another fun thread about long division! We were discussing the arithmetic of complex numbers in precalculus, and I asked students how we would divide them. One student half-jokingly suggested we try long division. So we did!
(1/8) pic.twitter.com/VpodeX0lgd
— Patrick Honner (@MrHonner) November 1, 2022

December

I usually don't engage with trending topics here on Twitter, but in this case I'll make an exception: You can find me on #Mastodon at phonner@mathstodon.xyz.
— Patrick Honner (@MrHonner) December 16, 2022

Resources Teaching

Workshop — The Geometry of Linear Algebra

I’m running a workshop for math teachers tonight titled The Geometry of Linear Algebra. We’ll take a purely geometric approaching to developing the important properties of linear transformations and explore how those properties connect to fundamental notions of linear algebra like vectors, matrix multiplication, and change of basis.

The workshop is part of the ongoing learning that’s happening as a result of teaching linear algebra at the high school level. I’ve taught linear algebra many times, but only in recent years did the course start making sense to me as a whole. The key, as it has been so often in my teaching career, was to see it as a geometry course.

I’ll be offering the workshop through Math for America, where I’ve given talks and offered workshops on linear algebra, geometry, and many other topics.

Numbers Teaching Writing

How Big is Infinity? — Quanta Magazine

My latest column for Quanta Magazine explores one of my favorite topics: infinity!

At the end of the Marvel blockbuster Avengers: Endgame, a pre-recorded hologram of Tony Stark bids farewell to his young daughter by saying, “I love you 3,000.” The touching moment echoes an earlier scene in which the two are engaged in the playful bedtime ritual of quantifying their love for each other. According to Robert Downey Jr., the actor who plays Stark, the line was inspired by similar exchanges with his own children.
The game can be a fun way to explore large numbers:
“I love you 10.”
“But I love you 100.”
“Well, I love you 101!”
This is precisely how “googolplex” became a popular word in my home. But we all know where this argument ultimately leads:
“I love you infinity!” “
Oh yeah? I love you infinity plus 1!”

Learn how a staple of high school math — functions — can help mathematicians understand infinity and even describe the different kinds of infinities there are! The full column is available here and includes a few challenging exercises at the end.

By MrHonner, 4 yearsOctober 2, 2022 ago

Workshop — Learning to Love Row Reduction

2022 — Year in Review

2022 in Tweets

Workshop — The Geometry of Linear Algebra

How Big is Infinity? — Quanta Magazine

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