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Workshop — The Geometry of Statistics

I’m excited to present The Geometry of Statistics tonight, a new workshop for teachers. This workshop is about one of the coolest things I have learned over the past few years teaching linear algebra and writing a book on statistics: Finding the line of best fit for a set of data is really a geometry problem, but not the geometry problem you might think it is!

In this workshop we’ll see how finding the regression line is equivalent to finding the shortest path from a point to a plane in a curious high dimensional space. This geometric context helps make sense of many mysterious things in regression, like mean-centering (thanks, All 1s vector!) and the correlation coefficient. It also ties into advanced applied mathematical ideas like Principal Component Analysis (PCA) and the Singular Value Decomposition (SVD).

As is often the case when I learn mathematics, the turning point occurred when I finally understood why I didn’t understand. I look forward to sharing that understanding with others!

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Books I Read in 2023

Here’s a selection of books that made an impact on me in 2023.

Superforecasting tells the story of psychologist Philip Tetlock’s project to systematically evaluate the predictions of experts. What exactly does an advisor mean when they tell the President that a military operation has a “good chance” of being successful? It wasn’t so long ago that no one thought to even ask such a question, and as Tetlock shows, the consequences couldn’t be more real. Tetlock’s work led to the development of the Good Judgement project, a forecasting competition designed to identify the characteristics of “superforecasters”, individuals with a quantifiable talent for predicting how world events will unfold. It’s a great book, and one I was partly inspired to read because of my involvement in a student forecasting tournament based on the Good Judgement project (where our students took first and second place overall!)

I finally read The Lady Tasting Tea, by David Salsburg, which had been on my list for a while. It’s an excellent history of the development of statistics, told through fascinating characters and interesting anecdotes. It immediately joined my student lending library, and it also took second place on the list of statistics book I’ve learned the most from (to be fair, it’s first on the list of books I’ve learned from by reading it rather than writing it). It’s full of fun little details, like this quote I shared with my linear algebra class the very day I read it.

Manil Suri’s The Big Bang of Numbers was a highlight of my year, both because it’s a unique book that tells a whimsical origin story of mathematics full of insight, humor, and even spirituality, and also because I had the privilege to interview Manil Suri at the Jaipur Literature Festival this past year (video here).

Made to Stick, by Chip and Dan Heath, is the book that I’ve been thinking most about as a teacher this year. Why do silly ideas go viral while important ideas struggle to take hold? It’s a question every teacher should consider, and Made to Stick offers lots to think about. Months later I’m still pondering the power of generative metaphors, story as simulation, and why people should care about duo piano. Thanks to my (former) student Satvik for the recommendation!

Atomic Habits by James Clear was another book that had been on my list, and it was a worthwhile read even if confirmed many previously held beliefs. A core idea of the book is very mathematical, namely that the impact of habits compound like interest in a bank account, generating exponential (hopefully, positive) personal growth.

I feel a bit funny saying that John Fleischman’s Phineas Gage was probably the best book I read this year, seeing as its target audience is middle school students. But this infamous story of the 19th-century man who blasted a railroad spike through his brain and lived to tell about it is so vivid, engaging, and expertly contextualized in the history of science that it keeps coming up in thoughts and conversations.

In fiction, I enjoyed Susanna Clarke’s Jonathan Strange and Mr. Norrell, a fantastical history of magic in Britain told through the story of the apprenticeship-turned-rivalry of the title characters. Amor Towles’s A Gentleman in Moscow was one of the loveliest books I’ve read in a long time. And I enjoyed every moment of Elmore Leonard’s Get Shorty. Leonard also authored the stickiest advice I read in 2023: don’t write the parts that the reader skips.

In addition to getting back to my year-end lists (sorry, 2022) I’ve been trying to be more active on Bookwyrm, the ActivityPub-based social network dedicated to reading and reviewing. You can find me there at phonner.

And thanks, as always, to the (shamefully underfunded) Brooklyn Public Library for making it so easy to read this year and every year.

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2023 — Year in Review

As I reflect on my professional 2023 I keep coming back to the line “Normal is normal again.” Not the world, certainly, and not for everyone, but since changing schools nearly five years ago this is the first year when being in the classroom hasn’t felt extraordinary for extraordinary reasons.

Still, it’s been a mix of the new and the old. In addition to my normal lineup of geometry, calculus, and linear algebra courses, I’ve been doing more mathematical modeling with students this year. In the spring we had a team of modelers invited to compete in the International Mathematical Modeling Contest (IM2C), thanks to their excellent work on last year’s High School Mathematical Contest in Modeling (HiMCM), and I’ve been working to expand the program at school. This year interest was high enough to have eight teams compete in the HiMCM, and we’re looking forward to new modeling opportunities this spring. In addition, a colleague and I mentored around 70 students who competed in a national forecasting tournament inspired by the Good Judgement project, and our teams took first and second place!

An extracurricular highlight this year was interviewing mathematician and author Manil Suri for the Jaipur Literature Festival. We had a lively talk about his excellent new book, The Big Bang of Numbers, and also about math, writing, and teaching, and the Asia Society of New York made the entire video of our conversation available here.

As usual, I continued to design and run workshops for teachers this year, including a new entry in my ongoing linear algebra series titled Learning to Love Row Reduction. I also gave two talks at this year’s NCTM Annual Meeting: So, You’re Teaching Pre-Calculus, and A Case for Linear Algebra. I’m already looking ahead to new talks this coming year, including an upcoming workshop on the geometry of linear regression I’ll be presenting in February.

Writing my column for Quanta Magazine was as challenging, and fulfilling, as ever, with pieces aimed at bridging the gap between classroom and research math focused on the newly discovered aperiodic monotile, the algebra of secret codes, graph theory and cliques, a high school student’s amazing proof, and what three-point turns tell us about a hundred-year-old geometry problem.

And with the landscape of social media continuing to change, I’ve been enjoying my time on Mastodon more and more in 2023.

Platforms based on decentralization, user autonomy, and interoperability definitely seem like the right way forward. And I’ve been trying to do a better job of archiving what I write by cross-posting some of my social media posts here on my blog.

It’s been a good 2023, and here’s hoping for another good, and relatively normal, 2024!

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NCTM 2023

I’ll be in Washington, DC later this week for the National Council of Teachers of Mathematics (NCTM) Annual Meeting, where I will be giving two talks.

On Thursday, Gary Rubinstein and I will be presenting “So, You’re Teaching Precalculus”.

With the College Board’s new Advanced Placement Precalculus course on the horizon, a lot of math teachers will be teaching a brand new course in 2023. What are the big ideas in AP Precalculus? And how might AP Precalculus differ from the courses already taught at your school? In this session we’ll look at the themes that define the AP Precalculus framework and how they link important ideas in algebra, geometry, and trigonometry to what lies ahead in a calculus course.

And on Friday, I’ll be making “A Case for Linear Algebra”.

Students need as many pathways to mathematical success as we can give them, and linear algebra offers a flexible and versatile course option that can fit alongside an established sequence or help define a new one. Come learn about the whys and the hows of teaching linear algebra, and see where the core ideas pop up in the classes you already teach.

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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.

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