Last night I ran a workshop for teachers about mathematical modeling. Modeling can be nebulous and overwhelming to those unaccustomed to applied math, so my goal was to give teachers an accessible introduction to the modeling process that allowed them to experience what distinguishes modeling from what might be considered “school math”.

The workshop was based on the work I’ve done building and running a mathematical modeling program at my school the past three years, where I’ve drawn heavily on resources from the Consortium for Mathematics and its Applications (COMAP) and modeling competitions like the MathWorks M3 Challenge.

Modeling is a wonderful way to get students doing authentic applied math, and even though I’ve got a lot to learn myself, I was happy to share what’s worked for me and my students as we have built our program.

Related Posts

• Workshop — The Geometry of Statistics
• Workshop — The Geometry of Linear Algebra
• Workshop — It’s All Linear Algebra

I saw some dispatches from the NCTM (National Council of Teachers of Mathematics) annual meeting this past week, and I’m always disappointed at what constitutes professional discourse in math education. Beyond the facile messages of “thought leaders” and influencers, even the messages of purported substance seem like a continual re-telling of what should be obvious to everyone. Get students doing mathematics. Engage them intellectually and socially. Pay attention to how they think. These should not be revolutionary ideas.

Originally posted on Mastodon.

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!

Related Posts

• Introducing Painless Statistics
• Workshop — The Geometry of Linear Algebra
• Workshop — It’s All Linear Algebra
• The All 1s Vector

People tell me my job is easy.

You get summers off.

You only work nine months of the year.

You’re done at 3 pm.

You get paid to babysit.

Students at that school won’t succeed anyway, so you don’t have to do much.

Students at that school will succeed anyway, so you don’t have to do much.

Teaching advanced courses is easy. My students don’t even know the basics.

It must be easy to teach those students. Mine can’t handle that kind of work.

I wish I got to teach those students. Mine aren’t that engaged.

You just walk around asking questions. Your students are the ones doing everything.