NCTM 2024, Chicago

For the big list of all presentations, see here. My talk, Numerical Computing with Data, is described below!

Numerical Computing with Data

The slides for my presentation are available here, but they are insufficient on their own to really communicate the workshop. I try to give some additional context below, but oh boy am I tired.

When I went to college (started in physics then switched to electrical and computer systems engineering), it was amazing to finally see applications of some of the math that I had almost learned in high school. I wondered why I hadn't seen any of these wonderful applications before.

Later, in graduate school for robotics, it only became more clear that there is a tremendous amount of accessible and relevant math that we just ignore in high school (while still including some gross math).

There is so much to say about the content that gets included and the content that gets ignored. A lot of people have said it. There is way more nuance to this than I'll address here. There could be asterisks all over this page, but this isn't meant to be a well supported argument.

Since I started my career in 2006, right out of college, the single biggest most obvious missing piece in math education is computing. I don't mean computer science. I mean computing with computers in authentic ways.

• Ask any math teacher if they've ever used a spreadsheet.
• Ask them if spreadsheets are a part of their curriculum.

(Of course some do! This is one of those asterisk places. Most don't. Trust me.)

It is actually pretty wild that we focus on content that seems so oriented toward engineering without actually ever reaching engineering. In fact, there are multiple points where we get tantalizingly close but quit right before it gets good.

Lots of Algebra 2 and Precalculus textbooks tease the beginnings of matrices and matrix arithmetic, but then don't do anything with it. In my wildly successful research career, I used two things: Linear Algebra and Trigonometry. That's 90% of science.

• Ask an engineer, any engineer, if they have ever used MATLAB.
• Ask a math teacher if they have ever taught a numerical computing platform.

Computers were invented for math!*

There are so many opportunities to engage students with authentic tools and problems. Certainly, students will not be having the same experiences as professional scientists, etc. But there are too many places where we barely hint at a topic and then move on to the next unit. Matrix arithmetic is frick'n dope. Linear algebra is one of the most fundamental and applicable branches of mathematics, and we walk right up to it but don't touch it.

Why do we teach math? There's so much to say about this, but it definitely isn't to train future mathematicians.

High school mathematics...

• is not like the math that mathematicians do.
• is removed from applications that engineers and scientists care about.
• could, but does not leverage tools that mathematicians, engineers, and scientists use.

How to fix math education in two easy steps:

1. Teach students how to use spreadsheets.
2. Learn MATLAB (really Octave) and start solving better problems.