Book review: “How Not to Be Wrong: The Power of Mathematical Thinking” by Jordan Ellenberg

I was perusing the virtual shelves of my local library on Libby (naturally, the nonfiction section) when I stumbled on Jordan Ellenberg’s How Not to Be Wrong: The Power of Mathematical Thinking. I had already been scrounging up ways to try to engage my students in my math courses. This semester, I am teaching a college math fundamentals course and a biostatistics course. I have added a participation component that includes a few TED talks and 3Blue1Brown/Numberphile videos. I’m having the county epidemiologist visit as a guest speaker. And I flood my slides with xkcd comics. But a whole book? I was already deep down the nerd hole, but I’ll keep digging.

This book was a gold mine! I have struggled to teach statistical concepts in the past; last year, I taught a statistics unit in my engineering lab course. I kept it very practical, and didn’t move very found out of lab-driven examples. I made some apps where we could collect simulated datasets and perform back of the envelope statistical tests without needing to rely on programs. I also made several interactive animations that I thought beautifully illustrated how statistics worked.

While there was some good feedback here and there, on the whole it appears to have fallen flat. Students got distracted with the code instead of the visualizations and got overwhelmed that they would be expected to do that. And some of the graphics may have fit better in a “second look at statistics” scenario instead of a first dip. I continue to try to tune how I introduce statistical concepts, and I’m glad to have another field.

Ellenberg’s book isn’t going to teach you math. It isn’t a textbook. But it isn’t meant for that. Ellenberg’s book is kind of apologetics for math. It tries to answer the question of the ages: When am I going to use this? He virtually avoids mathematical symbols almost entirely, but is able to write engaging encounters with expected value and linear regression. For me, this is candy jar of examples I can use in my lectures, perhaps as ways to introduce a concept.

One of my favorite examples that sticks out is the MIT students and the Massachusetts lottery. Some MIT students did a bit of math and realized that the expected value of a lottery ticket was greater than the purchase price. So if you buy a LOT of tickets you are guaranteed a profit. They dumped tens of thousands of dollars on tickets and made a hefty profit.

A book like this is great for someone who has only used math in a practical fashion. We engineers use math like we do a hammer. But mathematicians look at a math problem like a puzzle to be solved. I have at times appreciated the elegance of a theorem or equation. Fourier transforms really captured my imagination there. But to revisit these problems and look at them from different perspectives, asking why they work, isn’t my forte. Just teach me the math I need to do this problem, and skip the dramatics haha.

There was one other portion of the book I was hoping would help my students. The question When am I going to use this is dreaded by most math teachers. I have my own answers, and I appreciate engaging with other instructors for their own ways of approaching the problem. Ellenberg includes his own answer in the preface of the book. I pulled a passage from it and stuck it on a Canvas page in the hopes of inspiring a struggling student. I’m grateful for the math educators who wrestle with these questions. Not just about the math problems, but how to make them relevant to students and how to assuage some of the terror that can be associated with math. I have a really hard time slowing down at times to see things from the students’ perspective. I have a few more books like this one queued in my reading list, and I hope to absorb some of their wisdom in helping students learn math.

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