Michael Pershan’s Problem Problems

I have enjoyed math teacher Michael Pershan’s work for a long time. I follow him on Twitter, and I wrote about his website Math Mistakes a few years ago because, darn it, mistakes are interesting! A couple years ago, he started another blog, Teaching with Problems, at a URL I love, problemproblems.wordpress.com.

I never taught the elementary and middle grades Pershan teaches, and I’m out of the classroom altogether now, but I am always excited to see one of his posts in my blog feed. I find his writing extraordinarily thoughtful, and he is humble, passionate, and thorough in his posts. In a recent, slightly meta, post, he wrote about one reason that might be. Some math bloggers write quick posts that deal with one smaller idea at a time, and that’s great. But he prefers to “slowly, painstakingly, dutifully carve out posts.” He loves taking the writing seriously, and it means great, but not always frequent, posts from him. It also means you want to read them slowly and thoughtfully rather than skimming.

I had somehow missed the launch of Teaching with Problems, but I started reading it after finding — and being blown away by — this post about a student he calls Rachel. She is a smart kid who has a strong command of math concepts and a lot of trouble with basic arithmetic. I don’t want to try to summarize the post. Just go read it. Another 0f my favorites is this post about whether third graders think fractions are numbers. Point: “NO a fraction is not a number a fraction is only part of a number.” Counterpoint: “Fractions are a certain category of numbers because without numbers fractions would just be lines.” 

Last month, I spent a lot of time thinking about ancient Mesopotamian mathematics because researchers published a new paper about Plimpton 322, a tablet I was familiar with from my math history teaching days. (I wrote about why I don’t agree with their interpretation here.) So when I was looking through the problemproblems archive, I was happy to see that Pershan had coincidentally written about Plimpton 322 and Mesopotamian mathematics as a teaching tool in July. In his post, he writes about how some of the earlier mathematicians who studied Plimpton 322 and other tablets imposed their more algebraic view of mathematics onto the tablets in anachronistic ways and homes in on a dilemma of looking at ancient mathematics from the point of view of a modern math teacher: “The historical question is whether this mathematics would have been meaningful to the ancients. The pedagogical question is whether it could be meaningful to our students.” He ends the post pessimistic about whether the geometric Mesopotamian methods can help students with the algebraic concepts and notes that perhaps, “It’s only when you understand both that you can look back and see the connections between them.”

A week or so ago, the New Yorker shared one of their old articles, the one about how political science professor Andrew Hacker thinks math is about nothing, in a tweet. It caused a bit of a dustup in the math Twitter world, as it tends to. As high school math teacher Patrick Honner pointed out after attending a debate last year between Hacker and mathematician James Tanton, it’s frustrating that we’re listening to Hacker and not math teachers here. I was thinking about that as I read Pershan’s blog and thought about writing this post. When he writes about whether ancient Mesopotamian tablets can help teachers communicate the difference of squares method to students, he has a much more realistic understanding of what students can make of that than I do. If you’re looking for math teachers to listen to, he’s a great one to add to your list.