Category: Pedagogy

I see or hear some variation of this often from mathematics teachers: “The answer to 4+5 is 9.” “So if we’re given (5+3)/2, that means we add five and three, then divide the result by two, and that gives us the answer.” In regular plain English, answers are coupled with questions. Expressions, though, aren’t questions,…

I’m currently reading “Why Don’t Students Like School?” (second edition) by Daniel T. Willingham. While there is a lot of good stuff in this book and I’m feeling fired out about setting my educational train back on its tracks, I winced at his cheerleading for mnemonics. And then: I reframed. He suggests the use of…

Ask a general person on the street to define mathematics, and they’re likely to say something about manipulating or combining numbers. Ask a mathematician to define mathematics, and they’re likely to talk more about patterns. Here, for instance, is the first sentence of the definition provided by MathWorld: “Mathematics is a broad-ranging field of study…

This video and its comments got me thinking about how difficult it really is to read an analog clock: There are multiple comments on TikTok sneering at how inane and unintelligent modern children must be to need more than ten minutes, let alone more than two days, to learn how to read a clock. So…

The question is the bane of the math teacher’s existence. It probably comes up in other classes as well, but it seems to be particularly associated with mathematics. Here are two truths (and no lies): From the time I graduated from high school in 1985 to the time I started training to be a math…

I woke up this morning thinking about sets. I recently bought the (Canadian) French, (Mexican) Spanish, and German editions of “Dog Man”. This gave me a set of books in languages I can at least make a real effort to read, and the child already has a set of “Dog Man” books in English. Yesterday…

There are two basic conceptual ways that multiplication is explained: Repeated addition and the area model. Many people who are adept at multiplication (including teachers) take for granted what many students have trouble connecting; in the case of multiplication, it’s not immediately obvious why repeated addition and the area of a region ought to result…

The other day I saw this TikTok by the inimitable Howie Hua: This is a common topic: What is the long division algorithm about anyway? I’ve likely even seen Hua talking about it in the past, but this time, something clicked in my mind. I don’t personally recall struggling with long division. I suppose there…

Note: This is not a polished edit, just some somewhat disorganized thoughts. Hopefully, I’ll write something more organized later. For a long time, I thought I understood set theory. Then, a few years ago, I realized I had somehow messed up what is a fairly rudimentary concept: That sets, by standard definition, do not have…

I’m currently reading “Sweller’s Cognitive Load Theory in Action” by Oliver Lovell, specifically the section on reducing extraneous load during education (ca. p. 32; I’ve got the e-book). This leads me think about story problems, such as those on the SAT, which often contain information that’s irrelevant to the problem. For example: Carrie invites some…