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Skemp on two approaches to teaching and learning mathematics: My response Three things made me stop while reading this article. First, Skemp's idea of "faux amis",  false friends. A teacher and a student can both say "understanding" and mean completely different things, without knowing it. That made me think: how many times have I believed my students and I were on the same page when we really weren't? Second, the story about the 7-year-old boy with an IQ of 140 who cried over his math homework. He wasn't bad at math, he was trying to truly understand it in a classroom that only offered him rules. That's heartbreaking, and it shows the damage this problem can do. Third, the map example. Learning routes is like memorizing steps. Learning a map means you can find your way anywhere, and if you make a wrong turn, you can fix it. I also noticed something else: Skemp admits his own examples are "heavily biased" toward relational math, so I kept a...
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Battleground Schools: three stops

  Battleground Schools: three stops First stop: the dichotomy table. The table of conservative vs. progressive stances stopped me because it clarified something I'd felt but couldn't name. I've heard people argue about math education for years without realizing they were operating from completely different assumptions about what mathematics  is,  authoritative and infallible versus exploratory and evolving. What struck me most is that this isn't just a debate about teaching methods. It's a debate about the nature of mathematical knowledge itself. If you believe mathematics is a set of perfect Platonic forms handed down through history, your classroom will look one way. If you believe it's patterns emerging from lived experience, it will look entirely different. I also noticed that the table labels one column "conservative" and the other "progressive," but I'm not sure those political labels always fit. The article itself points out that N...
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