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 asking myself, is he being fully fair to the other side?
Where do I stand? Mostly with Skemp. Rules without reasons can break down fast, like the student who multiplied 20 cm by 15 yards and said the area was "300 square centimeters" because "area is always in square units." That student had a rule but no understanding. But I don't think instrumental math is useless. Sometimes you need a quick rule, and even Skemp says expert mathematicians use them. So my view is: rules are fine as tools, but they should sit on top of real understanding, not replace it. My bigger worry is that Skemp wrote this almost 50 years ago, and most classrooms still teach the instrumental way. He diagnosed the problem well, but we still don't have the cure. And that makes me wonder: is it really a teaching problem, or is it a testing problem? As long as exams reward quick right answers, teachers and students will keep choosing rules over reasons. That's the hard question Skemp raises but doesn't fully answer, and it's the one I keep thinking about.
Comments
Post a Comment