This reminds me of one of the math teachers I had, who used a technique I found quite interesting and effective compared to how other teachers taught us about new concepts.
He would rarely come up with some theorem, ask us to solve a few exercises, and go on to the next chapter. When he wanted to introduce a new concept, he'd usually ask us to solve an equation or a more concrete probleme (I can remember something like the fence problem mentioned in the article, which was used to introduce us to finding the maximal output of a 2nd degree expression). After that, we would either find a solution through some struggle — and then try to figure out a more efficient approach — or we'd stumble on a problem by trying to use approaches we'd been taught before — and therefore try to find a better way to represent the problem.
On an amusing sidenote, while we were each working individually, he'd walk around in the class, looking at what we were doing, and crossing out with a red marker pen mistakes we'd made.
He would rarely come up with some theorem, ask us to solve a few exercises, and go on to the next chapter. When he wanted to introduce a new concept, he'd usually ask us to solve an equation or a more concrete probleme (I can remember something like the fence problem mentioned in the article, which was used to introduce us to finding the maximal output of a 2nd degree expression). After that, we would either find a solution through some struggle — and then try to figure out a more efficient approach — or we'd stumble on a problem by trying to use approaches we'd been taught before — and therefore try to find a better way to represent the problem.
On an amusing sidenote, while we were each working individually, he'd walk around in the class, looking at what we were doing, and crossing out with a red marker pen mistakes we'd made.