Gilbert Strang and two others discuss how to teach math effectively. They argue for concrete examples over abstract proofs, using rotations in 3D and higher dimensions to build intuition and reveal underlying structure.
Do you think, for teaching and in general thinking about new concepts? Do you think it's better to plug in the numbers or to think more abstractly? So looking at theorems and proving the theorems or actually, you know, building up a basic intuition of the theorem or the method, the approach and then just plugging in numbers and seeing it work. Yeah, well.
Certainly many of us like to see examples first. We, we understand it might be a pretty abstract sounding example like a three dimensional rotation. How are you going to, how are you going to understand a rotation in 3D or in 10D or. But, and then some of us like to keep going with it to the point where you got numbers, where you got 10 angles, 10 axes, 10 angles. But the best, the great mathematicians probably, I don't know if they do that because they, they, for them, for them, an example would be a highly abstract thing to the rest of it.
Right. But nevertheless, working in the space of examples. Yeah, examples, it seems to.
Examples of, of structure.
Our brains seem to connect with that.
Yeah.
Yeah.
