But other people disagree. I used to think it was only my students who did badly at math who had the 'wrong' idea that math was about memorizing. Math people will tell you it's not about memorizing, but many of them do think memory has a bigger place than I give it.
What do you think?
Here's what needs to be in your memory, eventually:
- addition 'facts' (if add 1, double, and add 2 to an even are easy, then there are 25 harder facts)
- multiplication 'facts' (2 is doubling, 4 is doubling twice, 5 is easy, 9 can be easy; only 9 facts left)
- circumference and area of a circle (I know which is which by using dimension - circumference is 1D and has r, area is 2D and has r2. If I'm unsure of the formula, I can also check reasonableness of my answer by estimation.)
- Pythagorean theorem (a2+b2=c2 for right triangles)
- quadratic formula
- [edited to add ...] sine and cosine, tangent and reciprocal identities (the rest of trig pretty much follows, 6 facts)
When I started teaching, I had a BA in math and still didn't have 7x8 memorized. I also didn't have the quadratic formula memorized. Whenever my topic of the day would include quadratic formula, I'd put it at the top of my notes. 7x8 I could figure out in 2 or 3 seconds.
To me, math is all about connections. When I think of slope, I think of a rise and a run (and a little right triangle under the slanty line, showing them). I know steeper lines want a bigger slope, so the rise has to be on top in the ratio that compares rise and run. To me, that's not memorizing.
So tell me what I'm forgetting. ;^) What more do we have to memorize in math?