|And as I've said, after figuring the same ones over a period of time, the higher frequency ones just stuck with him.
This is true. Dice and board games work, too.
|Memorizing math facts is just a way of teaching to the test.
Actually, I think it's about lowering processing time. This didn't work for me. It's not that I never TRIED to memorize the math facts, just that when it became time to use them I'd draw a blank. If I sat there long enough and thought hard enough I could probably bring up the answer or at least make a good guess. But, for me at least, it's easier and faster to remember the pattern or do a calculation.
What I never understood is why the other students in the class (most of whom had the answers memorized) were still slower than I to answer the questions, and got more of the questions wrong. We used to do speed drills in elementary school and I usually won. How can that be if most everyone else is using simple recall?
Sort of like remembering dates in history. I'm a complete dunce at that. But I always aced the essay questions because I really UNDERSTAND history.
|When I tried to do mental multiplication, I would actually draw the numbers in my head and mentally move them, crossing certain numbers out, carrying, mentally writing stuff below the line, etc.
That is so fascinating to me. I can't do that at all because the numbers swim around in my head and I lose track of what step I'm on. I have to write everything down.
Teaching place value is really important for v-s students. I also break things down and regroup in my head, so does my DH. Strangely enough, the numbers don't swim when I do that. Only when I try to calculate conventionally.
And don't even get me started on my personal nightmare: long division. The whole show-your-work thing drove me bonkers. I'd usually answer the questions and then go back and write down the work. Which drove my teachers crazy as sometimes the work would be all wrong but the answer correct.
I used to do this in Algebra2, too. We were supposed to simplify the problem and then draw a graph to display the answer. I'd simplify and graph but leave out the "plotting step". I didn't need to do it as I already knew what the graph would look like. This became useful during testing time when we'd have multiple-choice answers (display a graph and then ask what line is displayed).
Anyway, in this century recall of memorized facts isn't actually that useful. Internet, anyone? Besides, once you get to binary and hexadecimal math the whole math-facts thing breaks down entirely. Quick: What is 1010+1101? Answer: 10111 Easy as pie!
Can we say: assembly programming?
In fact, I don't think I REALLY understood place value until I learned binary math.