the teaching of math (babble)

[nosebeepbear]

When I was taught multiplication, my teacher explained it, then said "if you do this backwards, it's division, and it looks like this: ... " then she went back to multiplication. Nothing more than that, but when division came up the people who came from her class had an easier time of it because the concept was already in their heads. I think when

Comments

[totient]

radians are great for getting to another thing you supposedly can't do, which is raise a number to an imaginary power. But apart from that, I don't think in them either.

[babalon_it]

That's very enlightening. I really like how you described it. Can I show it to others? Or would you care to write it up as an article I can post for you?

[nosebeepbear]

Sure, you can share. I'm glad you liked it.

[dglenn]

This is why, when I was teaching math, I preferred to say, "we haven't learned how to ____ yet," or, "we haven't invented a way to ____ so far in this [curriculum|course]," instead of, "you can't ____".

It gave me the opening to say, later on, "Before, we didn't have a way to subract a larger number ftom a smaller number. But what if we could? How would that work? Well, it goes like this: we need a new kind of number ..." And that way I could present the different classes of numbers as solutions to "you can't do ____ with the numbers we've learned about so far" problems.

When I was teaching in a classroom (6th/7th/8th grade math & computers), that was exactly how I introduced negative numbers, rational numbers, irrational numbers, and at the class' request because I'd made an offhand reference to probably learning about them in 12th grade, imaginary and complex numbers. ("I'm going to skim over this and it won't be on the test, but since so many of you asked...")

[nosebeepbear]

I preferred to say, "we haven't learned how to ____ yet,"

Yes, exactly. So much of math is memorizing rules - memorizing rules that don't actually exist just makes a mess of things.

[debboamerik]

Just what did these teachers expect to happen when their students encountered negatives? Not only are they going to have a harder time with the concept than necessary, but they're going to rightly wonder if *anything* they know about math is correct.Two quick points

[totient]

7-year-olds are not capable

Most 7-year-olds. But that generalization is a disservice to the 7-year-olds like me who were doing complex arithmetic already.

[debboamerik]

hat generalization is a disservice to the 7-year-olds like me who were doing complex arithmetic already.

And that is a disservice to the 99.9% of 7-year-olds who aren't you.

[debboamerik]

Sorry if the above was a bit snarf-o-riffic. However, your comment does not address my point, and it does come off as a bit of "Hey, look at me! I was way ahead of myself developmentally! Aren't I cool!"

Many ground-breaking scientists and mathematicians were perfectly developmentally typical; some were behind. It is unfair (and ridiculous) to suggest that the teaching they received, geared as it was to their developmental level, made them incapable of more complex thinking for life. It is even unfair to say that it created problems. For most kids, it just doesn't.

[not_the_pope]

My father was sitting at the kitchen table one night when I was 7 or so (in the 3rd grade, anyway) with a book and a pad of paper, figuring. I asked him, "Whatcha doin' Daddy?" and uttered the fateful words, "Can I help?" This resulted in my father teaching me to read logarithm tables. Logarithms didn't really stick in my brain at that point, but later when I encountered them in a math class I knew they weren't very hard because Daddy already taught them to me over the kitchen table when I was 7. I just needed "reminding".

I kinda wish he'd done that with statistics. Oy.

[nosebeepbear]

but later when I encountered them in a math class I knew they weren't very hard because Daddy already taught them to me over the kitchen table when I was 7

You hit on an important point there - you were able to learn it because you knew it wasn't hard. Somewhere along the way, people seem to get the idea that these things are harder than they have to be, and that's a big part of my concern. Not that it doesn't take work, and I know different brains work differently, but, well, it's sort of like Voldemort - if you only talk about it in whispers it becomes a whole lot scarier.