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

[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.

[nosebeepbear]

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.

I did not mean to suggest that teaching to an expected developmental level is what's causing the problem. Saying "we're not going to be taking bigger numbers from smaller numbers in this class" is perfectly reasonable, and a teacher who says that can go about their business without teaching higher concepts *and* without saying anything that isn't true.

[papertigers]

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

no, it really isn't; it's an accurate statement about a group of people that may or may not apply to every individual in that group. what would be a disservice would be to teach mathematics to all 7 year-olds as if they were capable of understanding abstract concepts in a way that most of them are not.

[nosebeepbear]

The problem there comes from the whole idea of trying to teach everyone in the same ways. I'm not saying there's a magic solution to that, but if teaching either way is unfair to somebody, there's a problem. When I was in elementary school there seemed to be more flexibility for teaching people in a single class at different levels; I'm not sure what was different.

I also think that most children are capable of a lot more than they're given credit for (I mean in general, not by you specifically), and different teachers/schools/textbooks/areas have different ideas about what kids can learn at certain ages. At the same age my husband was being told negative numbers don't exist, my class was working with them.

None of this was originally my point, but since the topics were brought up, I babbled :).

What's frustrating about teaching math is...

[dglenn]

"I also think that most children are capable of a lot more than they're given credit for"

Agreed. Not just a few exceptional ones.

But I think a key part of the problem, as I've opined before, is that too many elementary school teachers (and even middle school and somr high school teachers) don't really understand the math they're teaching, themselves! They know "how" but not often enough "why". They don't see how it hangs together.

And they teach their students that math is a) hard and b) inexplicable/confusing/arbitrary.

As a classroom teacher and as a tutor, the vast majority of my work was undoing the damage from earlier math teachers. And that was frustrating and disheartening

[nosebeepbear]

I'm not suggesting teaching negative numbers earlier. It's not the order of actually teaching the concepts that bugs me - it's the practice of saying things about math that are blatantly wrong rather than saying "yeah that happens, but you don't have to worry about it yet." I think kids can deal with "this is possible but we're not going to do it right now" without getting confused or feeling the need to fully understand the concept, but saying it's *not* possible confuses them later. To use my language example again, there's a big difference between saying "we're only going to use English in this class" and "other languages don't exist."

I'm not sure I agree with your statement that most people aren't permanently screwed up by it - I think it's a large part of the reason so many people are terrified of math.

[selki]

I'm not sure I agree with your statement that most people aren't permanently screwed up by it - I think it's a large part of the reason so many people are terrified of math.

Seems plausible to me (lying to kids about math for a moment's explanatory convenience messes some of them up somewhat for learning more math later)