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

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.

I'll never know whether I was really especially gifted in math through some quirk of brain wiring, or all of my seeming talent was the result of simply Not Getting Screwed Up By Bad Math Teachers early on. But I know that the way I learned math early (Montessori method) did at least help, and that I had an incredibly good teacher from 8th grade to 12th (as I found out when I tried teaching in a classroom and, for all my math skill and all my tutoring skill, I couldn't come anywhere emulating that man).

As for the "it was familiar" thang in a different thread: when it came time to learn about other bases, I went, "oh, it's just like binary that Dad taught me, but with more digits!" When I learned how to multiply polynomials, I thought, "this seems awfully famili... oh! It's exactly like multiplying integers if you substitute "10" for "x", and it's the same steps; that's why it feels like I've done this before." Exponential notation <= colour-coding of digits (and visualising four digit numbers as "this many thousand-cubes, that many hundred-squares, so many ten-bars, and this many one-beads" when I first learned to add).

Every "hey, this is a lot like that other thing I already know" moment in math education is important. Teachers should be looking ahead and planting the seeds of those.