And a bit more about math...
This is why engineering schools are dominated by Asian students who know the theory AND the calculation process.
I mean, point taken, there are places where they manage to teach both the concept and the math, and probably in middle school, and clearly I do want my kids to compete with anyone out there. At the same time, they come to me with extremely weak math skills, which my school's math teachers are doing their darnedest to bring up to and beyond grade level. And there are many, many ways in which the science I teach supports that effort. We measure things all the time. I taught them to measure in basic SI units before they saw it in math. We compute averages, we describe relationships between variables, we graph early & often, we learn formulas and sometimes figure out how to manipulate the formula to tell us something different...
There are a limited number of days in a week, and I have found myself rather often bogged down in teaching the kids to handle math concepts and getting stuck on one topic for much longer than I intended or thought appropriate. Usually, it happens when I don't realize exactly how far back I will have to go to bring them up to speed on the particular math concept. In the end, I usually beat it into the them one way or another, but I sometimes feel like they lose sight of the science concept in all the backing up and practice math problems.
So I'm learning to pick my battles. There are times when the math is so fundamental to understanding the science that I must teach it. There are times when the math is just not that hard (F=ma) and worth throwing into the mix. There are times when the math concept itself is really important (precise measurement; graphing) or piggybacks nicely with what the math teachers are doing at that time, thus it is worth it. But there are times when I want to focus on teaching a science idea well, not taking twice as long teaching math algorithms so-so and science ideas so-so.
Personally, in middle school, I was taught all the technical stuff about simple machines, but understood none of it intuitively or deeply. I don't feel that I was taught how to think it through, just how to plug in numbers here and there. Now I am trying to sort out the best approach for presenting this material - mechanical advantage, efficiency, simple machines - so that the kids get it in their bones. Math will play some role, since we will do experiments to calculate the amount of force needed to lift something straight up versus up an inclined plane, and the distance over which it moves, and so on. I m still figuring out exactly what role.
Also, it's worth noting that mathematical thinking doesn't always need numbers. For example, if I introduce a formula and the kids can explain how it shows the ratio between two variables (what happens to force if distance increases?) that is a math idea, regardless of whether or not we put real numbers in.
Personally, I wish I'd been taught calculus with as few numbers and practice problems as possible, and far more graphs, descriptions, and essay questions. I have this sense that it is a beautiful way of describing phenomena, making predictions, solving problems on a theoretical plane. Later, the numbers and symbols can go in.
*Lately, I feel really thin-skinned in terms of what people are saying here. I think it's just me, being too sensitive for a myriad of personal reasons. Criticism is good. But please phrase it gently or at least directly, with a minimum of sarcasm. And remember that the comments are not intended to be a platform for stump speeches on your favorite topic. If every comment you make always has to do with the same thing, you can get your own blog for free at Blogger.