I recently read that Dr Norman Wildberger has updated the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit. Cool! I mean, I always liked trigonometry but looking at it from another perspective is always refreshing. Yes, I'm a total nerd.
When I was a kid learning this stuff seemed weird and officious. Half of the time I thought the teachers were nuts when they explained how numbers could be used, as though they were trying to convince us to buy Amway. When I was excited to "discover" something about them, something which we would be later taught in some methodical fashion, the teachers would often wonder what I was talking about. This sounds very computationally elite and snobby of me but sometimes I think I understood the nature of numbers better than they did because I didn't have the good sense to be terrified of math.
I thought I would probably stop taking math after high school. It seemed to be more of memorization than anything. It was boring and nobody ever bothered to explain the connections. When I was older, the larger concepts began to unfold more sensibly. I finally saw the grander picture. Why don't more high school teachers encourage kids to think in terms of math? Probably the better question is, why does it have to be such a terrifying experience in grade school?
I think there should be mathematics specialists in elementary schools to make sure kids develop a comfort with numbers and their various uses. Many elementary-level teachers aren't very math savvy. I nearly completed a teaching degree at one point, with the goal of teaching middle school math. For a number of reasons I didn't complete it. While on this path, I took various courses on elementary math instruction and can tell you that a good percentage of my fellow students were on their 2nd time in the classes (after receiving failing grades initially.) Many of these future teachers admitted being terrified of taking these classes because they "always hated math." And they went on to teach. It may be a case of the chicken and the egg.
We've somehow raised generations of math phobics. However, the generation before them is just as queasy about math and so on and so on. As a result, subsequent generations of teachers are often very single-minded in their approach to mathematics education, relying on memorization of formulas and even confusing the use of manipulatives. Too many kids are learning rote methods of computation. If a kid has a question that is not directly dealt with in the teacher's manual, it may not be addressed and a curious child will become a hardened one. They don't get the play with the numbers and see what they can do. No monkey bars with 4, no tag with 7, nothing.
Kids need to learn that it's ok to take their numbers out to play, that there is more than one way to divide or multiply. It freaks people out when I can calculate sales tax AND add it to the price of an item with a single calculation. I use the calculator function of my cell phone to do it in line for the cash register so I can have exact change. If the line is long, I'll just work it out in my head. It's fun and slightly cruel to imply that I knew the total because I am psychic.
Hey, this soapbox is kind of high and I'm a little lightheaded. Time to get off.