the problem with math(s) is, we start kids off with algerba, and while it is a place to start, we keep at it..for ages.. i liked math so much better when i started to learn other branches... non-euclidian geometery, geometery, numbers (and bases binary, octal, hex, and all the other ones) fibonacci numbers, golden ratio's... there are so many wonderful ideas.. and we get get bogged down doing long division to 5 places!--
I have to disagree. The problem is that we cover so many different things and none of them well. This is one of my primary gripes with the Standards and Practices adopted by the NCTM. Throughout their document they shut off contrary views by simply stating, "Well, there's no supporting evidence for that opinion." And then, for one of their major points, all of the data points away from what they're saying and suddenly their defense is, "Well, there's no reason to think otherwise!"
Here's the exact point - according to their data! Other advanced countries pretty consistently do better at math than we do, but they teach it differently. They cover topics at a slower rate, but in much more depth. The advantage is that they really learn the subject before proceding. This means when they come back to the subject later, they don't have to spend all their time reviewing what students didn't learn in the first place. We cover many more topics than they do in the other countries; however, we spend a lot of time reviewing, etc. By the time kids graduate, the kids in the other countries have covered more topics in more detail - because they learned the topic before going on. Does the National Council of Teachers of Mathematics infer that possibly they're doing something right? No way! Their response is "well, there's no reason to think it wouldn't work just as well our way!" (Well, other than the fact that we're already doing it our way and they're smoking us - according to their own documentation.)
When I was about 5 or 7 my dad swam me out to the middle of a lake and dropped me off. He was so sure I'd just start swimming, but I sank like a rock - was absolutely terrified of the water for years later. Eventually, someone took the time to teach me and I've loved it ever since. I'm better now than I ever was as a kid. And I've been sure to teach my kids - first spending a long time getting them accustomed to the water and then getting them in classes and then a team. This August they start with a more advanced trainer.
It would have been easy for me to have settled for the shallow end. There are all sorts of things I can do and admire without swimming a stroke and -- those things are worthwhile things to do. I could just play marco polo and toss balls and "dive" for things. I could watch the other people swim and do real diving. Life would have been okay for me. But I would not have learned to swim. To my mind, doing math without mastering algebra is like playing in the water without learning to swim.
I think we have very different experiences with the new math. I was a victim at the tail end of it. I failed the second grade and when I was in the third grade they would walk me to the far end of the school to take math with the first graders - quite a humiliating walk, though it may have been for the best.
I oscillated from thinking that I was a complete idiot and wondering if just maybe the teachers didn't understand much of what they were teaching. Already, I had some inkling that when I said I understand something I had a very different thing in mind than what other students meant when they said the same thing for themselves. They felt that if they could copy whatever the teacher was doing that they understood it.
Fortunately in the fifth grade I got my first real teacher. My worst subject (math) became my best over night. They quit fluttering around half-teaching things and started to really get into how things fit together.
In retrospect, I can see several problems. 1) Teachers - particularly in the lower grades - often don't know much more about a subject than exactly what they're teaching. 2) In some cases (hopefully small, but I'm not sure), teachers only know the mechanics of what they're doing. They don't even know their own subject very well. 3) Possibly the most important, they very seldom have much practical experience with the kinds of math they're teaching, so they hem and haw around it when students ask for examples or more detailed explanations. 4) Another important one - PARENTS pass on their math-o-phobic tendencies to their kids, not through genetics of course, but through their actions, sometimes subtle and sometimes overt. 5) Current testing regimens allow teachers to use "teaching to the test" as an excuse for covering too many different subjects far too shallowly. 6) (not sure how important this really is) The NCTM's standard justifies teaching shallow knowledge, while recommending preventing students who ARE capable of taking advanced math from doing do. 7) Modern textbooks are written to be flashy and pretty while carefully concealing the important information - almost as an aside. 8) Very often work-sheets that teachers have students do are nonsensical or just silly, indicating to me that the people who make these worksheets (from workbooks the teachers have) don't really understand the subject very well.
I've witnessed "poor students," math-o-phobes to a Tee, actually get excited about learning the boring stuff and ask perfect questions - only to be rebuffed by a teacher who couldn't admit he didn't know the answer. It happens a lot.
(There should be no problem saying "I don't know" and if a teacher doesn't say that a few times a week, then she probably isn't pushing her students hard enough.)
These are what I think are the real problems. I realize there are people who believe otherwise and they're welcome to believe that way. No one can do otherwise than learn from his own experiences. But if I'm the only person to maintain it, then so be it. We could just as well say that students should not have to spend so much time learning spelling and grammar. In fact, I think we could make more of a case for this, since linguistic redundancy ensures that people can usually read text in the face of ambiguity, contradiction, and damned-near unparsability. Or we might maintain that one needn't read a single literary classic - as the Cliff Notes contain everything one really needs to know. We could maintain any of these things, but I think they're all mistaken - and for the same reason - we're settling for the wading pool.
k
