|Re: Another viewpoint|
Message #12 Posted by Ed Look on 22 Apr 2008, 11:39 a.m.,
in response to message #9 by designnut
Conceptually, I agree with you. Unfortunately, I see two issues involved here. Firstly, children DO NEED to learn the mechanical tedium of taking a square root by hand, or taking a function in rectangular coordinates and converting and replotting in polar space, etc., but after it was explained to them why it works. (This might work better with cube roots.) And then, unlike years ago, I have seen and heard that some of today's teachers really don't have a true grasp on the material they teach.
Without enthusiasm-by-example, even if derided on the surface or initially by the loudmouth "cool" kids (who really have deep seated problems but kids of that age don't really see or understand), some kids, at the minimum will catch on. If the teacher demonstrates by body language, tone of voice, or facial expression that the material is a dreadful bore, then the children will unconsciously pick that up and form a like opinion of it- even before it is presented!
I mean, we can use mathematics as the hardware store of big boy toys and goodies for the builders and tradesmen of physics, chemistry, and engineering to model (even more than) the physical universe! How cool is that?!
But kids are naturally taken by such silent communication, which most often can be negative, the disapproval of their "cooler" peers, and their own innate laziness. There is much to overcome, and it won't be easy.
I was forced to do trigonometric manipulation of secants and cosecants without knowing what it was all about or why. I don't think I learned a thing,except to hate it. Are we still pushing kids through courses with no understanding or comprehension, no explanation? While it's best to know how to make change etc. I've seen supermarket checkers have to touch every can to count them even though there were 5 by 6 rows. I guess thats why they were checkers. I don't think long division or taking square root is really a learning process. What does a square or cube mean seems more basic and useful. I think we need to teach concepts and applications rather than that's what I was taught in school. Sam