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(Disclaimer - I am most likely biased since I suffered through twelve years of US public school math, often racking up low grades from boredom even while distin
by v3rt 17y ago
(Disclaimer - I am most likely biased since I suffered through twelve years of US public school math, often racking up low grades from boredom even while distinguishing myself in math competitions)
I agree that the US system teaches mathematics in too formulaic and granular a way. The way I see it, a good way to divide math students into two categories is to look at those who will use math in their future careers as scientists, engineers, etc, and those who will not and are only studying math to "see the world from another angle".
In either case, a spitting-back-of-formulas approach is counterproductive: Scientists and engineers need to (or at least would do very well to) understand how the mathematics they use works. On the other hand, those who will not use math in the future have no real need to pack their brains full of formulaic tidbits; they will get the most value through pursuing a problem-solving approach that generalizes well to other areas of life.
In short, no matter what the class's level, mathematics definitely needs to be taught from a more problem-solving, integrated perspective. "Pre-med math" that consists mainly of memorization and regurgitation does nobody any good.
The main problem, I imagine, would be recruiting teachers that can actually teach mathematics in this way. That raises a whole different question, though - why do we have "teachers" and not mathematicians teaching math; why do we have "teachers" and not historians teaching history? It seems that much of what education school teaches is how to keep order and run a classroom of bored and antsy students, but wouldn't it be more effective to simply teach interesting material and keep the kids engaged?
- jibiki 17y ago> In short, no matter what the class's level, mathematics definitely needs to be taught from a more problem-solving, integrated perspective. I'm always looking for examples of how this is done. How did you learn how to solve problems? (Did someone teach you?)
- v3rt 17y agoI suspect the foundations of my mathematical problem-solving skills were laid when my parents signed me up for extracurricular math classes with teachers from the local Russian community, when I was in elementary and middle school. I started on competition-type problem solving with my middle school math team coach, an extraordinary teacher contrasted with the largely incompetent ones in the curricular program. However, the majority of the techniques I applied to competitions, and I suspect the majority of my overall problem-solving skills, I accumulated through self-study, not a small part of which was from the Art of Problem Solving books from the website linked in the original post. If those were used as textbooks and the teachers knew (and felt) the material, then I think the mathematical education in this country would get a significant boost. If some of the material turned out to be too hard for those less talented at mathematics, the approach would still be the one to use in simpler textbooks.
- sokoloff 17y agoI think your division into two camps is missing the largest cohort of math students by far: those who are taking math because it is required as a checkbox item on a "before you get your degree <or diploma>, you must have passed at least this much math classes". "Will this be on the test?" is a far more common query in my experience than "Could you show me some additional math so that I may better understand the universe and world that I live in?"