Path: utzoo!utgpu!news-server.csri.toronto.edu!torsqnt!tmsoft!masnet!rose!david.lloyd-jones From: david.lloyd-jones@rose.uucp (DAVID LLOYD-JONES) Newsgroups: comp.edu Distribution: world Subject: Subtle Math Questions Message-ID: Date: Sat, 4 May 91 11:25:00 EST Organization: Rose Media, ON, CANADA Lines: 79 > >Nevertheless, the good teacher of mathematics will have a deep appreciation >of the way mathematics is actually used in the world at large and not just >a good understanding of a traditional list of arithmetical and algebraic >algorithms and formulas. The student who sees his mathematics teacher as >inadequate, not only in the internal mechanics of the subject, but in >success in making the subject relevant to the world at large, will correctly >reason (YES, students are capable of reasoning) that this person has nothing >of importance to tell him. I think this is very good, and is much more than the bland truism it looks like. Have you thought about how you would identify people with such a deep appreciation? What would you consider sound tests or screening processes? What would you think sound recruiting processes for such people? * * * Just as the coach of the football team is >normally expected to be a good athlete well beyond the capabilities of >the average high-school athlete, so should a high-school or even elementary >school mathematics teacher be a source of inspiration. Here, by contrast, I disagree with you; on the first half, not the second. The coach of a football team can operate from a wheelchair, or from crutches in the stands. What would be important, it seems to me, would be knowledge of the game and the intention to teach the kids the visualisation of learning strategies toward that knowledge. I agree with you, though, about inspiration. Again, as above, how do you intend to identify it? Or what would you consider a reasonable and testable proxy? * * * > >Currently, of course, we cannot attract people with the requisite combination >of people and technical skills into the school system, particularly at the >lower levels. There's an answer to this: it's called money. How much? When the candidates are half male, half female, you know you're hiring from the labour pool, not the cheap-labour pool. That's your first cut. Then you run your screening tests. If that doesn't give you enough, then you crank up the money to get more candidates. Some other benchmarks: if average income across the economy is $45,000 per family, then this should probably be your entry-level salary for teachers. (Or do you think teachers should be from the below average sector?) If the normal income of an anaesthesiologist is around $245,000 then you've got the range for a person with supervisory responsibility in currciculum. If the President of a major corporation usually gets $300 to 700,000, then you know what you ought to be paying State and Provincial top educational administrators. * * * > >Of course, the mathematics community itself is not immune to criticism in this >regard. Take the college level, at which I have some experience. The >"sexy" subject, regarded as the principal goal of a good engineering and >science student is Calculus, which, in my experience, is one of the most >bizarre and arcane subjects students ever encounter, being obsessed with >complex derivative and integral calculations of dubious value. > >The dreary subject, reserved for "slow" student and non-specialists, is >"Finite Mathematics". In my opinion, the topics in this course are far >more relevant to the ordinary experiences of people than first year calculus. Calculus was the fun paradigm for the age when change became general. I agree with you bout finite math: appropriate paradigm for the digital age. -dlj. ---