balden@wimsey.bc.ca (Bruce Balden) (05/06/91)
In article <a44e62141e672822fc7c@rose.uucp> david.lloyd-jones@rose.uucp (DAVID LLOYD-JONES) writes: >>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? > Identifying such people is not particularly difficult. However, enticing such people not to make three times as much in private industry is much harder. In addition, such people don't necessarily fare well in the current educational environment. Support in the form of classroom materials and school board policy is also necessary. For example, imagine the hue and cry that would ensue if a teacher said "I don't CARE if Johnny can multiply or not. Grow up! I have news for you. Einstein wasn't great at it either. Churchill was a positive dunce from this narrow perspective. Why do you suppose computers were invented? I care if he can ESTIMATE and APPROXIMATE, and, in general, do without exact data" > > 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. > The high school coach may be in a wheelchair, but more than likely he was once a fine (not necessarily a professional) athlete. His past achievements inspire the students as much as his current capabilities. >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? > Probably the simplest way would be to require a degree, preferably a Master's degree, in the subject. Currently, however, the system cannot afford this level of expertise. It can barely function at all. However, the onus is not entirely on the teacher himself, but on the system that surrounds him. A teacher, even a lacklustre one, can inspire a student if mechanisms exist for mathematics to be made prominent. In my original post, I was, indeed, thinking mostly of teachers who had been a part of the research community (not a Ph.D., but some sort of researcher assistant or lesser position) and so understood the role of the subject in the world and was not trapped into the vicious circle of artificial and unconvincing examples from the hoary past (eg. How old is Ann?) Therefore, we must think in terms of the athletics model, which involves people from everywhere, and deliberately avoids ghettoizing the subject. Even non-athletes can get involved via the school band, cheerleading, etc. > * * * >> >>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. > This is of course, a very important part of it: not enough importance is attached to the subject. People think that five years of math instruction in high school can erase the 7 years of brainwashing in the elementary schools. People are carefully taught from a very young age that mathematics is an elitist, difficult, and abstruse subject of little interest to anyone except a rocket scientist, and even discussions with rocket scientists (engineers) reveal their disdain for the subtleties of the subject. Presumably if we ever got past this mindset, there would not be such a thing as a whole establishment of elementary school teachers and the public at large with this attitude. Let us never forget that we're talking about a political agenda here: we are promoting the value of scientific thought from the earliest age. Just as present-day educators are called "The School Promoters", we are promoting the more general use of mathematical precision throughout human society, for that would be the inevitable result of more balanced mathematical education. Let us hope that we are ready for it if it happens. > * * * >>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. Calculus is a great topic, but not in its classic form, which like its analogues in primary school, it based on a model of algorithms and calculation rather than understanding. The advent of sophisticated mathematical desktop tools such as Maple has made the once impressive task of integration a matter of routine machine calculation. > Thanks for your support on this very important issue. > > -dlj. > P.S. further remarks are posted to sci.math > > >--- > > > -- DISCLAIMER: Opinions expressed are my own, not those of my employer. ******************************************************************************* * Bruce E. Balden Computer Signal Corporation Canada * * Thaumaturgist 225B Evergreen Drive *