balden@wimsey.bc.ca (Bruce Balden) (05/03/91)
In article <1991May3.124454.12758@watdragon.waterloo.edu> mcramer@watdragon.waterloo.edu (Mert Cramer) writes: >> Perhaps I should have elaborated when I suggested that >> math teachers should be given more help in motivating their students. >> This, I believe, would certainly include being able to show the real world >> relevance of the topic. > >The notion that, within the present framework, any change in maths instruction >will make a difference is naive. An informative discussion of the development >(or not) of maths skills in pre-school children is in a BBC documentary called >"Four plus four equals the wings of a bird". Among the points it makes: >1. For most people math is something you do at a desk and has no relivance to > life problems. >2. The formal method of teaching math makes the subject which the student > encounters which is NOT concrete (numbers apply to anything) hard to > visualize. >3. The teaching of math concepts by exploration rather than by lecture is > a more effective technique. > >This film was presented on David Suzuki's "The Nature of Things" program a >few years ago. I recorded it but since is was the first use of my VCR it is >a bit ragged. If you are in the Waterloo, Ont. area and want borrow the tape >let me know. > >One the major points in the film is that the curiosity about math and numbers >is largly destroyed by the usual techniques of promary teaching. You might say >that anyone who has an interest in math by the time they get to university >has survived in spite of all formal education has tried to do to them. >Of course, the university maths education is in exactly the same distructive >mold as all that went before so that anyone who survives at the univ. level >is either really dedicated and intersested in math or a masochist (or both). I agree with the BBC program's points, but I as I said in the post to which Mr. Kramer replies, the problems run deeper than mere motivation. The "let's discover mathematics in everyday life" approach IS very useful. However, the mathematics they discover there will not necessarily be identical with the traditional topics discussed in the schools. Generally speaking, once you succeed in getting people interested in scientific investigation, of which mathematics is the most general tool, then their appetite for mathematical sophistication can grow quite quickly. The game played between physicists (the real-world modellers) and the mathematicians (the high priests of logic) is legendary. Physicists are constantly trying to use the latest and greatest mathematical machinery. Nevertheless, solving physics-style questions generally requires too much machinery to be practical at a young age. In addition, such questions are not at the root of everyday life. Another field of endeavour that is very important is economics. Here in Canada, the income tax system recently changed from a system of tax-deductions to "non-refundable tax credits." Basically, under the old system, familiar to Americans, if your Net income is A and your deductions are B, then in the lowest tax bracket your federal income tax is 0.17*(A-B). Under the new system your federal income tax is 0.17*A, but you have a "non-refundable tax credit" of 0.17*B. This difference socks you if you're in a higher tax bracket. My point is that this new system is driving Canadians CRAZY and acocuntants cannot explain it to the majority of their clients no matter how hard they try, even though for the majority of taxpayers (those with lower incomes), it makes practically no difference at all. This inability of the Canadian (and probably American) public to understand the simplest economic/mathematical ideas seriously impairs the quality of public debate in Canadian society. Returning to my original point, understanding economics requires some participation in a model economy, such as Harvard business students do in the Harvard Business Game, and may require a completely different emphasis in education than that of the traditional mathematics curriculum. In other words, mathematics is everywhere, from the budget of the football team, to the acoustics of the gymnasium to cooking in the school cafeteria, to world economics, to music, and I feel that "mathematics", per se, must become a subject that students DEMAND in order to fully understand these other things. This requires a more scientific and quantitative approach to these other endeavours, but nothing else will make the subject relevant. The football coach knows that success for his team involves more than good players and practice sessions: it requires constant pep talks, and involvement of the entire school to be point where other players in the school complain. I DARE scientists and mathematicians to enter the body politic of the school in this forceful a manner. MEET the football coach on his own terms. COMPETE fgor the hearts and minds of the students. They have limited time for the school. The FOOTBALL COACH and the DRUG DEALER are winning. -- DISCLAIMER: Opinions expressed are my own, not those of my employer. ******************************************************************************* * Bruce E. Balden Computer Signal Corporation Canada * * Thaumaturgist 225B Evergreen Drive *
doner@henri.ucsb.edu (John Doner) (05/05/91)
In article <1991May03.151809.17836@wimsey.bc.ca> balden@wimsey.bc.ca (Bruce Balden) writes: >This inability of the Canadian (and probably American) public to understand >the simplest economic/mathematical ideas seriously impairs the quality >of public debate in Canadian society. Perhaps things aren't all that bad. My own experience is that it takes patience and a little creativity in formulating explanations. A few years ago, I was foreman of a jury considering a personal injury case. The plaintiff's lifetime earnings were going to be substantially less as a result of the injury. The judge instructed us, as the law required, to use a table giving present value of future income in figuring damages--we were supposed to supply our estimate of the appropriate discount rate (interest rate) to use for the table. My fellow jurors did not understand the concept involved. But after I explained it about five times in as many different ways, they got the idea. In the hallway after the trial, we chatted with the lawyers. One said, "You USED the table? I don't understand that; the JUDGE doesn't understand it. You're the first jury I've had that used it." There's a communication gap between the mathematically inclined and others. Abstract concepts which seem trivially simple to us may be obscure to the average person. So don't give up too easily when you need to explain some mathematical idea. John E. Doner doner@henri.ucsb.edu (805)893-3941 Dept. Mathematics, UCSB, Santa Barbara, CA 93106
balden@wimsey.bc.ca (Bruce Balden) (05/05/91)
In article <11053@hub.ucsb.edu> doner@henri.UUCP (John Doner) writes: >In article <1991May03.151809.17836@wimsey.bc.ca> balden@wimsey.bc.ca (Bruce Balden) writes: >>This inability of the Canadian (and probably American) public to understand >>the simplest economic/mathematical ideas seriously impairs the quality >>of public debate in Canadian society. > >Perhaps things aren't all that bad. My own experience is that it >takes patience and a little creativity in formulating explanations. A [ OMITTED: Uptlifting story about juries, when properly instructed understanding annuity tables, despite judges not understanding said tables] I, in fact agree, that the average person, even the mythical mathematical blockhead has the ability to understand sophisticated concepts WHEN PROPERLY MOTIVATED. I should have amended my original comment to: The ignorance of the Canadian and American publics of the basics of mathematics and economics ... I DO NOT imply that it is hopeless to teach them, but rather that their experience with the subject tends to make them regard the subject as either irrelevant or far more complex and difficult than it really is. >few years ago, I was foreman of a jury considering a personal injury >case. The plaintiff's lifetime earnings were going to be >substantially less as a result of the injury. The judge instructed >us, as the law required, to use a table giving present value of future >income in figuring damages--we were supposed to supply our estimate of >the appropriate discount rate (interest rate) to use for the table. >My fellow jurors did not understand the concept involved. But after I >explained it about five times in as many different ways, they got the >idea. > >In the hallway after the trial, we chatted with the lawyers. One >said, "You USED the table? I don't understand that; the JUDGE doesn't >understand it. You're the first jury I've had that used it." > >There's a communication gap between the mathematically inclined and >others. Abstract concepts which seem trivially simple to us may be >obscure to the average person. So don't give up too easily when you >need to explain some mathematical idea. > >John E. Doner doner@henri.ucsb.edu (805)893-3941 >Dept. Mathematics, UCSB, Santa Barbara, CA 93106 -- DISCLAIMER: Opinions expressed are my own, not those of my employer. ******************************************************************************* * Bruce E. Balden Computer Signal Corporation Canada * * Thaumaturgist 225B Evergreen Drive *