My students would often ask me why mathematics was inflicted upon them. If the student was in the sciences, the answer was more or less obvious but seldom expressed: You have a problem. You collect data, organize it and use the organized data to solve the problem. That is what mathematics is about.
Mathematics also provides techniques to solve particular kinds of problems and unfortunately courses in mathematics give a lot of time to techniques and very little to understanding.
Pre-med students were particularly vocal in their distain of, say, algebra. But it seems to me that diagnosis is the collection of data, organizing the data, and using the data to deduce the cause of a patient's discomfort. Not too much different that finding out how long it takes Joe and Harry to paint the house together.
Of course the budding doctors do have a point in that the algebra course (and prehaps the required calculus course) was probably more about memorization than investigating the power of rational thought in solving problems.
I must admit that the ability to memorize is a valuable skill for a doctor, all those bones and blood vessels have names. I wish I would have thought of that point when I was teaching the course. Or maybe not. Why would I think of ways to justify a teaching technique that I think is counter productive to rational thought.
I think that rational thought should be an element in all teaching. It can't hurt. An artistic person told Richard Feynman that knowing the chemical composition of a rose didn't give one an appreciation of the rose. Feynman replied that he may not see everything in a rose that an artist does but that it can't it can't hurt to know more about a rose.
Mathematics is a model of rational thought. If a person doesn't want to think rationally I guess that's their business. I had a person tell me that they didn't believe in rational thought. They made their decisions intuitively. Well, it's a free country and I suppose if a person wants to intuit their way through life, then so be it. But even if a person always decided to follow their gut feeling, how much could it hurt to put a little rational thought into the hopper.
I guess how much it could hurt is another topic for another day.
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Phil Maersch
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Agreed: If the student WERE in the sciences, the answer WOULD BE more or less obvious. Interesting premise: If a student is "in the sciences" then he must have mathematics. The contrapositive: If a student does not take mathematics then he must not go into the sciences. The vast majority of students do not go into the sciences, so why are they subjected to mathematics? An aside: I define "Mathematics" as Algebra and up -- everything else is arithmetic, which, unfortunately, is taught so poorly that mathematics is made doubly difficult for teacher and student. When an algebra book has a chapter on percents we are in trouble! Yes, doctors use rational thought -- don't we all? --and yes, mathematics is a model for rational thought. Premise: Mathematics --> rational thought. But be careful not to reason from the inverse: no mathematics --> no rational thought. I do not accept the premise that learning mathematics makes you a better thinker. I believe that for that majority of students who do not need mathematics the learning of it is so frustrating that, rather than enhancing their thinking, it makes them stop thinking completely -- they learn algebra, for example, as a "bag of tricks" rather than a logical thought process; they become worse thinkers!
But the solution to our problems with mathematics education does not lie in the positing and discussing of these premises. I propose a two pronged solution. Make sure that by the 9th grade all students are as good at arithmetic and they can be -- and I mean substantial arithmetic, like the stuff I had to learn in 8th grade (I'm 70). By the way, 5th graders studying "algebra" is oxymoronic! There's a lot of subtle algebra in good arithmetic problems. Second: indentify and/or channel each students interests and abilities so that by 9th grade they will know whether they want to go into the sciences and therefore continue into mathematics. Let them make the decision rather than subjecting them all to mathematics and make the "decision" one borne out of frustration. Two benefits: because they are good at arithmetic the mathematics will come more naturally and we won't have to water the course down -- and thereby cheat the good students -- in order to accomodate that vast majority of students who shouldn't be there in the first place.
Thanks!
The vast majority of students do not go into the sciences, so why are they subjected to mathematics? An aside: I define 'Mathematics' as Algebra and up : everything else is arithmetic, which, unfortunately, is taught so poorly that mathematics is made doubly difficult for teacher and student.
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