Xref: utzoo comp.edu:1847 sci.math:5338 Path: utzoo!attcan!uunet!lll-winken!ames!mailrus!csd4.milw.wisc.edu!markh From: markh@csd4.milw.wisc.edu (Mark William Hopkins) Newsgroups: comp.edu,sci.math Subject: Re: the why of math Message-ID: <366@csd4.milw.wisc.edu> Date: 12 Jan 89 22:48:53 GMT References: <605@ucrmath.EDU> <6578@killer.DALLAS.TX.US> <783@odyssey.ATT.COM> Sender: news@csd4.milw.wisc.edu Reply-To: markh@csd4.milw.wisc.edu (Mark William Hopkins) Organization: University of Wisconsin-Milwaukee Lines: 65 In article <783@odyssey.ATT.COM> gls@odyssey.ATT.COM (g.l.sicherman) writes: >In article <6578@killer.DALLAS.TX.US>, elg (Eric Green) writes: >> in article <605@ucrmath.EDU>, marek@ucrmath.EDU (Marek Chrobak) says: >> > Xref: killer comp.edu:1858 sci.math:5231 sci.physics:5475 >> > a proof. In Herman's terms, the question WHY does not cross >> > their mind. They just want to know HOW. ... >> > It would be silly to blame the students for this. This is the >> > way they have been taught in school, it's no wonder this is >> > what they expect from college. >> >> Sounds like you're blaming the teachers. You shouldn't. They're doing >> the best they can, with what little knowledge they have. Blame college >> curriculums which do not include any "Basics of Mathematics" courses, >> only tons of courses in equation manipulation (Algebra, Trig, ... But it is very easy to blame the emphasis the curriculum places on teaching topics divorced from their CONTEXT. And that is the essential problem. And if courses had been taught with that kind of emphasis of teching topics in the context of their use in high-school (as common sense should have disctated) then there would not be such a need for the remedial courses of the college curriculum. No human being who has mastered a human langauge (which takes much more effort than learning any mathematical field), should be having problems learning math if it were taught the right way. In a basic Algebra course, context means real-life "word problems". In a Calculus course it means teaching Calculus and Physics together as one course (as they should have been in the first place). The reader is urged to build up more examples of this nature. (:-)) When you rip away at the delicate interrelatedness of the major sciences, you end up refashioning all of Mathematics as an abstract pen-game, and their "applications" as esoteric fields that use the abstract math that no one could learn very well because it was taught in the abstract. We have to remember that humans develop abstractions on the basis of prototypes. They cannot learn new abstractions until they have been thouroughly grounded in prototypical examples. Likewise, they cannot fully understand the significance of those self-same "applications" until they have learned the "theoretical" issuies behind it. I make no distinction between "theory" and "application", because I don't make the mistake of trying to learn something out of its context. In fact, this is how I was able to teach myself calculus in high-school in a relatively short time -- I was using it to work on a Physics-based orbit simulation. >(Engineers are) biggest "consumers" of mathematics, and they need techniques >rather than derivations for nearly all their work. For any good (= non recipe reading) engineer, techniques *are* derivations -- and that is how "deriavtions" should be taught. >If they are interested in the derivations, they can take "honors" mathematics. >But I would rather cross a bridge built by an engineer who knows the formulas >thoroughly than by one who knows some of the formulas and can derive >the rest! I'd rather cross a bridge made by engineers who have both the basic intuition of their field *and* the deep knowledge of "theoretical" mathematics (as well as a good background in the Humanities and a good ability to write good expositories). >> Is it any wonder why your typical bright and impatient student hates >> "math"? It's BORING! I have yet to meet a person who I couldn't help overcome that delusion.