Xref: utzoo comp.ai:1359 comp.edu:896 comp.cog-eng:478 Path: utzoo!utgpu!water!watmath!clyde!burl!codas!killer!elg From: elg@killer.UUCP (Eric Green) Newsgroups: comp.ai,comp.edu,comp.cog-eng Subject: Re: Becoming CAI literate Message-ID: <3437@killer.UUCP> Date: 21 Feb 88 08:23:55 GMT References: <1988Feb19.204048.3727@utzoo.uucp> Organization: Bayou Telecommunications Lines: 77 There's a lot of interesting points in this discussion. Rather than post 15 replies, I'm going to heavily summarize (Chuq, don't faint! Someone read your guide to USENET posting!). First: Mathland, and "relevance": People who say "if it's taught, it should be relevant" generally are the same people who say "god, I'm lousy in xyz, I don't want to take it at all, I shouldn't have to take it". For example, it's common to hear CS freshmen at USL comment, "god, I wish I didn't have to take {history, foreign language, english literature}, I'll never use it, so what's the use?". Inevitably, you find out that he's barely literate, or is atrocious in grammar, or otherwise is not good in that subject. In general, saying that children will not be able to "relate" to software that embodies the "mathland" concept is grossly under-estimating the native intelligence of children. For example, I've seen a 7 year old playing "Cave of the Word Wizard" off and on for the last 6 months (it's basically the same thing as that old TI "Speak & Spell" game)... that 7 year old isn't interested in "relevance". All he cares about is that it's interesting and challenging. The following comments are about the contention that calculators are harmful, hours and hours of math drills are useful and entertaining, and our school children do not need to learn mathematics, all they need is arithmetic: Re: It was good enough for yesterday, why isn't it good enough for today? The answer is simple: It wasn't good enough for yesterday (at "elite" academies, the children of the well-to-do recieved much more math education than today's children), and it's not good enough for today. If you remember the statistics I posted about engineering enrollments, the primary reason 70% of our engineering enrollment is foreign-born is that most Americans do not have the math education to succeed in engineering school. Re: Drills help later in life, when you want to apply what you've learned in elementary school to higher mathematics: I remember when I first saw simple algebra problems. "What's all these funny x and y and z things? I thought all you could add was NUMBERS!". One problem I had was that I thought of numbers as something concrete, instead of as arbitrary symbols that happen to sometimes be related to physical phenomena. Note that I do NOT say that math drills and teaching computation methods should be banned from our schools. Merely that they should be minimized in favor of teaching actual mathematics. The main problem, of course, is that there are no elementary school teachers who KNOW mathematics... which is why the fabled "New Math" of the 1960's failed utterly and totally. Not only was it "new" to the students.... it was new to the teachers, too! Not to mention that those textbooks were as sterile as the current ones... most mathematics textbooks seem to think that mathematics occurs in a vacuum, and make no attempt to relate new ideas to ideas already assimilated (perhaps even actual PHYSICAL things, egads.... e.g. derivatives & falling objects). Which is probably why 50% of one professor's students fail, and only 10% of another professor's students fail... one scribbles the textbook on the board, the other makes an attempt to actually explain the cryptic material in the textbook. Since an elementary school teacher is incapable of explaining the cryptic material in the textbook, such an approach was doomed to failure from the beginning. Re: Heinlein's "Tunnel in the Sky": I've always wondered why (some) people praise Heinlein (or at least "early" works of his). The book is lousy. But there's one scene, where the protagonist is watching wagon trains go through the "tunnel", where we learn that he, a high school student, has passed well beyond Calculus in his mathematics education -- and that such is the norm for high school students in his society. What an optimist Heinlein was! Oh dear. I must apologize for this long and rambling bulletin. The state of our educational system is one of my "pet peeves", as I believe that education is inexorably tied in with the rest of our society: the social problems of crime and poverty (both mostly the province of the poorly educated), social injustice, the future of humanity, and other things of that nature. -- Eric Lee Green elg@usl.CSNET Asimov Cocktail,n., A verbal bomb {cbosgd,ihnp4}!killer!elg detonated by the mention of any Snail Mail P.O. Box 92191 subject, resulting in an explosion Lafayette, LA 70509 of at least 5,000 words.