Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!decvax!decwrl!pyramid!hplabs!hplabsc!taylor From: taylor@hplabsc.UUCP Newsgroups: mod.comp-soc Subject: Re: Calculators and Understanding Message-ID: <401@hplabsc.UUCP> Date: Tue, 1-Jul-86 18:25:30 EDT Article-I.D.: hplabsc.401 Posted: Tue Jul 1 18:25:30 1986 Date-Received: Wed, 2-Jul-86 07:04:15 EDT References: <383@hplabsc.UUCP> Reply-To: hplabs!weemba@brahms.berkeley.edu Organization: Hewlett-Packard Laboratories Lines: 125 Approved: taylor@hplabs -------- This article is from weemba@brahms.berkeley.edu (Matthew P. Wiener) and was received on Tue Jul 1 12:58:41 1986 -------- Seems we just had this debate concerning word processing! In article <383@hplabsc.UUCP> gmp@rayssd (Gregory M. Paris) writes: > >Discourages understanding? How does memorizing the multiplication tables >from 1 to 13 encourage understanding of multiplication? How does doing >endless addition of 4 digit numbers encourage understanding of addition? >These are things that children are forced to do in elementary school, and >I contend that these things are counter to understanding. I fail to see >how adding tedium to a child's education, or to any task in general, can >aid understanding. This is seems even more apparent when dealing with >complex engineering or scientific matters, where complex mathematical >tasks are carried out by computers, leaving humans to do the interpretation >and understanding of the results. Computers and calculators have *freed* >people to concentrate their mental abilities on understanding the problem >at hand. In the vernacular above, this is a good thing. You've touched a nerve here. First off, there's a lot of bad teaching out there, and you are kidding yourself if you are blaming it on the material. Using calculators does not change this. Indeed, I believe they encourage bad teachers to do worse. I do not believe understanding of anything difficult can come cheap and easy. I do not believe that having a computer changes that. I believe having a computer allows for greater realism in designing curricula. And nothing more. I am not happy with the standard curricula, by the way. But that has nothing to do with my beliefs concerning calculators and computers in the classroom. These machines come with an aura of perfection. Why? I have no idea. But this aura is very damaging to students. Most of them have no sense of magnitude anymore. They assume they entered the data in perfectly. They can't do back-of-the-envelope calculations. They are unable to estimate. They turn in pages of output called results. They give ans- wers with meaningless precision. (Even the ones who know better will reflexively quote their digital watches if asked for the time. Aargh!) [Jon Bentley (`Programming Pearls') has an amusing anecdote about the precision of answers - he asked a student once how long a program took to run. The student answered "about 150" "150 what?" "Umm..either micro- seconds or milliseconds, I'm not sure". Needless to say, there is a BIG difference between the two! -- Dave] Do the students learn to think now that the computer has "freed" them? No. They learn how to run someone else's program. They learn how to specify options on a command line. Do they learn how to understand what they are doing? No. They become industrial strength bean counters. When the task gets complicated, do they first approach the easy cases? No. They have learned to jump right into the hardest messes, because of the unlimited power the computer gives them. They will go for the three hundred parameter model when a mere five will do, enamored of their numeric power, hypnotized by the formal simplicity, and blissfully unaware of the ludicrousness of their enterprise. They have no failsafe instincts. They have no way of checking anything. They are the vanguard of the new innumeracy. They will wander in foggy Numberland forever if permitted. ------------------------------------------------------------------------ The above article refers to students, and is based on what I've seen far too often, even among "A" students. Who "they" are is not really spelled out, of course. And once "they" get out into the real world, some common sense returns. But a lot of damage is done first, and I believe the way computers are used is a major contributor to this process. ------------------------------------------------------------------------ I'd like to quote Forman S Acton _Numerical Methods that Work_, pp245-6, with a parallel attitude to a slightly different concern: Although we have no desire to blunt the enthusiam of the neophyte computor, many of whose excesses must be charged to the educational process, we would be remiss if we did not raise the spectre of uncritical wastage of computa- tional resourses by persons who are old enough to know better. We grudgingly concede that there are times when it is better to use the computer inefficiently than to saddle a professor with a laborious search for a better algorithm; nevertheless enough identifiable nonsense goes on in th computer room to justify a brief but hopefully cautionary exhibit. We begin with a personal experience. [1949 2 day inversion of a 16x16 matrix of 10-digit num- bers. Turned out the matrix was orthogonal, which could have been verified in 10 minutes from the original formu- lae for the matrix entries.] We were less than overjoyed, although--philosophically speaking--it was a good test of our inversion routine. In this day of electronic computation one might argue for the uncritical inversion of such a matrix on the grounds that it only takes fractions of a second while the proof of orthogonality would require minutes and might not then succeed--indeed, the matrix might not even be orthogonal. Why not invert and be done with it? But in 1949 we who had striven mightily for two days had no such perspec- tive. We were angry and with reason. Somebody had not done his proper homework and we had to suffer for it. Your author, in 1970, still opposes this kind of uncrit- ical, shoot-from-the-hip computation. It is an outward and visible sign of an inward and intellectual deficiency. It epitomized the "Why think? Let the computer do it" re- action that, unchecked, quickly undermines any critical review of either the direction or the value of an inves- tigation. The computer is a precision tool. It should not be used as a bludgeon or a substitute for thought. As the S Harris cartoon punchline goes (roughly): "Yu meen Iv bin using a defektiv speling program?" ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720