taylor@hplabsc.UUCP (06/28/86)
ties on understanding the problem at hand. In the vernacular above, this is a good thing. [An interesting point...it seems we need to really define what 'knowledge' is. A similar problem exists in the AI community - what exactly IS intelligence? Does the Turing test still exist as the bottom line?? If not, what IS the criterion for intelligence? -- Dave]
taylor@hplabsc.UUCP (07/01/86)
-------- This article is from ihnp4!rayssd!gmp (Gregory M. Paris) and was received on Mon Jun 23 05:31:07 1986 -------- 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. [An interesting point...it seems we need to really define what 'knowledge' is. A similar problem exists in the AI community - what exactly IS intelligence? Does the Turing test still exist as the bottom line?? If not, what IS the criterion for intelligence? -- Dave]
taylor@hplabsc.UUCP (07/02/86)
-------- 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
taylor@hplabsc.UUCP (07/02/86)
-------- This article is from taylor@hplabs.HP.COM (Dave Taylor, the moderator) -------- >Matthew Wiener comments on some of Gregorys' comments; >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 don't agree. I think that the quality of teaching is completely independent from the tools available to the teacher. It's all too common to hear teachers lament that they don't have good enough textbooks, or fast enough computers or whatever and so their teaching suffers. Well, from my experience as both a student and a teacher, the materials are a MEANS to the END, NOT the END. That is, if a person is a good teacher, they can be given a nail and a slab of clay and can teach their students MORE than the person next to them with their high-powered computing environment. Some of the best teachers I've ever had were forced to pay for Xeroxes for the class out of their own pockets, or requested that all the students go and buy some (cheap) book for the class... On the other hand, one of the worst teachers I've ever had, in College, had at his disposal millions of dollars worth of computing equipment and assumed that it could REPLACE his teaching. Needless to say it didn't work real well. Calculators are the same way ... >I do not believe understanding of anything difficult can come cheap and >easy. I do not believe that having a computer changes that. I disagree again. I think that a teacher who is really excellent can introduce extremely complex subjects in such a way that the students intuitively grasp the basic fundamental concepts involved and then build up from there. Again, from my experiences, the way I help people learn Pascal is to turn away from the computer and talk to them until THEY understand the problem, THEN they can figure out the program. Again, it's a question of HOW you teach. >These machines come with an aura of perfection. Why? I have no idea. Because that's how teachers, and by inference, society, views them. If a teacher turned around to their students and said "here's a typical dumb machine - let's figure out how to force it to do what we want" then it'd be totally different to the current "here's the *hushed voice* computer we'll be using this quarter..." >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. Again, it's a function of the teaching. Just like any other subject. Let's look at writing, for a second... Most English teachers are of the 'grammar and rules' school of writing, and when students turn in papers they are immediately downgraded for typos, or grammatically awkward phrases. No heed is paid to the CONTENT, just the FORM. By comparison, teachers who concentrate on the CONTENT and assume that the FORM will improve by virtue of the student caring more about their work help students LOTS MORE. Peter Elbow wrote a very interesting book on this sort of topic called `Writing Without Teachers'... I think that we've hit a signficant juncture in this conversation, actually. The form versus content debate seems to be just the right one for this entire discussion - should we be concerned with students learning to 'depend' on calculators for simple math, or should we be concerned with students being able to solve more complex problems by virtue of being able to utilize a calculator efficiently. Like it or not, the days when we would spend years computing 'PI' to the five-hundredth digit are long gone... >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. This is a function of the teaching style - having a more powerful problem solver doesn't help anyone if they don't know how to approach solving problems...I think that it wasn't as critical in the 'old days' since it was so rare that people would try to solve substantial problems, of the magnitude of, say, what NASA Ames does with their multiple Crays... >They will wander in foggy Numberland forever if permitted. Sounds like a mathematics graduate student to me! *humour* > It epitomized the "Why think? Let the computer do it" reaction that, > unchecked, quickly undermines any critical review of either the direction > or the value of an investigation. The computer is a precision tool. > It should not be used as a bludgeon or a substitute for thought. Agreed. But it's not reasonable to place the blame on the students with the pejorative "they should know better". As Bell Telephone system used to try to convince us; "The System IS the Solution" -- Dave
taylor@hplabsc.UUCP (07/04/86)
This article is from Eugene Miya <ames!aurora!eugene> and was received on Wed Jul 2 18:52:16 1986 In reply to Greg. There is fuzzy, not well understood value in rote behavior (not that I encourage full time rote behavior). Before we throw the TIMES tables away, we should discuss it a little bit. It should be a bit more than past discussions about the loss of tying shoelaces. (Did you follow any of that?) People (humans) have an amazing capacity to infer information in many ways based on past rote beahvior. Much of it has to do with pattern recognition. Feynman and other relate an interesting story that Bethe, he, and another a third scientist simultaneously solved a problem: Bethe got the order of magnitude and first digit, (I note a lot of interesting in Jon Bentley's recent column on back of the envelope checking), the third scientist used a slide rule getting three digits (not much slower), and the guy (I think Feynman) used a calulator: more digits (needed), but slowest. I don't think removing rote behavior would make us more creative, but I think we should consider what we are trying to achieve in learning/teaching. Give them calculators, but only after they have a degree of understanding. Another posting, worried about Big Brother monitoring the work place sounds more like a problem with managers. It sounds like management has become a rote number calculation rather than a creative, human endeavor. Too much power to unthinking MBAs? The problem lies with the people teaching managers in this in appropriate way. If giving people calcuators is going to result in the above, time to go into hiding..... Start "the revolution." "The usual disclaimers." from the Rock of Ages Home for Retired Hackers: --eugene miya NASA Ames Research Center eugene@ames-aurora.ARPA
taylor@hplabsc.UUCP (07/08/86)
This article is from pyramid!utzoo!henry (Henry Spencer)
and was received on Mon Jul 7 15:12:29 1986
> [...assorted comments about how calculators are ruining education...]
I'm told that a couple of centuries ago, it was a mark of an educated
man that he could tell time without mechanical assistance. Nowadays,
most everybody relies on mechanical aids, i.e. wristwatches. Nobody
complains about this degeneration of essential skills.
In a similar vein, somebody once asked Grace Hopper about the purported
"dehumanizing" aspects of computer-mediated communications. Her reply
was "I remember when they said that about telephones".
Henry Spencer @ U of Toronto Zoology
{allegra,ihnp4,decvax,pyramid}!utzoo!henrytaylor@hplabsc.UUCP (07/13/86)
This article is from pyramid!prls!philabs!pwa-b!mmintl!franka and was received on Sat Jul 12 22:53:56 1986 >> [...assorted comments about how calculators are ruining education...] > >In a similar vein, somebody once asked Grace Hopper about the purported >"dehumanizing" aspects of computer-mediated communications. Her reply >was "I remember when they said that about telephones". Of course, they may have been right. I'm at least half-serious here. Any intermediary in communication reduces the quality of the communication. This includes computers, telephones, the written word, the neighborhood gossip, and what have you. The flip side, of course, is to ask what communication would have occurred without the technology. Very often, the answer in each of these cases is "none" -- in which case the technology is a clear win; or some other intermediary is used -- in which case it often is. But there are cases where the technology is harmful, not beneficial; and one cannot a priori rule out the possibility that such harm outweighs the benefits. That said, it seems clear to me that in general, the benefits of new communications technology *does* outweigh the disadvantages. Frank Adams ihnp4!philabs!pwa-b!mmintl!franka Multimate International 52 Oakland Ave North E. Hartford, CT 06108