870158a@aucs.UUCP (Benjamin Armstrong) (02/03/88)
I have, of late, become fascinated by the as yet unexplored possibilities for the use of computers in all levels of our education systems. A book called "Mindstorms" by Seymour Papert has been most influential in inspiring me to seek out and digest as much information regarding computers in education as I can. I have not yet, however, found discussions on the net concerning such topics as: the design and evaluation of educational software; the effects of introducing computers into the schools on the social organization of classrooms; "computer as teacher" vs. "computer as learning tool"; and the availability of microcomputers to students. I hope that someone out there will either offer me some opinions on the above topics or direct me to a newsgroup where such discussions take place.
870158a@aucs.UUCP (Benjamin Armstrong) (02/03/88)
This is the first time I have posted to the net. My .signature file was accidentally omitted from my previous note. Here it is:
870158a@aucs.UUCP (Benjamin Armstrong) (02/03/88)
Sorry, here's that .signature:
870158a@aucs.UUCP (Benjamin Armstrong) (02/03/88)
I'm really sorry about the last two failures to include my .signature file. I
didn't know about testing things locally before sending them. So here it is at
last, my .signature:
--
_______________________________________________________________________________ Ben Armstrong at Acadia University, Wolfville N.S. UUCP: {uunet|watmath|utai|garfield|mnetor}!dalcs!aucs!870158a BITNET: 870158a@Acadia INTERNET: 870158a@ACADIA.BITNET@CUNYVM.CUNY.EDUbwk@mitre-bedford.ARPA (Barry W. Kort) (02/09/88)
Benjamin Armstrong asks about computers in education. Sherry Turkle of MIT has written an excellent book on this subject entitled The Second Self: Computers and the Human Spirit. I found her book to be well-researched and well-written, sensitive, insightful, and thoroughly entertaining. I highly recommend it. She explores computer-mediated learning at all levels from pre-school (Merlin and Speak 'n' Spell) through primary-level software (e.g. Logo) to graduate level AI projects. Her main thesis is that computers are changing the way we think, and the way we think about the process of thinking. On Saturdays, I work at Computer Place at the Boston Museum of Science. Computer Place is a resource center where youngsters can explore the world of personal computers, with emphasis on educational software. A common theme in educational software is to set up the learning experience as a game, with amusing graphics and sound effects. I especially like the world geography lesson packaged as "Where in the World is Carmen Sandiego". Computers are accurate, infinitely patient, and highly interactive. In this regard, they surpass classroom teachers. I foresee the day when computers will mediate 80% of the learning, freeing educators to focus on special problems and enrichment beyond standard curricula. --Barry Kort
rapaport@sunybcs.uucp (William J. Rapaport) (02/09/88)
In article <817@aucs.UUCP> 870158a@aucs.UUCP (Benjamin Armstrong) writes: >...direct me to a newsgroup where such discussions take place. Try comp.ai.edu
rapaport@sunybcs.uucp (William J. Rapaport) (02/09/88)
In article <822@aucs.UUCP> 870158a@aucs.UUCP (Benjamin Armstrong) writes: > >I'm really sorry about the last two failures to include my .signature file. I >didn't know about You also might want to subscribe to news.announce.newusers, which, among other things, has a complete list of newsgroups.
dwt@zippy.eecs.umich.edu (David West) (02/12/88)
In article <23938@linus.UUCP> bwk@mbunix (Barry Kort) writes: >Computers are accurate, infinitely patient, and highly interactive. >In this regard, they surpass classroom teachers. Well, yes, but the things computers are best at teaching humans are, by and large, things that humans used to have to do only because they didn't have computers. Why train humans to emulate machines if you have adequate machines? -David West
elg@killer.UUCP (Eric Green) (02/15/88)
in article <776@zippy.eecs.umich.edu>, dwt@zippy.eecs.umich.edu (David West) says: >>Computers are accurate, infinitely patient, and highly interactive. >>In this regard, they surpass classroom teachers. > Well, yes, but the things computers are best at teaching humans are, > by and large, things that humans used to have to do only because they > didn't have computers. Why train humans to emulate machines if > you have adequate machines? Not to mention that while computers may be infinitely patient, students certainly aren't. After fairly rigorous research last fall in the major education journals, I came to a number of conclusions. First, teachers generally don't know what computers are or can do... images of huge rooms with whirring tape drives and white-smocked supplicants still are the image of computers for most teachers (as it is for the vast majority of the American people). I got a laugh out of a teacher who didn't know the difference between a terminal program and a modem. I got an even bigger laugh out of Education Digest actually printing the hair-brained article! (wherein the teacher discovers how to dump text from one Commodore 64 computer in his school, to another computer at another school). And second, when teachers do discover computers, inevitably it's used to inflict the three-B's of educational software upon unsuspecting students -- that is, software that's Boring, Banal, and just plain BAD. Come on, now, hasn't ANYBODY learned that there's more to intelligence than the filling station motif of learning? Pavlov's dogs and Skinner's rats are rats and dogs, fer cryin' out loud, not HUMANS! Hair-brained things such as multiplication drills in an age of $5 calculators are just plain silly.... I know that in grade school, I, at least, would have been FASCINATED to know WHY the multiplication algorithm worked. After all, it obviously did work... if I added up four 22's, I came to the same answer as 4*22... but nobody could tell me why. --- 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.
edwards@dogie.edu ( Mark Edwards) (02/16/88)
In article <3316@killer.UUCP> elg@killer.UUCP (Eric Green) writes: >>>In this regard, they surpass classroom teachers. >> Well, yes, but the things computers are best at teaching humans are, >> by and large, things that humans used to have to do only because they >> didn't have computers. Why train humans to emulate machines if >> you have adequate machines? >Come on, now, hasn't ANYBODY learned that there's more to intelligence than >the filling station motif of learning? Pavlov's dogs and Skinner's rats are >rats and dogs, fer cryin' out loud, not HUMANS! Hair-brained things such as >multiplication drills in an age of $5 calculators are just plain silly.... I >know that in grade school, I, at least, would have been FASCINATED to know WHY >the multiplication algorithm worked. I for one am certainly glad that I was drilled in multiplication tables and so on. I use them everytime I go to the SuperMarket. Of course if I was wealthy I would have some one else go for me. You see the prices on different items vary greatly. Sometimes its better to buy in bulk, sometimes its better to just buy more of the smaller packages. I guess I could always take a calculator with me, but it takes time to punch in the numbers, and I would forget it sometimes. Sometimes the computer breaks down, and the store clerks do the addition with pen and paper, or even a calculator. Sometimes the store clerks can't even add 1 + 1. With the advent of the UPIC codes, now the clerk justs shoots the gun at the thing I am buying. After these things are in use for a while, they will forget how to punch in the price the old fashion way. Now what if the gun breaks ? Life gets scarier and scarier every day. I have forgotten many things but I still can do my multiplication drills!!! mark -- edwards@vms.macc.wisc.edu UW-Madison, 1210 West Dayton St., Madison WI 53706
tlh@cs.purdue.EDU (Thomas L. Hausmann) (02/16/88)
In article <3316@killer.UUCP>, elg@killer.UUCP (Eric Green) writes: > in article <776@zippy.eecs.umich.edu>, dwt@zippy.eecs.umich.edu (David West) says: > ... when teachers do discover computers, inevitably it's used to > inflict the three-B's of educational software upon unsuspecting students -- > that is, software that's Boring, Banal, and just plain BAD. This I agree with, all too many "eduacational software packages" are video game-ish glorified drill and practice sessions. These effectively distract the student from learning to zapping aliens. > > ... Hair-brained things such as > multiplication drills in an age of $5 calculators are just plain silly.... I HOPE you mean that PROGRAMS to do multiplication drills are silly. For if students are trained to use calculators instead of doing the simple arithmetic by hand, they will be crushed down the road when it comes time to solve equations symbolically (having to do some symbol pushing.) The skills developed by NOT using a calculator are invaluable. I can forsee complaints like "...what do you mean "solve in terms of x, x is not a number!" coming from students because they are used to having push button answers. Use of calculators in the classroom is not a solved issue. However, I advocate that teachers either observe carefully how they are used or simply do not allow them on examinations (in high schools.) I fear that too many students will use them as a crutch for true understanding. (For example, I have seen college students use the stat functions to enter data and do calculations and arrive at correlation coef's of 1.2 or negative probabilities. All because they believe the "calculator is right." I fully realize that if they KNEW WHAT THEY WERE DOING they wouldn't make these mistakes. It is important (at least to me) that students understand they don't NEED a calculator to do everything. (Can you say divide by 10? 10000? 10E-50?) > > --- > 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. .^.^. Tom Hausmann . O O . tlh@mordred.cs.purdue.edu ( ARPA ) . v . ...!purdue!tlh ( UUCP ) / | | \ ./ \. "Whooo do ya think you're foolin' " ______mm.mm_____ \_/
hes@ecsvax.UUCP (Henry Schaffer) (02/17/88)
One can try to meet multiple needs when constructing an examination. Before calculators existed (B. C. E.?) calculation was included as part of the exam because it was part of ensuring that the person could solve the problem in real life. With calculators, the requirement for hand calculation has changed - and therefore the exam can change. Emphasis can be removed from the calculation, per se, to the principles. Fine - but how can this be done. One way I have used is to give exam questions which were simpler numerically - in which the numbers were (small) integers - so that the arithmetic became simpler to do - but the decision on *what* to calculate was no easier than before (and so it is now a larger part of the total work - of course it can also be made more difficult.) One can also pretty much leave out even that smaller amount of arithmetic and ask for the answer to tell what calculation has to be done. I was able to change my exams in this manner, and then it didn't make any perceptible difference whether or not the student brought a calculator to the exam. (In fact I used to warn my students that they would probably work more slowly with a calculator unless they had become fairly proficient in the use of all the functions they might have to use.) This does not address the question of whether proficiency in non-calculator arithemetic is desireable. (I personally am in favor of it - but perhaps I'm just being old-fashioned.) --henry schaffer n c state univ
nasa@ms.uky.edu (Eric T. Freeman) (02/17/88)
> I for one am certainly glad that I was drilled in multiplication tables and >so on. I use them everytime I go to the SuperMarket. Of course if I was... I think you are missing the point here...Nicholas Negroponte says what I am thinking far better than I ever could... Take a six-year-old from anywhere in the world and plunk him down in Paris to live for a year and they'll learn French - why not create a fictitious country called Mathland (in a computer) in which you could drop a child into and the child would learn math. This idea was originally Seymour Papert's. I think this type of application would enable a child to come away knowing far more and more importantly having a deeper understanding for math than simple drills. Eric Freeman Eric Freeman University of Kentucky Computer Science nasa@g.ms.uky.edu freeman@ssvs.gsc.nasa.gov
jad@dayton.UUCP (John A. Deters) (02/17/88)
In article <26@dogie.edu> edwards@dogie.macc.wisc.edu ( Mark Edwards) writes: > I for one am certainly glad that I was drilled in multiplication tables and >so on. I use them everytime I go to the SuperMarket. You see the prices >on different items vary greatly. Sometimes its better to buy in bulk, >sometimes its better to just buy more of the smaller packages. (tongue-planted-firmly-in-cheek) I shop at a store that prints 'unit of measure' pricing on the tags on the shelf ... ;-) -- -john deters Dayton Hudson Department Store Company uucp: rutgers!dayton!jad MIS 1060/700 on the Mall/Mpls, MN 55402 ARTHUR: "A scratch? Your arm's off!" BLACK KNIGHT: "It's only a flesh wound."
elg@killer.UUCP (Eric Green) (02/17/88)
in article <26@dogie.edu>, edwards@dogie.edu ( Mark Edwards) says: > In article <3316@killer.UUCP> elg@killer.UUCP (Eric Green) writes: >>>>In this regard, they surpass classroom teachers. >>> didn't have computers. Why train humans to emulate machines if >>> you have adequate machines? >> Hair-brained things such as >>multiplication drills in an age of $5 calculators are just plain silly.... I >>know that in grade school, I, at least, would have been FASCINATED to know WHY >>the multiplication algorithm worked. > > I for one am certainly glad that I was drilled in multiplication tables and > so on. I use them everytime I go to the SuperMarket. Wow. What an old argument. I grew up before the era of cheap calculators, and I STILL heard that argument from 90 year old math teachers (most of whom are still teaching the same thing that they taught 50 years ago, despite that the world has changed an aweful lot since then!). I, too, go shopping. Estimation skills are more useful than multiplication skills (gee, is 16oz at $1.73 a better bargan than 12oz at $1.34?). Can you say "straw man argument"? Spending hours and hours improving your speed of computing numbers was worthwhile before the advent of $5 calculators. But I would much rather that our school children be taught MATHEMATICS for those multitude of hours. Sure, teach them computation skills. But don't make mere arithmetic computation the only thing taught to our students, like it is today (at least in this state... from grades 1 through 6, adding, subtraction, multiplication, and division, day after day... blech!). Is it any wonder that the majority of the students in the local "gifted and talented" program despise "math" class, calling it boring and repetitive? Hey, has anybody read Heinlein's novel "Tunnel in the Sky" anytime in the last 30 years? Gosh, if only the future of math education had been so sparkling! Instead, we're still stuck in the 19th century.... -- 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.
smoliar@vaxa.isi.edu (Stephen Smoliar) (02/17/88)
In article <3221@arthur.cs.purdue.edu> tlh@cs.purdue.EDU (Thomas L. Hausmann) writes: > >I HOPE you mean that PROGRAMS to do multiplication drills are silly. For if >students are trained to use calculators instead of doing the simple arithmetic >by hand, they will be crushed down the road when it comes time to solve >equations symbolically (having to do some symbol pushing.) The skills >developed >by NOT using a calculator are invaluable. I can forsee complaints like >"...what do you mean "solve in terms of x, x is not a number!" coming from >students because they are used to having push button answers. > >Use of calculators in the classroom is not a solved issue. However, I >advocate that teachers either observe carefully how they are used or simply >do not allow them on examinations (in high schools.) I fear that too many >students will use them as a crutch for true understanding. (For example, >I have seen college students use the stat functions to enter data and do >calculations and arrive at correlation coef's of 1.2 or negative >probabilities. >All because they believe the "calculator is right." I fully realize that >if they KNEW WHAT THEY WERE DOING they wouldn't make these mistakes. It is >important (at least to me) that students understand they don't NEED a >calculator >to do everything. (Can you say divide by 10? 10000? 10E-50?) > I think that a good deal of the problem stems from teachers who think the objective of mathematics education is to get the student to "effectively emulate" a calculator. While such emulation practices are valuable in a clutch, overemphasizing them takes time away from the cultivation of skills which should not rely on the calculator. "Knowing what you are doing" is certainly a case is point. A more modest example is estimation. In all the formal education I received, I never had a teacher who emphasized getting the right order of magnitude for a result, as opposed to getting ever last digit exactly right. Since I come from the dark ages of the slide rule, I had to train myself in this technique in order to get any use out of that tool. Now it wouldn't surprise me to learn that this skill may have deteriorated entirely.
edwards@dogie.edu ( Mark Edwards) (02/18/88)
In article <8369@g.ms.uky.edu> nasa@ms.uky.edu (Eric T. Freeman) writes: >I think you are missing the point here...Nicholas Negroponte says what I >am thinking far better than I ever could... > > Take a six-year-old from anywhere in the world and plunk him down in > Paris to live for a year and they'll learn French - why not create a > fictitious country called Mathland (in a computer) in which you could > drop a child into and the child would learn math. > >This idea was originally Seymour Papert's. I think this type of >application would enable a child to come away knowing far more and >more importantly having a deeper understanding for math than simple drills. Perhaps I was. Mathland is an intriguing concept. However a year in France does not a Frenchmen make. The problem the six year old will have in learning math is that it is not relevant to anything he he finds of value. He can't eat it. It doesn't protect him. It can't resolve any of his bodily needs, or psychological needs. At the period of time in life that those math drills are being taught (or administered) the child has not progressed enough in development that he would understand any of the reasoning behind it anyways. It may quite possibly only be that the methodology that is currently in use limits this learning behavior. I think the breakthroughs are going to come when the computer is truly more intelligent than the child is. The computer will have to process speach, and be able to converse with the child. The current state of the art in Educational programming is quite primative. A humanlike robot probably will be a better teacher than a simple computer and keyboard. mark -- edwards@vms.macc.wisc.edu UW-Madison, 1210 West Dayton St., Madison WI 53706
tlh@cs.purdue.EDU (Thomas L. Hausmann) (02/18/88)
In article <3340@killer.UUCP>, elg@killer.UUCP (Eric Green) writes: > in article <26@dogie.edu>, edwards@dogie.edu ( Mark Edwards) says: > > In article <3316@killer.UUCP> elg@killer.UUCP (Eric Green) writes: > >>>>In this regard, they surpass classroom teachers. > >>> didn't have computers. Why train humans to emulate machines if > >>> you have adequate machines? > >> Hair-brained things such as > >>multiplication drills in an age of $5 calculators are just plain silly.... I > >>know that in grade school, I, at least, would have been FASCINATED to know WHY > >>the multiplication algorithm worked. > > > > I for one am certainly glad that I was drilled in multiplication tables and > > so on. I use them everytime I go to the SuperMarket. > > Wow. What an old argument. So what, so are proofs of the Pythagorean theorem and the infinite number of primes; they are still valid. > ... I grew up before the era of cheap calculators, and > I STILL heard that argument from 90 year old math teachers (most of whom are > still teaching the same thing that they taught 50 years ago, despite that the > world has changed an aweful lot since then!). I, too, go shopping. Estimation > skills are more useful than multiplication skills (gee, is 16oz at $1.73 a > better bargan than 12oz at $1.34?). Can you say "straw man argument"? How did you arrive at your ability to do estimation? Hmmm ... oh I don't know... SA- er ah PRACTICE? > > Spending hours and hours improving your speed of computing numbers was > worthwhile before the advent of $5 calculators. I contend it is still worthwhile. Can you say rational arithmetic? If I had a buck for everybody I have met who could not determine if 3/5 was greater than 4/7 without a calculator... Trivial operations like those taught in grades 5 and 6 are largely forgotten by people using calculators to the extent that mixing recipes for 12 people instead of 5 (for example) become a chore. (Hmmm let's see I need 4.128 cups of this...dang, is that right?) What has changed the MOST in the last 50 years is not MATHEMATICS, but TECHNOLOGY. I contend the best mathematicians today were educated in the same fashion as the best mathematicians 40 or 50 years ago. > ... But I would much rather that > our school children be taught MATHEMATICS for those multitude of hours. Sure, > teach them computation skills. But don't make mere arithmetic computation the > only thing taught to our students, like it is today (at least in this state... > from grades 1 through 6, adding, subtraction, multiplication, and division, > day after day... blech!). Is it any wonder that the majority of the students > in the local "gifted and talented" program despise "math" class, calling it > boring and repetitive? Do you then propose that we do NOT teach children to do long division? IF that is the case, when they are exposed to synthetic division of univariate polynomials in junior high, the generalization is not as simple. Also, I am almost sure you were exposed to elements of geometry, rational arithmetic and unit conversions while in elementary school. Long multiplication and division are taught in 4th grade (Minnesota) leaving time for more than just ARITHMETIC in elementary school. Likewise, knowing the multiplication facts leaves me more time to THINK about MATHEMATICS and I don't have to dink with ARITHMETIC. Similarly, memorizing integral tables my freshman year leaves me more time to think about MATHEMATICS and not CALCULUS. > > Hey, has anybody read Heinlein's novel "Tunnel in the Sky" anytime in the last > 30 years? Gosh, if only the future of math education had been so sparkling! > Instead, we're still stuck in the 19th century.... > No, I confess to not having read this book. However, you have piqued my curiosity. > -- > 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. My feeling is that elementary teachers often spend too much time having to discipline the kids. Further, el ed majors have spent too much time with pedagody and sometimes possess attitudes about math that then get communicated to the children. I have overheard conversations about how "I am no good in math, ...but I like children so I am in el ed...") But that is a whole new issue. .^.^. Tom Hausmann . O O . tlh@mordred.cs.purdue.edu ( ARPA ) . v . ...!purdue!tlh ( UUCP ) / | | \ ./ \. "Whooo do ya think you're foolin' " ______mm.mm_____ \_/
edwards@dogie.edu ( Mark Edwards) (02/18/88)
In article <3231@arthur.cs.purdue.edu> tlh@cs.purdue.EDU (Thomas L. Hausmann) writes: %In article <3340@killer.UUCP>, elg@killer.UUCP (Eric Green) writes: %> > %> > I for one am certainly glad that I was drilled in multiplication tables and %> > so on. I use them everytime I go to the SuperMarket. %> %> Wow. What an old argument. % %So what, so are proofs of the Pythagorean theorem and the infinite number of %primes; they are still valid. % %> ... I grew up before the era of cheap calculators, and %> I STILL heard that argument from 90 year old math teachers (most of whom are %> still teaching the same thing that they taught 50 years ago, despite that the %> world has changed an aweful lot since then!). I, too, go shopping. Estimation %> skills are more useful than multiplication skills (gee, is 16oz at $1.73 a %> better bargan than 12oz at $1.34?). Can you say "straw man argument"? % %How did you arrive at your ability to do estimation? Hmmm ... oh I don't %know... SA- er ah PRACTICE? ~ Many great arguments deleted. I agree that perhaps there should be time spent discovering new ways of instruction, and learning. However until then what has been proven to work in the past, has to be used today. I wish it were otherwise. Another argument for the drills is observation. I've seen so many people who could not add properly, do percentages (lets see whats a 20 percent discont on $18.99. Ah, well, thats 2 dollars right?), don't bother to compare prices etc. Perhaps this is an argument that there isn't enough time spent on drills! Perhaps it illustrates that not enough time is spent on practical drills (or giving students examples how they can be used in real life situations). mark -- edwards@vms.macc.wisc.edu UW-Madison, 1210 West Dayton St., Madison WI 53706
ok@quintus.UUCP (Richard A. O'Keefe) (02/18/88)
{I read this in comp.ai, but am following up in comp.edu, because
the discussion seems to have very little to do with AI.
}
In article <3340@killer.UUCP>, Eric Green writes
> Spending hours and hours improving your speed of computing numbers was
> worthwhile before the advent of $5 calculators. But I would much rather that
> our school children be taught MATHEMATICS for those multitude of hours. Sure,
> teach them computation skills. But don't make mere arithmetic computation the
> only thing taught to our students, like it is today (at least in this state...
> from grades 1 through 6, adding, subtraction, multiplication, and division,
> day after day... blech!). Is it any wonder that the majority of the students
> in the local "gifted and talented" program despise "math" class, calling it
> boring and repetitive?
>
> Hey, has anybody read Heinlein's novel "Tunnel in the Sky" anytime in the last
> 30 years? Gosh, if only the future of math education had been so sparkling!
> Instead, we're still stuck in the 19th century....
I read "Tunnel in the Sky". I don't remember anything particularly
sparkling about it; Panshin's "Rite of Passage" handled the theme
rather better, and had more to say about education generally.
I don't know how it's done here, but back home we picked up the
"New Mathematics" where children are taught all about sets and converting
to different bases and how Egyptians wrote numbers and what a commutative
operator is. Talk about *boring*. Talk about *remote* from the interests
of the children. Fortunately I just missed it. I don't remember finding
arithmetic drills boring, but then, the teachers kept giving me harder
examples to do. I suspect this is a general phenomenon: *solving* puzzles
that are hard enough to require some work but not so hard that you can't
do them isn't boring. My experience of University-level mathematics was
that I was constantly appealing to my understanding of ordinary arithmetic
for analogies. Telling me that '+' was a commutative operator didn't
help me understand '+'; telling me that the operation of an Abelian
group acts like '+' *did* help me understand Abelian groups. My mathematical
and computational "intuitions" are rooted in the *experience* of arithmetic.
I think we need three things in elementary arithmetic teaching:
principles: "This is WHY the addition algorithm works."
"Look: multiplication is based on divide-and-
conquer just like addition."
relevance: Accounting/shopping/planning examples.
How to read newspaper figures sceptically.
"How to lie with statistics."
drills! In computation. In comparison. In estimation.
In checking the plausibility of answers.roberta@eleazar.Dartmouth.EDU (Roberta Millstein) (02/19/88)
>> In article <3316@killer.UUCP> elg@killer.UUCP (Eric Green) writes: >Spending hours and hours improving your speed of computing numbers was >worthwhile before the advent of $5 calculators. But I would much rather that >our school children be taught MATHEMATICS for those multitude of hours. Sure, >teach them computation skills. But don't make mere arithmetic computation the >only thing taught to our students, like it is today (at least in this state... >from grades 1 through 6, adding, subtraction, multiplication, and division, >day after day... blech!). Is it any wonder that the majority of the students >in the local "gifted and talented" program despise "math" class, calling it >boring and repetitive? I was in one of those "gifted and talented" programs at that age and I too thought math class was boring and repetitive...that was because generally more drill was involved in regular classes than was necessary. That's why they *have* gifted and talented programs, to provide a more stimulating learning environment. However, that doesn't mean that some good drilling in arithmetic wasn't useful--I am a firm believer that a having a good strong base in things like mathematics makes all the difference when you have to conquer more complicated concepts, like algebra, calculus, etc. The fact that the students were bored was a function of the fact that they were in a program that was too easy for them, not that the drills were useless. For those that need the hours of drill to become proficient, however, they are very worthwhile.
henry@utzoo.uucp (Henry Spencer) (02/20/88)
Once it was the mark of an educated man that he could tell time by the sun,
without mechanical assistance. Can you?
--
Those who do not understand Unix are | Henry Spencer @ U of Toronto Zoology
condemned to reinvent it, poorly. | {allegra,ihnp4,decvax,utai}!utzoo!henrygilbert@hci.hw.ac.uk (Gilbert Cockton) (02/20/88)
In article <3316@killer.UUCP> elg@killer.UUCP (Eric Green) writes: > >After fairly rigorous research last fall in the major education journals, I >came to a number of conclusions. First, teachers generally don't know what >computers are or can do... >a teacher who didn't know the difference between a terminal program and a >modem. I got an even bigger laugh out of Education Digest actually printing >the hair-brained article! (wherein the teacher discovers how to dump text from >one Commodore 64 computer in his school, to another computer at another school) How about some rigorous research in the history of technology difusion? Tools and techniques in the agrarian revolution could take years to travel a few miles and decades to pass between regions. Things are different now, but improved communications don't have an automatic benefit, especially in the contemporary information explosion. The teachers' ignorance, and the enthusiasm for sharing banal-to-some discoveries is nothing to laugh at. Ignorance and lack of sophistication is rarely voluntary, especially amongst people whose access to information and time for accessing it is limited. Net users are quite priveleged with the speed with which their ignorance is corrected, although the ignorant may resist the benefit at times :-) We are in a minority with regard to this privelege. -- Gilbert Cockton, Scottish HCI Centre, Heriot-Watt University, Chambers St., Edinburgh, EH1 1HX. JANET: gilbert@uk.ac.hw.hci ARPA: gilbert%hci.hw.ac.uk@cs.ucl.ac.uk UUCP: ..{backbone}!mcvax!ukc!hci!gilbert
crm@duke.cs.duke.edu (Charlie Martin) (02/20/88)
In article <8194@eleazar.Dartmouth.EDU roberta@eleazar.Dartmouth.EDU (Roberta Millstein) writes: Path: duke!mcnc!uvaarpa!umd5!ames!aurora!labrea!decwrl!decvax!dartvax!eleazar!roberta From: roberta@eleazar.Dartmouth.EDU (Roberta Millstein) Newsgroups: comp.ai,comp.edu,comp.cog-eng Date: 18 Feb 88 22:43:58 GMT Article-I.D.: eleazar.8194 Posted: Thu Feb 18 17:43:58 1988 References: <26@dogie.edu <3340@killer.UUCP Reply-To: roberta@eleazar.Dartmouth.EDU (Roberta Millstein) Organization: Dartmouth College, Hangover,NH Lines: 25 Xref: duke comp.ai:1385 comp.edu:1004 comp.cog-eng:484 In article <3316@killer.UUCP elg@killer.UUCP (Eric Green) writes: Spending hours and hours improving your speed of computing numbers was worthwhile before the advent of $5 calculators. But I would much rather that our school children be taught MATHEMATICS for those multitude of hours. Sure, teach them computation skills. But don't make mere arithmetic computation the only thing taught to our students, like it is today (at least in this state... from grades 1 through 6, adding, subtraction, multiplication, and division, day after day... blech!). Is it any wonder that the majority of the students in the local "gifted and talented" program despise "math" class, calling it boring and repetitive? I was in one of those "gifted and talented" programs at that age and I too thought math class was boring and repetitive...that was because generally more drill was involved in regular classes than was necessary. That's why they *have* gifted and talented programs, to provide a more stimulating learning environment. However, that doesn't mean that some good drilling in arithmetic wasn't useful--I am a firm believer that a having a good strong base in things like mathematics makes all the difference when you have to conquer more complicated concepts, like algebra, calculus, etc. The fact that the students were bored was a function of the fact that they were in a program that was too easy for them, not that the drills were useless. For those that need the hours of drill to become proficient, however, they are very worthwhile. There exists a neurological disfunction analogous to dyslexia that makes calculation difficult: hours of drill at which the person fails over and over again does not make arithmetic skills better, but rather simply convinces the person of their lack of any mathematical talent. I think the real solution here --assuming it can be done-- is to somehow recognize individual needs and teach or train to best meet those needs. Saying, for example, calculators are good or bad in general doesn't seem to be all that helpful. -- Charlie Martin (crm@cs.duke.edu,mcnc!duke!crm)
tlh@cs.purdue.EDU (Thomas L. Hausmann) (02/21/88)
In article <1988Feb19.204048.3727@utzoo.uucp>, henry@utzoo.uucp (Henry Spencer) writes: > Once it was the mark of an educated man that he could tell time by the sun, > without mechanical assistance. Can you? It was also the mark of a mathematician to do long laborious computations by hand. As others have said, we need no longer do this (by hand) but drills have their place. -Tom
elg@killer.UUCP (Eric Green) (02/21/88)
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.jjboritz@watcgl.waterloo.edu (Jim Boritz) (02/22/88)
In article <1988Feb19.204048.3727@utzoo.uucp> henry@utzoo.uucp (Henry Spencer) writes: >Once it was the mark of an educated man that he could tell time by the sun, >without mechanical assistance. Can you? >-- To take this a little further... A useful skill that children developed was to read the time by the position of the big hand and the little hand. The proliferation of cheap digital watches has almost eliminated this ability. -- Jim Boritz jjboritz@watcgl.waterloo.edu Computer Graphics Lab University of Waterloo {allegra,utai,clyde}!watmath!watcgl!jjboritz
avr@mtgzz.UUCP (XMRP50000[jcm]-a.v.reed) (02/23/88)
In article <3437@killer.UUCP>, elg@killer.UUCP (Eric Green) writes: > 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! Only by North American standards. In the Lukasiewicz curriculum (used in Poland and, in slightly modified form, in Hungary, Japan and Korea) the Calculus is taught in the 5th and 6th grades. Adam Reed (mtgzz!avr)
livesey@sun.uucp (Jon Livesey) (02/23/88)
In article <3649@mtgzz.UUCP>, avr@mtgzz.UUCP (XMRP50000[jcm]-a.v.reed) writes: > In article <3437@killer.UUCP>, elg@killer.UUCP (Eric Green) writes: > > ..... > > 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! > > Only by North American standards. In the Lukasiewicz curriculum (used > in Poland and, in slightly modified form, in Hungary, Japan and Korea) > the Calculus is taught in the 5th and 6th grades. > Adam Reed (mtgzz!avr) Seconded. When I attended High School in the UK, we attacked the Calculus starting at age fourteen. When I started to teach CS undergraduates in the US, I was amazed by what they did not know. Jon.
glb@uvacs.CS.VIRGINIA.EDU (Gina L. Bull) (02/23/88)
(many lines deleted) > > I think the breakthroughs are going to come when the computer is truly > more intelligent than the child is. The computer will have to process speach, > and be able to converse with the child. The current state of the art in > Educational programming is quite primative. A humanlike robot probably will > be a better teacher than a simple computer and keyboard. > This paragraph is an example of one perspective on using computers in education. The computer teaches the child. There is another way to use computers. Would you say that a blackboard teaches the child? Or that the overhead projector teaches the child? No, a teacher uses a blackboard, or overhead projector, or computer, to teach the child. A lot of educators, programmers, and lay persons seem to believe that the goal of using computers in education is to replace the teacher. If this were the goal, then present day computers (and associated software) do have a long way to go. However, there are many teachers in school systems today, using the technology and software available today, who are using the computer to enhance their own teaching ability and to enhance the children's motivation to learn. They are not using the computer exclusively to drill multiplication tables (though this use does have its own niche). A PC with a few sensors attached enables students to collect and analyze weather data. The addition of a speech card turns a PC into a talking word processor. Special Education teachers in Charlottesville make their own custom-designed switches for physically handicapped students. The switches enable students who could not use a keyboard to control a computer. In summary, don't write off the use of computers in education because they are not currently "Socrates in a Box". They are being used in very effective and innovative ways by a lot of very effective and innovative teachers. Gina Bull Internet: glb@uvacs.cs.virginia.edu UUCP: uunet!virginia!uvacs!glb Bitnet: rlb0p@virginia
ain@s.cc.purdue.edu (Patrick White) (02/23/88)
[this article is still being cross posted... since I'm new to this discussion, perhaps someone else can suggest which *one* group this should be continued in] In article <29@dogie.edu> edwards@dogie.macc.wisc.edu ( Mark Edwards) writes: >%> ... I grew up before the era of cheap calculators, and I, however, grew up just as cheap calculators were beginning to become available. I still remember wondering as a child why we couldn't just use calculators when they were so much easier and one made fewer "simple math errors" with them. Now, I'm actually glad that all that "basic" math was drilled into my head. I'm not delusioned about it being fun since it never was, but rather I'm glad that I know how to do this basic math without a calculator. If my teachers hadn't been so strong headed about drilling us and not letting us use calculators in class, I probably wouldn't be as comfortable with math -- especailly without a calculator. I, for one, think that counts for something. So, I support learning basic math skills -- even if it requires drilling -- as math is a *very* important skill (especailly with all this techonology around) and I feel everybody should be comfortable with it. > Another argument for the drills is observation. I've seen so many people > who could not add properly, do percentages (lets see whats a 20 percent > discont on $18.99. Ah, well, thats 2 dollars right?), don't bother to > compare prices etc. I too have seen this, and when I do, I'm sad for these people -- not because they can't do the math (after all, there are tools that allow anyone to be able to calculate), but because they become afraid of math. And *that* is what I see as the saddest part. So, in conclusion, I feel that *everyone* should be comfortable with math -- whether it requires that they use calculators or not (hopefully not :-) -- Pat White UUCP: k.cc.purdue.edu!ain BITNET: PATWHITE@PURCCVM
crm@duke.cs.duke.edu (Charlie Martin) (02/24/88)
Posting-Front-End: GNU Emacs 18.47.4 of Sun Aug 9 1987 on duke (berkeley-unix) With reference to technology diffusion, you might be interested in the technology transfer literature. There are a few journals and such. It ends up being a sociological sort of problem, so really rigorous research is hard (-> infinity) to do, but the research that is around suggests some odd things: transfer isn't necessarily driven just by novelty and usefulness, and (at least in software) it takes much longer than might be expected for technology to transfer (avg 15 years.) I'll try to post a couple of TT journal names later today. -- Charlie Martin (crm@cs.duke.edu,mcnc!duke!crm)
hes@ecsvax.UUCP (Henry Schaffer) (02/25/88)
"The Feeling of Power" is an old SF story (50's or earlier?) about a man who re-discovered how to do arithmetic in a society which had become completely dependent on its machines. (Does anyone else remember this one- and remember the author?) --henry schaffer n c state univ
hes@ecsvax.UUCP (Henry Schaffer) (02/25/88)
In article <3319@watcgl.waterloo.edu>, jjboritz@watcgl.waterloo.edu (Jim Boritz) writes: > In article <1988Feb19.204048.3727@utzoo.uucp> henry@utzoo.uucp (Henry Spencer) writes: > >Once it was the mark of an educated man that he could tell time by the sun, > >without mechanical assistance. Can you? > >-- > > To take this a little further... > A useful skill that children developed was to read the time by the > position of the big hand and the little hand. The proliferation of > cheap digital watches has almost eliminated this ability. > -- > Jim Boritz jjboritz@watcgl.waterloo.edu There may be a new skill being developed - one which I find difficult. This is the ability to judge a time span from a glance or two at the face of the wristwatch or clock. I can just glance at my watch and tell about how much time I have left until the end of lunch hour/the lecture/whatever. That is, I can do this unless the watch is one of the digital types. (And it gets really bad when the period does not end on an even hour.) Maybe our children will develop wonderful arithmetical skill from trying to tell if they are late for their favorite TV program? :-) (This might take care of addition/subtraction - now what about multiplication/division?) --henry schaffer n c state univ
anderson@c10sd3.Comten.NCR.COM (Joel Anderson) (02/26/88)
Subject: Re: Becoming CAI literate
REMEMBER! REMEMBER??!!??
Of course I do -
Ever heard of "Isaac Asimov"? He's kind of a little known
hack writer......
(It can be found in his book Opus 100, if nowhere else) edwards@dogie.edu ( Mark Edwards) (02/26/88)
In article <4668@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes:
:
: There may be a new skill being developed - one which I find difficult.
:This is the ability to judge a time span from a glance or two at the face
:of the wristwatch or clock. I can just glance at my watch and tell about
:how much time I have left until the end of lunch hour/the lecture/whatever.
:That is, I can do this unless the watch is one of the digital types. (And
:it gets really bad when the period does not end on an even hour.)
:
: Maybe our children will develop wonderful arithmetical skill from
:trying to tell if they are late for their favorite TV program? :-)
:(This might take care of addition/subtraction - now what about
:multiplication/division?)
I agree, but until know I thought it was just my opinion. I find it
more difficult to use a digital watch. There is a base conversion
(base 60??) that must be done with a digital watch. While the
analog version is more like an icon. Perhaps there is no math
done at all. The position of the hands are roughly equivalent to
numbers, so I don't calculate anything. Maybe numbers are just too
abstract and do not really register. While my memory for pictures
is more meaningful.
mark
--
edwards@vms.macc.wisc.edu
UW-Madison, 1210 West Dayton St., Madison WI 53706tmy6405@acf3.NYU.EDU (Ted M. Young) (02/26/88)
In article <4667@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: > >"The Feeling of Power" is an old SF story (50's or earlier?) about a man >who re-discovered how to do arithmetic in a society which had become >completely dependent on its machines. (Does anyone else remember this one- >and remember the author?) >--henry schaffer n c state univ From what I recall (me and my 1K of brain-RAM :-), that story was written by Isaac Asimov. I think the story had to do with the guy being able to calculate trajectories of missiles, etc., then again, I might be mixing this up with a similar story, so if anyone is *positive* I'd appreciate confirmation, or otherwise. -- Ted M. Young \ tmy6405@acf3.nyu.edu 3801 Hudson Manor Terrace (#4h) / tmy6405@NYU-ACF3.ARPA (I think) Riverdale, NY 10463-1111 \ CIS: 76703,4343 (forever, I hope :-) --------------------------------------------------------------------------- "With Basic you just use a GOTO, with Pascal you have to indent 99% of the program halfway across the page!" -- Me (A Basic programmer for 12 years) ===========================================================================
kmgopinathan@violet.waterloo.edu (Krishna Gopinathan) (02/26/88)
In article <4667@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: >"The Feeling of Power" is an old SF story (50's or earlier?) about a man >who re-discovered how to do arithmetic in a society which had become >completely dependent on its machines. (Does anyone else remember this one- >and remember the author?) Isaac Asimov was the author of that story. However, it is interesting that in his Robots of Dawn/Robots and Empire series, he does not portray the future of mankind as being excessively machine-dependent. He brings the story around to show a possible dead-end that might occur due to an overabundance of robots (Spacer society), but expresses a (misplaced?) confidence in man not to fall into that trap. >--henry schaffer n c state univ -- krishna
hes@ecsvax.UUCP (Henry Schaffer) (02/26/88)
In article <546@acf3.NYU.EDU>, tmy6405@acf3.NYU.EDU (Ted M. Young) writes: > In article <4667@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: > > > >"The Feeling of Power" is an old SF story (50's or earlier?) about a man > >who re-discovered how to do arithmetic ... > > From what I recall (me and my 1K of brain-RAM :-), that story was written > by Isaac Asimov. ... > -- > Ted M. Young \ tmy6405@acf3.nyu.edu I've also received 2 votes for Asimov by mail. With a hot streak like this going - it couldn't have been anyone else - so in the grand usenet tradition I declare it to be Asimov. (Anyone with real knowledge can just drop the matter now.) --henry schaffer inews requires the following line (no kidding) :-)
ok@quintus.UUCP (Richard A. O'Keefe) (02/26/88)
In article <4667@ecsvax.UUCP>, hes@ecsvax.UUCP (Henry Schaffer) writes:
: "The Feeling of Power" is an old SF story (50's or earlier?) about a man
: who re-discovered how to do arithmetic in a society which had become
: completely dependent on its machines. (Does anyone else remember this one-
: and remember the author?)
The author was Isaac Asimov. The punch-line of the story was that
the rediscovery of arithmetic would enable a military break-through:
the manned missile.ruffwork@orstcs.CS.ORST.EDU (Ritchey Ruff) (02/27/88)
In article <11128@duke.cs.duke.edu> crm@duke.cs.duke.edu (Charlie Martin) writes: [...mucho removed...] > >There exists a neurological disfunction analogous to dyslexia that makes >calculation difficult: hours of drill at which the person fails over and >over again does not make arithmetic skills better, but rather simply >convinces the person of their lack of any mathematical talent. > >I think the real solution here --assuming it can be done-- is to somehow >recognize individual needs and teach or train to best meet those needs. >Saying, for example, calculators are good or bad in general doesn't seem >to be all that helpful. >-- >Charlie Martin (crm@cs.duke.edu,mcnc!duke!crm) This points out the difference between teaching and tutoring. Most people I've talked to who have been involved in both agree that tutoring is much more efficient from the students viewpoint, but teaching is much more effecient from the teachers viewpoint. I think this is the first real win we might see in ICAI; use the few really good humans to teach to classes, and have the many ICAI tutors go one-on-one with the students to find the misunderstanding and holes in the students knowledge and try to plug them. I can also imagen that the ICAI program would give feedback to the teacher on what is coming across to the class and what the teacher needs to spend more time on (just like a good T.A. will for the prof who is interested). --ritchey ruff ruffwork@cs.orst.edu -or- ...!hp-pcd!orstcs!ruffwork
dave@lsuc.uucp (David Sherman) (02/29/88)
elg@killer.UUCP (Eric Green) writes: > dwt@zippy.eecs.umich.edu (David West) says: > >>Computers are accurate, infinitely patient, and highly interactive. > >>In this regard, they surpass classroom teachers. > > Well, yes, but the things computers are best at teaching humans are, > > by and large, things that humans used to have to do only because they > > didn't have computers. Why train humans to emulate machines if > > you have adequate machines? > > ... > And second, when teachers do discover computers, inevitably it's used to > inflict the three-B's of educational software upon unsuspecting students -- > that is, software that's Boring, Banal, and just plain BAD. There is certainly lots of bad courseware around, but with some effort it can be done right. We teach income tax, accounting and other courses to 1,100 Bar Admission students each year with CAI, and I like to think we've done it right. Our courses are challenging and appear extremely "intelligent"; although we don't use any AI techniques, the simple mechanism of asking open-ended questions and telling the student *what* they're doing wrong when they make a mistake makes them think the computer is almost human. To that you have to add a certain bulletproofing to let your software respond sensibly to just about anything the student does. (Many of our students have never touched a keyboard before; and they get no human assistance in using the system, so it has to be completely self-explanatory.) Many of our students tell us that they find our CAI much more useful than lectures. If anyone is interested in our experiences, I can send a copy of "Computer-Assisted Instruction and Evaluation at the Law Society of Upper Canada", a paper I gave at the National Educational Computing Conference (NECC'87) in Philadelphia last June. Let me know whether you want a paper or an electronic copy. (On-line, it's 30K, with [nt]roff macros.) David Sherman dave@lsuc.uucp The Law Society of Upper Canada Osgoode Hall Toronto, Canada M5H 2N6 (416) 947-3466 -- { uunet!mnetor pyramid!utai decvax!utcsri ihnp4!utzoo } !lsuc!dave
kludge@pyr.gatech.EDU (Scott Dorsey) (03/01/88)
In article <4667@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: >"The Feeling of Power" is an old SF story (50's or earlier?) about a man >who re-discovered how to do arithmetic in a society which had become >completely dependent on its machines. (Does anyone else remember this one- >and remember the author?) Yes! It's by Isaac Asimov, and is collected in one of his short story volumes (maybe Nightfall and Other Stories?). This should be required reading for anybody designing user interfaces. Scott Dorsey Kaptain_Kludge SnailMail: ICS Programming Lab, Georgia Tech, Box 36681, Atlanta, Georgia 30332 "To converse at the distance of the Indes by means of sympathetic contrivances may be as natural to future times as to us is a literary correspondence." -- Joseph Glanvill, 1661 Internet: kludge@pyr.gatech.edu uucp: ...!{decvax,hplabs,ihnp4,linus,rutgers,seismo}!gatech!gitpyr!kludge
andrea@hp-sdd.HP.COM (Andrea K. Frankel) (03/02/88)
In article <48@dogie.edu> edwards@dogie.macc.wisc.edu ( Mark Edwards) writes: >In article <4668@ecsvax.UUCP> hes@ecsvax.UUCP (Henry Schaffer) writes: >: >: There may be a new skill being developed - one which I find difficult. >:This is the ability to judge a time span from a glance or two at the face >:of the wristwatch or clock. > I agree, but until know I thought it was just my opinion. I find it > more difficult to use a digital watch. There is a base conversion > (base 60??) that must be done with a digital watch. While the > analog version is more like an icon. Perhaps there is no math > done at all. The position of the hands are roughly equivalent to > numbers, so I don't calculate anything. Maybe numbers are just too > abstract and do not really register. While my memory for pictures > is more meaningful. True story: About ten years ago, during a college "stop-out" period, I worked as a math teaching assistant at a local high school. Due to budget cuts, there were approximately n/2 classes after Christmas break, and the slower students in the classes that had been slightly behind were totally lost. Another assistant and myself held small tutoring classes in the study hall, to try to bring these students up to speed. What I discovered was a fundamental lack of grounding in basic concepts. I'm talking about "gut-level" understanding, e.g. of the difference between area and volume (which I finally got across through creative destruction of a ream of xerox paper ;@) Most of the difficulties came to light while working word problems, since they require students to think about the world and make the correlation to the mathematical concepts and formulas. Fractions were a big, big problem. And guess what? Those kids with the most problems with fractions had grown up with digital watches and digital clocks (or in a couple cases, no clocks) in their homes. Granted, this is far from a scientific sampling, but I was intrigued enough to question all my kids, and it came out to something over 85% of the kids who couldn't look at a pie chart and tell me that the red portion was about 1/3 of the pie, had digital-only backgrounds, and out of the rest of the class (who were not having serious problems with fractions) the average was only about 25%. There were a fair number of the "normal" kids who were now wearing digital watches, and had digital alarm clocks etc., but who had grown up with an analog Mickey Mouse strapped to their wrist. I bet there's some critical age interval when we assimilate that skill, of glancing at an unlabelled clock or pie chart and being able to tell what fraction of the hour or pie it represents. Myself, I'm more strongly kinaesthetic than visual, and I find it impossible to get a good *feel* for time when it's presented to me in numbers! And when I look at pie charts, larger fractions feel "heavier" to me, almost as if I were holding chunks of pie in my hands (on second thought, make that Brie ;@) The pie analogy, by the way, is how I finally got fractions taught - the students who couldn't tell me which pie slice represented a larger number had no problem telling me which piece of apple pie they'd rather be given! Andrea Frankel, Hewlett-Packard (San Diego Division) (619) 592-4664 "...like a song that's born to soar the sky" ______________________________________________________________________________ UUCP : {ihnp4|decwrl|sun|tektronix|<other hub>}!hplabs!hp-sdd!andrea or {nosc|hpfcla|sdcsvax}!hp-sdd!andrea Internet : andrea%hp-sdd@ {nosc.mil | sdcsvax.ucsd.edu | hplabs.HP.com} CSNET : andrea%hp-sdd@hplabs.csnet USnail : 16399 W. Bernardo Drive, San Diego CA 92127-1899 USA
gilbert@hci.hw.ac.uk (Gilbert Cockton) (03/02/88)
In article <2253@uvacs.CS.VIRGINIA.EDU> glb@uvacs.CS.VIRGINIA.EDU (Gina L. Bull) writes: >The computer teaches the child. There is another way to >use computers. Would you say that a blackboard teaches the child? Or >that the overhead projector teaches the child? No, a teacher uses a >blackboard, or overhead projector, or computer, to teach the child. Many Indo-European languages suffer from the pathological antinomy between subject and object. Either X effects Y, or Y effects X. Thus the computer TEACHES the child. The introduction of a human agent using computers/blackboards/OHPs as an instrument, does not change the fundamental activeness/passiveness of the subject-object relationship. Basque has an 'ergative' case, which has been characterised as carrying the role of a fully co-operating, active object. In Basque, 'to teach' takes the ergative. In this sense of teaching, a computer could only teach a child IF it was capable of co-operative interaction. Watch a good classroom teacher and you will see that interaction is a set of social skills, with good interaction defined differently according to the embracing culture(s). So the question is, can computers be programmed to demonstrate the social skills underpinning succesful interaction? Do the people who like programming most have these skills themselves :-) If not, computers can never rise beyond instruments in learning situations. they will not teach any more than a book does, or a flight-simulator without an instructor. -- Gilbert Cockton, Scottish HCI Centre, Heriot-Watt University, Chambers St., Edinburgh, EH1 1HX. JANET: gilbert@uk.ac.hw.hci ARPA: gilbert%hci.hw.ac.uk@cs.ucl.ac.uk UUCP: ..{backbone}!mcvax!ukc!hci!gilbert
dave@lsuc.uucp (David Sherman) (03/03/88)
ruffwork@orstcs.CS.ORST.EDU.UUCP (Ritchey Ruff) writes: >This points out the difference between teaching and tutoring. Most people >I've talked to who have been involved in both agree that tutoring is >much more efficient from the students viewpoint, but teaching is >much more effecient from the teachers viewpoint. I think this is the first >real win we might see in ICAI; use the few really good humans to teach >to classes, and have the many ICAI tutors go one-on-one with the >students to find the misunderstanding and holes in the students >knowledge and try to plug them. You don't need ICAI to do this. You need: (1) questions that are open-ended rather than multiple choice; (2) a log mechanism for recording unexpected answers; (3) an easy-to-use on-line comment capability that practically forces students to say what they think of the instruction [ours asks for comments on each signoff]; and (4) a mechanism for easily modifying your program or CAI script to deal with multiple incorrect answers. We've done it with our tax courses and students are amazed at how "intelligent" and responsive the CAI is, telling them *exactly* what they're doing wrong every time they make a mistake. What they're seeing is the product of endless revision of the course to fine-tune it to deal with the specific mistakes that students make. The fine-tuning is based on both the log files and the on-line comments. (To people who have requested a copy of my paper on our experiences: will be mailing it out in a few days.) David Sherman The Law Society of Upper Canada -- { uunet!mnetor pyramid!utai decvax!utcsri ihnp4!utzoo } !lsuc!dave
johnson@c10sd1.StPaul.NCR.COM (Wayne D. T. Johnson) (03/04/88)
In article <1988Mar2.125247.28809@lsuc.uucp> dave@lsuc.UUCP (David Sherman) writes: >What they're >seeing is the product of endless revision of the course to fine-tune >it to deal with the specific mistakes that students make. I must commend you and your institution on discovering what many instructors (and most software companies) have failed to realize, a program must be continued to be modified or "fine-tuned" throughout its life in order for it to be usefull to its users. So many times I have seen a program "die" because it was no longer being kept up to date. This is one of the needs that AI can provide to CAI, the computer can (without human intervention) adjust its methodes to best suite the individual student. I dare say I have seen a few human instructors that have been so set in their ways (i.e. curriculum) as to completly ignore the needs of the student.
rwojcik@bcsaic.UUCP (Rick Wojcik) (03/09/88)
gilbert@hci.hw.ac.uk (Gilbert Cockton) writes:
GC> Many Indo-European languages suffer from the pathological antinomy
GC> between subject and object. Either X effects Y, or Y effects X. Thus
GC> ...
GC> Basque has an 'ergative' case, which has been characterised as
GC> carrying the role of a fully co-operating, active object. In Basque,
GC> 'to teach' takes the ergative. In this sense of teaching, a computer
GC> could only teach a child IF it was capable of co-operative
GC> interaction. Watch a good classroom teacher and you will see that
I don't think that there is a real semantic difference between ergative and
accusative languages, as your note suggests. Both language types have subjects
and direct objects. The only real difference is in transitive sentences, where
an accusative language marks some relationship (e.g. verbal agreement) between
the verb and subject. An ergative language marks a relationship between the
verb and direct object. In fact, the pattern of an active transitive sentence
in an ergative language is similar to a passive sentence in an accusative
language. The superficial resemblance derives from the fact that ergative
sentence patterns often originate from passives historically. But this does
not mean that speakers of ergative languages have a different conception of
'activeness' of subjects and objects than do speakers of accusative languages.
--
Rick Wojcik csnet: rwojcik@boeing.com
uucp: {uw-june uw-beaver!ssc-vax}!bcsaic!rwojcik
address: P.O. Box 24346, MS 7L-64, Seattle, WA 98124-0346
phone: 206-865-3844henry@utzoo.uucp (Henry Spencer) (03/10/88)
>This points out the difference between teaching and tutoring. Most people >I've talked to who have been involved in both agree that tutoring is >much more efficient from the students viewpoint, but teaching is >much more effecient from the teachers viewpoint... More efficient from both viewpoints, actually, for many things, is to use people for tutoring and *textbooks* for teaching. I have never understood why it is desirable to lecture at people who know how to read. (Of course, these days one cannot take that for granted in freshmen...) The valuable time of the teacher should be used for demonstrations, questions, helping people who are having trouble, leading discussions, and so forth, *not* for regurgitating canned material. This does presume good textbooks or the equivalent, like mimeographed lecture notes. That is, it requires *preparation*, not a big favorite of lazy teachers. It also requires effort by the students, not a big favorite of lazy students. The only way to make sure this actually happens is constant feedback, i.e. frequent assignments or quizzes. Yes, I know there are some lecturers who can make the subject "come alive" in a way that a run-of-the-mill textbook can't. However, (a) there are damn few of them, and (b) they should be spending their time writing *good* textbooks so more people can benefit from their skills. (I should add that I think CAI has much promise as "interactive textbooks", although existing systems often don't do a very good job of it, and has at least limited promise for helping students with difficulties, many of which are just as stereotyped as the contents of a typical textbook. [And thus should be dealt with once and for all via printed matter or software, not with expensive human effort every time they occur.] One should consider first, though, whether mundane devices like books can do the job.) -- Those who do not understand Unix are | Henry Spencer @ U of Toronto Zoology condemned to reinvent it, poorly. | {allegra,ihnp4,decvax,utai}!utzoo!henry
dave@lsuc.uucp (David Sherman) (03/10/88)
henry@utzoo.uucp (Henry Spencer) writes: >(I should add that I think CAI has much promise as "interactive textbooks", >although existing systems often don't do a very good job of it, and has at >least limited promise for helping students with difficulties, many of which >are just as stereotyped as the contents of a typical textbook. If you ask open-ended questions (Down With Multiple Choice!), and log all unexpected answers, you can very quickly come up with all of the answers to students' difficulties. It takes a little effort on the part of the course author, and a centralized system (which is why our stuff is all UNIX-based rather than available on PC's). One also has to be somewhat creative in figuring out how the computer will respond to each particular error. ("You've correctly calculated the allowable capital loss, but you've forgotten that it can only be applied against taxable capital gains. Try again.") David Sherman The Law Society of Upper Canada -- { uunet!mnetor pyramid!utai decvax!utcsri ihnp4!utzoo } !lsuc!dave
870158a@aucs.UUCP (Benjamin Armstrong) (03/11/88)
In article <1988Mar9.183038.915@utzoo.uucp> henry@utzoo.uucp (Henry Spencer) writes: >More efficient from both viewpoints, actually, for many things, is to use >people for tutoring and *textbooks* for teaching. I have never understood Even in lectures where the degree of interaction is very low, a good lecturer (and I have had a few) can present the material in a much more accessible form than in the texts which accompany the course. I agree; the texts should be what teaches the student. However, the professor should give shape to the raw material provided by the texts in a way which fits her own style and the needs of her students in lectures before moving on to questions, demonstrations, etc. You can't expect the texts, even good texts, to be entirely suitable to the course. You might argue that in such cases, the professor should write lecture notes, photocopy them, and distribute them to the class. While this may work in some courses (e.g. introductory courses), I feel that the presentation of a lecture by word of mouth, particularly as the student progresses to higher level courses, is a vital element of the social fabric of the classroom. A great deal more of the lecturer goes into a lecture than can ever be put into lecture notes or a textbook, and without that expression of himself, I fail to see how the channels of communication between the professor and the students will be opened. Demonstrations and questions must be about something. Without the context of a lecture, the often vague recollections of the students are the only fuel for discussions. Why do we spend thousands of dollars inviting guest speakers to come speak at our universities when it would be much cheaper and, as you seem to claim, more efficient to just distribute copies of an article written by the would-be speaker? Is it just the thrill of hearing someone famous? Oratory, so far as I can see, will never be replaced by texts in our universities because it has proven over the centuries to be one of the most effective and engaging modes of teaching there is. >damn few of them, and (b) they should be spending their time writing *good* >textbooks so more people can benefit from their skills. Ask some professors if they have the time or resources to write a textbook. The ones I know don't. Have you ever written a textbook? If you have, tell me if it was easy. -- Ben Armstrong at Acadia University, Wolfville N.S. UUCP: {uunet|watmath|utai|garfield|mnetor}!dalcs!aucs!870158a | In quest of BITNET: 870158a@Acadia | a cure for INTERNET: 870158a@ACADIA.BITNET@CUNYVM.CUNY.EDU | technophobia...
cik@l.cc.purdue.edu (Herman Rubin) (03/13/88)
In article <934@aucs.UUCP>, 870158a@aucs.UUCP (Benjamin Armstrong) writes: > In article <1988Mar9.183038.915@utzoo.uucp> henry@utzoo.uucp (Henry Spencer) writes: > Even in lectures where the degree of interaction is very low, a good lecturer > (and I have had a few) can present the material in a much more accessible form > than in the texts which accompany the course. I agree; the texts should be > what teaches the student. However, the professor should give shape to the raw > material provided by the texts in a way which fits her own style and the needs > of her students in lectures before moving on to questions, demonstrations, > etc. You can't expect the texts, even good texts, to be entirely suitable to > the course. For the courses I have taught over the years, I have found few textbooks which I would even call reasonable. The only one which I consider well-written was written by two authors, with each part gone over by many people; unfortunately, this book was obsolete when it came out. I do know of a few fairly well- written books; in none of the cases is the book, even if there is only a single author, the work of a single person. I do not mean that some chapters are done by X and some by Y---I mean that no part of the book is the result of the efforts of one individual. Another problem is that the books are almost universal in slighting the concepts in favor of manipulation. One can question whether this is not unavoidable. For example, the calculus course has three concepts, and each of them can be stated, and well illustrated, in a few pages. I think that it should be considered criminal to pass a student who does not have a reasonable understanding of those concepts. I would be surprised if 20% of the students taking calculus meet these standards. I am not even sure how many of the teachers understand the concepts! The bulk of the course is devoted to those manipulations which can easily be done by computers. The ability to do these manipulations is useful, but without the concepts is even dangerous. A problem with teaching concepts is that one student learns them in minutes while another takes months. The solution clearly requires that we abandon some of the structure of our educational system, and our evaluations should denote only knowledge and ability, and time and effort should be ignored. BTW, I agree that a lecture is a bad way to present material. However, the lecture with discussion is a good one. Unfortunately, it is difficult to get students to ask questions _because they are afraid of betraying their ignorance_. How can we get them to realize that not asking questions is evidence of stupidity? And the question should be asked when the material is unclear. Frequently, the instructor should tell the student to work on the problem and come back if it is still unclear, but frequently the matter should be handled immediately. With a textbook, this is impossible. > You might argue that in such cases, the professor should write lecture notes, > photocopy them, and distribute them to the class. While this may work in > some courses (e.g. introductory courses), I feel that the presentation of a > lecture by word of mouth, particularly as the student progresses to higher > level courses, is a vital element of the social fabric of the classroom. > A great deal more of the lecturer goes into a lecture than can ever be put > into lecture notes or a textbook, and without that expression of himself, I > fail to see how the channels of communication between the professor and the > students will be opened. Demonstrations and questions must be about something. > Without the context of a lecture, the often vague recollections of the > students are the only fuel for discussions. > > Why do we spend thousands of dollars inviting guest speakers to come speak > at our universities when it would be much cheaper and, as you seem to claim, > more efficient to just distribute copies of an article written by the would-be > speaker? Is it just the thrill of hearing someone famous? Oratory, so far > as I can see, will never be replaced by texts in our universities because it > has proven over the centuries to be one of the most effective and engaging > modes of teaching there is. > Ask some professors if they have the time or resources to write a textbook. > The ones I know don't. Have you ever written a textbook? If you have, tell > me if it was easy. I have not written a textbook, nor do I have the talent. However, I have been a collaborator in writing books, and I have contributed to the writing of textbooks by others. I do not believe that, unless there is already a good textbook, a good textbook for a one-semester course can be written with less than two man-years of professor time. For a one-year course, the time should be at least three man years. Who is going to support this effort? About 25 years ago, some of my colleagues and I investigated the possibilities for one course, for which there still is no good text, and we found that no such funding was available. (I would not have been one of the people funded.) Textbooks should be written by those faculty members who are both good at exposition and are also active scholarly. Under the present circumstances, to do a good job they would have to almost abandon scholarly activity for a considerable period of time. They, and we, cannot afford that, with the possible consequences that their scholarly prowess may be harmed. Thus, the textbook situation will not improve. Even worse is the situation that many of my colleagues seem unable to teach a course without following a textbook. Of the courses I took, I claim that the better ones did not have a textbook! The problems are not going to be solved tomorrow. Our books try to limit the students to the level of the computer. Are these cookbook courses better than teaching nothing? In some cases, I believe the answer is no. Are our students brain-damaged before they even get to the universities. I emphatically say they are. Can this be reversed? I do not know. -- Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907 Phone: (317)494-6054 hrubin@l.cc.purdue.edu (ARPA or UUCP) or hrubin@purccvm.bitnet
johnson@c10sd1.StPaul.NCR.COM (Wayne D. T. Johnson) (03/15/88)
In article <934@aucs.UUCP> 870158a@aucs.UUCP (Benjamin Armstrong) writes: >Even in lectures where the degree of interaction is very low, a good lecturer >(and I have had a few) can present the material in a much more accessible form >than in the texts which accompany the course. This quarter I'm taking SPE105 (Introductory Public Speaking). In the very first chapter of the text there is a discuession on the way people "model" a public speaker's role. In one model the speaker/listener relationship is one way, the speaker speaks and the listener listens. The other model includes a feedback channel, where the speaker can sense the attitude of the audience and adjust their presentation accordingly. Example: If a number of students start yawning, it is obvious that the speaker needs to increase the audiances participation, via one of several methods. There is also feedback of a less immediate sort, how many students flunk the course. You also get into the question of how do we decide who these super lecturers are, so that they can write the texts that is. -Wayne Johnson
andrea@hp-sdd.HP.COM (Andrea K. Frankel) (03/16/88)
In article <707@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: >Another problem is that the books are almost universal in slighting the >concepts in favor of manipulation. One can question whether this is not >unavoidable. For example, the calculus course has three concepts, and >each of them can be stated, and well illustrated, in a few pages. I think >that it should be considered criminal to pass a student who does not have >a reasonable understanding of those concepts. I would be surprised if >20% of the students taking calculus meet these standards. I am not even >sure how many of the teachers understand the concepts! The bulk of >the course is devoted to those manipulations which can easily be done by >computers. The ability to do these manipulations is useful, but without >the concepts is even dangerous. > >A problem with teaching concepts is that one student learns them in minutes >while another takes months. The solution clearly requires that we abandon >some of the structure of our educational system, and our evaluations should >denote only knowledge and ability, and time and effort should be ignored. The only course I ever took which had a fairly satisfactory solution to this problem was the frosh physics course at CalTech. We used three different textbooks: the Feynman Lectures (big red books) for pure concepts, the L/V problem set books that went along with them, and "Holiday and Grundgenik" (I forget the real name) to learn the mechanics of manipulation of formulae and such. Lectures were based on Feynman and were 100% concepts; recitation sections were based on the other books and were devoted to teaching us how to do the problems. If you slacked off on reading Holiday and Grundgenik, doing the homework and attending recitation sections, and spent all your time grokking the great Feynman prose, it was possible to learn all the concepts beautifully and not be able to solve a single problem on the tests. However, if you managed to scribble convincingly on your test in a way that demonstrated mastery of the concepts involved in the question (but without making any headway on getting the answer), it was possible to pass (but just barely). I understand that they have since discontinued the three-textbook approach. Pity. Feynman was the only thing that made physics remotely palatable! Andrea Frankel, Hewlett-Packard (San Diego Division) (619) 592-4664 "...like a song that's born to soar the sky" ______________________________________________________________________________ UUCP : {ihnp4|decwrl|sun|tektronix|<other hub>}!hplabs!hp-sdd!andrea or {nosc|hpfcla|ucsd}!hp-sdd!andrea Internet : andrea%hp-sdd@ {nosc.mil | sdcsvax.ucsd.edu | hplabs.HP.com} CSNET : andrea%hp-sdd@hplabs.csnet USnail : 16399 W. Bernardo Drive, San Diego CA 92127-1899 USA
gls@odyssey.ATT.COM (g.l.sicherman) (03/16/88)
> More efficient from both viewpoints, actually, for many things, is to use > people for tutoring and *textbooks* for teaching. I have never understood > why it is desirable to lecture at people who know how to read. ... Benjamin Armstrong has replied fully to most of Henry's points. I'd like to add that the static quality of print is better suited for some subjects than others. When I was teaching c.s., I found that I could portray things that were *happening* in the computer with some quick eraser work on the chalkboard, far more effectively than the textbook could portray them with sequences of diagrams. You can overwrite memory on a chalk- board; you can't on a printed page. Then, too, c.s. is hard for most of the students who take it up, and their difficulties and misunderstandings require especial apprehension and wit to clear up. My students, bless them, were quick to interrupt with questions for me, and I in turn threw plenty of questions at them. Of course you can say the same of lecturers as of textbooks--the good ones are too few! -- Col. G. L. Sicherman ...!ihnp4!odyssey!gls