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A recurrent feaure of this forum is a thread in which we all decry the use of calculators by school children. But rarely does anyone here espouse the other side. Consider this
Quote:
Great as has been the impact of the technical calculator, it is small in our society compared with that of the simple fourfunction machine. For every professional calculator sold, dozens of these "four bangers" find their way into the average persons hands. ... ... the ordinary calculator makes instant errorfree arithmetic available to everyone. Clerks and waiters use them to add bills, housewives use them to compare prices and check the clerks, school children use them to do thier homework.
Whenever a new tool of wide utility appears, everyone who grew up with having to do the job the hard way feels relieved. But at the same time he is denied the sadistic pleasure of watching his children endure the same hardships. The use of the pocket calculator by children is a prime example. Today's parents are asking "Is my child really learning arithmetic? In my day we had to practice long division for years. Today all they do is push buttons." I'm sure the same questions were asked when logarithms were invented. Certainly they were when the slide rule came into widespread use.
Whenever such an innovation occurs something is lost and something is gained. I think we must be prepared to find our children less facile than we at carrying out arithmetic operations in longhand; they will have had less practice. But for the same reason more of their time can have been spent learning the concepts and priinciples, not only of arithmetic, but of higher mathematics as well. Many young people used to be turned off early by the drudgery of arithmetic or later by the boredom of interpolating in log and trig tables. These youngsters developed emotional blocks that have made them hate math. Today there is no need for this; an arc cosine is as accessible as an integer. ..."
Could it be that we are all just Luddites in disguise?
Palmer
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Could be true, but doesn't have to be. Looking forward to a stampede of math wizards showing up  but fail so far to see or hear them :/
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Hi, Palmer:
Palmer quoted:
"But for the same reason more of their
time can have been spent learning the concepts and priinciples, not only of arithmetic, but of higher mathematics as well."
Wishful thinking of the highest caliber I've ever seen.
All the time kids save thanks to buttonpushing they don't intend to spend "learning the concepts and principles not only of arithmetic, but of higher mathematics as well" but in playing with their PSP or chatting online.
Get real.
Best regards from V.
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Well, get ready for some strong opinions. As a math teacher, I sometimes think the best thing we can do is to ensure that each student knows how to do the four arithmetic functions: add, subtract, multiply, and divide. Once they know how to do those, let them use calculators for the grunt work while they attempt to learn higherorder concepts.
The unfortunate fact is that many kids don't know the basics, and it is generally NOT because they are using or have used calculators.
Then there are those who say we should stop teaching fractions. We have already stopped teaching how to diagram sentences, but is that the reason so many students cannot express themselves using proper grammar? I don't know, but I doubt it. I don't think there are easy answers to such questions.
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I decry the use of formuals from books slavishly, as in CAS. I found quick solutions to my EE problems with RPN and the repeating t register that are not available in algebraic. I like RPN ability to change units during a solution, and using partial answers during a solution, not easy with algebraic. I rather feel that using textbook formulas defeats the learning process; to know why each symbols place in the formula has meaning. I decry the use of programming for things easily done manually. Sam
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Quote: I like RPN ability to change units during a solution, and using partial answers during a solution, not easy with algebraic. I rather feel that using textbook formulas defeats the learning process; to know why each symbol's place in the formula has meaning.
Agreed. The push to have algebraic in school is that it lets you enter the equation exactly as you see it on paper. But in reallife situations, you will not often have an equation on paper to follow, and thinking about what you need to do next generally works better in RPN. Classmates usually just memorized forumlas; but without totally understanding the concepts behind them, if they remembered something incorrectly, the error would get carried through the whole process without getting caught. If they totally forgot the formula, they were lost and could not rederive it from understanding the concepts behind it.
From the O.P.:
Quote: the ordinary calculator makes instant errorfree arithmetic available to everyone.
I must strongly disagree here. When I was in high school in the mid70's, my algebra teacher said a problem with "new math" was that it told students that 5x7=7x5, but nobody told them it was 35. And with no ability to get approximations in one's head, no mental flags go up when erroneous input makes their calculator give them results that are way, way off.
Edited: 21 Apr 2008, 5:48 p.m.
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Of the many people I’ve tutored, there’s been a recurring theme. At one point they all say, “This stuff is so much easier to do when you are here.”
To which I respond, “It’s easy to find your way when you are following my voice, but you need to learn to find the path yourself.”
The people that actually master the material keep working on it without me. The ones who use me as a crutch barely squeak by in class.
It’s been my experience that the concepts become evident while doing the work. Once the process is automated, learning stops.
A person using a calculator as a tool is fine. But I see them used more and more as a crutch that stifles learning.
Very respectfully,
David
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You may have a point; I myself didn't really like interpolation with trig or log tables. But learning the theories of analytical geometry, calculus, etc. was more enjoyable. Perhaps children should be given more theoretical explanation in class, to be followed up with "nuts and bolts" homework like interpolation, actually integrating by parts, or proving a geometric theorem.
But to really enjoy calculator use, a student has to be at a point where he can at least on a rudimentary level understand how to set up algorithms and problem solving, which would highlight the power of the calculator, especially the programmable ones.
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I was forced to do trigonometric manipulation of secants and cosecants without knowing what it was all about or why. I don't think I learned a thing,except to hate it. Are we still pushing kids through courses with no understanding or comprehension, no explanation? While it's best to know how to make change etc. I've seen supermarket checkers have to touch every can to count them even though there were 5 by 6 rows. I guess thats why they were checkers. I don't think long division or taking square root is really a learning process. What does a square or cube mean seems more basic and useful. I think we need to teach concepts and applications rather than that's what I was taught in school. Sam
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Designnut wrote:
Quote:
I've seen supermarket checkers have to touch every can to count them even though there were 5 by 6 rows. I guess thats why they were checkers.
Before you start degrading the Checkout person, you might want to know that the store management most likely has instructed the checkout person to swipe EVERY item. I know many stores actually have signs on the cash registers reminding the cashier that every item MUST be scanned.
I think it has more to do with mistakes that can be made by entering the wrong count or more likely that very similar, but different, items would be counted as the same item. Example would be purchasing six cans of cat food, each can a different flavor, but ends up getting scanned as a single item with a count of six. This will result in the inventory being thrown off.
Bill
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Bill, these were counted not scanned and merely touched to count oblivious to the multiplication process. I like some checkput people, it's stupid I find deplorable. Sam
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Conceptually, I agree with you. Unfortunately, I see two issues involved here. Firstly, children DO NEED to learn the mechanical tedium of taking a square root by hand, or taking a function in rectangular coordinates and converting and replotting in polar space, etc., but after it was explained to them why it works. (This might work better with cube roots.) And then, unlike years ago, I have seen and heard that some of today's teachers really don't have a true grasp on the material they teach.
Without enthusiasmbyexample, even if derided on the surface or initially by the loudmouth "cool" kids (who really have deep seated problems but kids of that age don't really see or understand), some kids, at the minimum will catch on. If the teacher demonstrates by body language, tone of voice, or facial expression that the material is a dreadful bore, then the children will unconsciously pick that up and form a like opinion of it even before it is presented!
I mean, we can use mathematics as the hardware store of big boy toys and goodies for the builders and tradesmen of physics, chemistry, and engineering to model (even more than) the physical universe! How cool is that?!
But kids are naturally taken by such silent communication, which most often can be negative, the disapproval of their "cooler" peers, and their own innate laziness. There is much to overcome, and it won't be easy.
Quote:
I was forced to do trigonometric manipulation of secants and cosecants without knowing what it was all about or why. I don't think I learned a thing,except to hate it. Are we still pushing kids through courses with no understanding or comprehension, no explanation? While it's best to know how to make change etc. I've seen supermarket checkers have to touch every can to count them even though there were 5 by 6 rows. I guess thats why they were checkers. I don't think long division or taking square root is really a learning process. What does a square or cube mean seems more basic and useful. I think we need to teach concepts and applications rather than that's what I was taught in school. Sam
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I don't think we give kids credit for how fast they can pick up new things. It occurred to me we might gain something by teaching them calculus earlier in their schooling. I remember how I felt enlightened. "So that's where all these formulas we have been using came from!" It is basically simple in concept, the accumulation off infinitessimals. A lovely concept. It seems to me that we might have used statistics earlier to good effect. I suggest a conceptual or "survey course" in the mathmatical science branches rather than rote learning. I suggest a science and physics survey course might improve the general outlook at the sciences in the general public. I wasn't hurt by learning something about lathes and milling machines in shop. After all the business of America is largely machine manufacturing. I recall how little impressed the visiting Chinese Officials were in a machine making spring rolls until they were told it made 5 million a day.
Teach something of the world, rather than dullness distilled. No surprise kids dislike school, theres no wow factor. Sam
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I understand your points. But there is one more thing about kids they can't sit still; i.e., the wow! factor changes form and identity in a matter of days, months if we're lucky. This is why so many are addicted to TV, the Internet, online or other electronic games, IRC, etc. there is a constant and changing attraction.
The real downside of this besides robbing them of valuable time that could have been devoted to studying something worthwhile is that they do not develop the habits and attitudes (like patience) needed to even begin studying something worthwhile.
And this goes back to calculators in a big way it's the easy way out of drudgery. But that drudgery is instructive.
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Quote:
Today's parents are asking "Is my child really learning arithmetic?"
Palmer quotes from a typical "why oh why" space filler in the Sunday newspapers which should be taken with a pinch of salt. :)
Any parents that want to know what their child is learning should first ask the child's teacher.
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Quote:
Palmer quotes from a typical "why oh why" space filler in the Sunday newspapers ...
Not so. The quotation is an excerpt from the article "The pocket calculator: Its advent and impact" by Bernard M. Oliver which appeared in the Volume Two, 1977 issue of The HewlettPackard Personal Calculator Digest. Mr. Oliver was VicePresident of Research and Development at HP at that time. I stumbled upon the article when the magazine was included with a pile of HP material hat I purchased at a church rummage sale.
The entire article is well worth reading from a historical standpoint. It includes a summary of the development of the HP35 and the quote with which I started this thread. In 1977 the HP67 was the latest pocket calculoator in the HP product line and it would be two years before the HP41 was released. Even so, Mr. Oliver made some interesting observations:
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"... An interesting side effect of the calculator is that the fear of the computer has largely disappeared. ..."
That reminded me that back in those days people were starting to talk about computers in the home. One of my colleagues said of that idea "OK for aerospace, but not safe around the home."
Quote:
... the pocket calculator handles only numbers. To make it really useful in other areas where larger calculators and computers are used, it should handle alphabetic characters as well. When our technology allows us to display many numbers and a great deal of text at one time with low power drain, and when we learn how to enter the data from a compact, uncluttered keyboard, we will enter a new era: that of the pocket computer. ...
and
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A calculator with alphabetic capability can, in principle, do symbolic mathematics as well as numeric calculations. It is not out of the question, indeed it is probable, that portable machines having the ability to do algebraic problems and even symbolic calculus will be available before the end of the century. When this happens an even more drastic change will occur in the teaching of mathematics. Again, the need will arise to distinguish between the learning and the principles being learned and to emphasize the latter.
That all seems a bit prescient. Of course, Mr. Oliver had a better vantage point that most individuals had at that time.
Finally, I note that Mr. Oliver used the generic word "machine" to describe these products. I have been criticized when I used that characterization in this forum. It turns out that I was in good company.
Palmer
