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moonman239
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I'm just wondering. When do you think kids should be introduced to the idea of using a calculator to do math?
AlephZero said:Never, IMO. Mathematics ##\ne## arithmetic.
And ban calculators from all math tests and exams, of course. If you want to give people an educational qualification for knowing how to use a calculator, that fine, so long as the certificate doesn't include have word "mathematics" on it.
Interesting idea - considering that it's use as an aid suggested is by taking over the tedious parts of the calculation: i.e. the arithmetic.In general the calculator should be introduced as an aid to estimate uneven roots and graph polynomials and that type of stuff. It should never be given as a tool for doing arithmetic.
AlephZero said:Never, IMO. Mathematics ##\ne## arithmetic.
And ban calculators from all math tests and exams, of course. If you want to give people an educational qualification for knowing how to use a calculator, that fine, so long as the certificate doesn't include have word "mathematics" on it.
Good point. I do suppose it can be used for arithmetic. But I think it's good that students do as much arithmetic as possible on their own. I understand where you are coming from. I can't honestly say that I remember much of my high school math (I went into the military for a couple of years before I went to college, where I am now) BUT, if my memory serves me correctly, we used easy numbers when studying new concepts to focus on the math and not the arithmetic and then gradually went on to fractions etc. What I do remember, is that we weren't allowed calculators for tests and people who used the extensively for homework didn't get A's.Simon Bridge said:Interesting idea - considering that it's use as an aid suggested is by taking over the tedious parts of the calculation: i.e. the arithmetic.
At HS - calculators are useful for teaching math where you need the students to pay attention to the math and not the numbers. Smart calculators can be useful for displaying quick relationships.
This is not to say that skills such as sketching graphs and mental arithmetic should not be taught. Everyone has experienced punching a calculation into a machine severa times and getting several different results (mostly by mis-hitting keys) and yet people are more willing to trust the machine over their own brain. One of the things that needs to be explicitly taught in this computer-age is how to check your answers. How often do we see a question on PF which is the student asking "here's my calculation: did I get it right?"
moonman239 said:I'm just wondering. When do you think kids should be introduced to the idea of using a calculator to do math?
This sounds completely reasonable to me. The part about "pushing buttons" blindly reminded me of when I used to teach at a community college. A physics instructor who had an office near mine told me about a student who had come to see him during his office hour. She had done a calculation, but her answer was off (too small) by a factor of 10. When he told her that, she immediately grabbed her calculator to multiply her answer by 10. Before she could start punching buttons, he grabbed the calculator, to try to get her to use her brain.chiro said:When they are able to do arithmetic without a calculator at a competent level, and understand the processes behind the methods.
If you don't have this then you have students pushing buttons without knowing what the hell they are doing, and if you force students to have to do everything manually then you are taking up their time with useless problems while sacrificing time for them to focus on more important higher level tasks like putting the math into focus.
Kids should not be given calculators when they start learning arithmetic and numbers but once they demonstrate a good enough understanding of arithmetic, what it means in context, and how to do it independently at a minimum standard, they should not need to waste any more time on computation when there is a better tool to do the job.
lurflurf said:Kids should be introduced to the idea of using a calculator to do math the same day they are introduced to the idea of doing math. Why are all these technophobes on the internet? Calculators and computers are faster, cheaper and more accurate than humans. When I need to make 57389 or so calculations I do not do them by hand. Who here can compute 357*79135=28251195 in less than 1.0 milliseconds?
lurflurf said:Kids should be introduced to the idea of using a calculator to do math the same day they are introduced to the idea of doing math. Why are all these technophobes on the internet? Calculators and computers are faster, cheaper and more accurate than humans. When I need to make 57389 or so calculations I do not do them by hand. Who here can compute 357*79135=28251195 in less than 1.0 milliseconds?
Using a calculator when you do not know what you are doing can be quite helpful, one can explore a problem and make sample calculations that provide insight. People should be able to make simple calculations (like my example), but the time needed to make more complicated calculations, to do them quickly, and accurately are better used for something else.chiro said:But again, would you want someone who knows how to push buttons without knowing what the hell they are doing? If not, then what is the minimum standard you would want for the new generation of youths and students not only in specialized science, engineering, and math programs, but for people in general?
If they cannot make such calculations they need a calculator more. Some basic arithmetic is helpful. It is like bicycles and automobiles, learn to use both. If you need to travel at 100 kph no amount of bicycles practice will help. If you need to travel 17 kph hours use the one best for the situation. If you think you should improve your cycling then do so.Mentallic said:And what kids that're just beginning to do math are required to make such calculations?
lurflurf said:If they cannot make such calculations they need a calculator more. Some basic arithmetic is helpful. It is like bicycles and automobiles, learn to use both. If you need to travel at 100 kph no amount of bicycles practice will help. If you need to travel 17 kph hours use the one best for the situation. If you think you should improve your cycling then do so.
If they cannot make such calculations they need a calculator more. Some basic arithmetic is helpful.
This is a very bad idea, IMO. They should be competent at arithmetic operations first.lurflurf said:Kids should be introduced to the idea of using a calculator to do math the same day they are introduced to the idea of doing math.
Faster and cheaper, sure, but not always more accurate.lurflurf said:Why are all these technophobes on the internet? Calculators and computers are faster, cheaper and more accurate than humans.
I'm reasonably sure most of the regulars here at PF can do this calculation, but it will take more than a millisecond. However, we might be able to do the calculation more accurately. Suppose that instead of using a calculator for this product, I write a computer program to do it for me, say in C. Suppose also that the computer I'm working on has an old (pre 1997 or so) compiler that stores int values in 16 bits. The compiler would be unable even to store the 79135 value, let alone be able to do the multiplication. Admittedly this is a contrived example, but I can think of examples that are not contrived.lurflurf said:When I need to make 57389 or so calculations I do not do them by hand. Who here can compute 357*79135=28251195 in less than 1.0 milliseconds?
Stephen Tashi said:I think calculators or computers shoudl be introduced early in the elementary school curriculum. They certainly should be used in any situation where performing arithmetic begins to distract from the mathematical concepts. (Do students nowdays still do manual interpolations of logarithms and trigonometric functions? If you are teaching the concept of interpolation that's fine, but it detracts from teaching trigonometry and logarithms. )
I think programming should also be introduced in the elementary school curriculum. If it's done on a calculator, the machine should use something resembling a traditional programming language - not too many "special function" keys.
Sure, because it is impossible to make a decimal place error in hand calculation.Studiot said:Unfortunately that is what leads to basic drug errors and the administration of 10 times too much drug.
That is like saying before you can use a hammer you should be competent at nailing by hand. If one wants to improve at hand calculation they can practice and use a calculator when helpful. Most people will not continue to practice past a certain point as it is not a worthwhile activity. If hand calculation is such a valuable skill as its enthusiasts claim they should be able to demonstrate it, not treat calculators like spindles in sleeping beauty.Mark44 said:This is a very bad idea, IMO. They should be competent at arithmetic operations first.
Faster and cheaper, sure, but not always more accurate.
I had a teacher once whose lessons were even less useful than hand calculations. Once he poured a bucket of bearings into a metal can while flipping the lights on and off and said "that is what is was like to be in world war one". Another time he required each student to report a current event, I reported the Pentium chip error and was given a diatribe that the error was not of any importance to anyone ever. The error makes one question intel's ethics and serves as a reminder to check results. The error has been estimated to occur once per several million or billion calculations. How many errors would a human make in a million divisions done by hand? How long would they take? Hand calculations failed William Shanks and he was a better calculator than most people. I would take my chances with a flawed Pentium chip and outdated compiler.Mark44 said:...Pentium chips
Computers can perform exact and high precision approximate calculations. There is a speed trade off. Some interesting work involves computers that are faster and less accurate than usual. If a calculation can be done by a human in reasonable time a computer can perform numerous checks in the same time. Frequent use of calculators allows one to predict and deal with problems.Mark44 said:When it comes to arithmetic that involves real numbers, the fact that computers and calculators are unable to perform exact calculations leads to some surprising problems, such as the inability to add 0.1 and 0.1 and get the correct result.
I don't entrust a calculator to do my thinking, I use a thinkulator for that. When my hammer breaks I get a new one, same for a calculator. If it happens often enough carry spares. http://www.obsoleteskills.com/skills/skills Technology is often used poorly in education, but the answer is to use it better not eliminate it. Properly used calculators lead to more (and somewhat different) learning and reduction in tedious tasks.Mark44 said:The thing about totally entrusting a calculator to do your thinking for you is, what happens if you drop the calculator and it breaks, or you forget it, or the batteries die?
chiro said:Although I think the curriculum in high school is rather pointless, wasteful, and underchallenges many students, your proposal would be something for more gifted students and not for the norm.
Angry Citizen said:Thus I think the only calculators kids should have are elementary arithmetic calculators, through all stages of their development.
Angry Citizen said:I don't think kids need to be taught things like long division algorithms at all. What exactly does it teach them? To this day I don't know how to do long division using that ridiculous algorithm. Calculators should be introduced the minute they get beyond the times-tables.
I haven't used a dedicated graphing calculator (MATLAB excluded) since my pre-calculus days. I don't need them or want them. I have a solid knowledge of what a graph of a given elementary function ought to look like. Kids need to learn how to graph functions. It teaches you a LOT about how functions behave, and I think it helps make the transition to concepts like continuity much easier. Thus I think the only calculators kids should have are elementary arithmetic calculators, through all stages of their development.
Studiot said:Forcing programming on schoolchildren was an experiment that was tried twice and failed miserably twice in the UK during the 80s and 90s.
Languages and fashions change in programming such that anything learned at school will be hopelessly out of date often before the child has left, let alone later in life.
That is not to say that programming study not be available as an option for those who want or need it.
Number Nine said:I've encountered too many people who can't reality test even the most basic of computations done with calculators because they've never actually done any calculating themselves, and have no idea what a reasonable answer looks like. The ability to perform basic calculations is such a useful and easily acquired skill that I can't imagine why anyone would forego learning it.
Studiot said:Chiro, I really don't have a clue what you mean.
I would also venture that you don't have much idea of what I was talking about, given your response.
Do you have first hand experience of the events I described?
Please all let's remember the original question was
When should calculators be introduced?
not
should calculators be introduced?