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When should calculators be introduced to the curriculum?

  1. Jun 28, 2012 #1
    I'm just wondering. When do you think kids should be introduced to the idea of using a calculator to do math?
     
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  3. Jun 28, 2012 #2

    Simon Bridge

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    We don't have to introduce kids to that idea - they come to us with it already.
     
  4. Jun 28, 2012 #3

    AlephZero

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    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.
     
  5. Jun 28, 2012 #4
    Calculators have pretty much nothing to do with mathematics.
     
  6. Jun 28, 2012 #5
    I understand where you are coming from.

    But calculators do have some place within High School education. I think teachers should show and test students on their ability to use tools to solve complex problems. Hell, we do it every day.

    I use calculators, excel, matlab, etc. every day to help solve numerical problems at work. Why shouldn't we devote at least some time developing student's skill to use a calculator to help solve problems?

    Most of the time yes, students should not be relying on these instruments. They should be learning the core concepts. I agree with you. But if we do not teach them at some point to properly use tools to solve complex problems, where should they learn it? There simply isn't another mandatory subject where that skill fits into as well as "Math class".
     
  7. Jun 28, 2012 #6

    Simon Bridge

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    Because mathematics is not arithmetic, you need not ban calculators from exams etc. You can set up your questions so you test the mathematics and not the ability to plug numbers into a machine.

    You know, there was a time when slide-rules were not permitted in math classes ... or books of tables.
     
  8. Jun 28, 2012 #7
    This question is being asked in another guise in many walks of life.

    For example, should nurses (and doctors) be able to read an old fashioned thermometer and be examined on this ability?

    Should nurses and doctors be able to take a pulse the old fashioned way

    or should they be allowed to use a machine with a digital readout in an exam?

    My wife teaches drug calculations and it is suprising how many 'trained' ie exam passed staff get it wrong with a calculator and don't realise they have it wrong when they draw up the medication.
     
  9. Jun 28, 2012 #8
    Hard to give an exact age... 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.

    I'm not sure I'm all for banning the use on exams. A calculator in the hands of an educated user is basically a way to quickly check your answers. And if you can check your answers and understand how and why an answer make sense, it means you understood the problem.
    It's all about building habits. Because I never used a calculator for arithmetic when I was younger, I still don't. What I do, however, is if a question involves graphs, for an example, is that I check my answers. It saves me from losing points on problems I know how to solve because I forgot a minus sign or something else somewhere.
     
  10. Jun 28, 2012 #9

    Simon Bridge

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    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?"
     
  11. Jun 28, 2012 #10

    pwsnafu

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    Naive at best. All high school mathematics courses worldwide will do statistics at Year 9~11.
     
  12. Jun 28, 2012 #11
    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.
    I quickly learned to use it for what you just said, checking solutions.
     
  13. Jun 28, 2012 #12
    I got introduced to four-function calculators in grade 5, graphing calculators in grade 7 and I was required to have my own graphing calculation by grade 9. I think this is about perfect.

    Similar to what Studiot said, I find it silly that we are required to have cold things that are no longer useful. The amount of trig formulas I know and will never use is incredible, simply because I'd just plug it into a calculator. To me saying calculators don't belong in mathematics is like saying I shouldn't be allowed to write my english paper on my computer because I should have to handwrite it.

    The realistic approach is to teach kids the 'old way' (a.k.a. the manual way) of doing things, then show them the modern (often times fast) way of doing things, and allow them to show proficiency through the modern way in every case but when checking to see if they can do it the old way.

    In trig for my final we had two tests. One was all proofs and derivations showing that we could do things the manual way (no calculators allowed), with very little numerical effort required. And the second was all numerical with the calculator permitted to show that we can present actual answers.

    A good mix is required, leaning too far on either side is wrong to me.
     
  14. Jun 28, 2012 #13

    chiro

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    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.
     
  15. Jun 29, 2012 #14

    Mark44

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    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.
     
  16. Jun 29, 2012 #15

    lurflurf

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    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?
     
  17. Jun 29, 2012 #16

    chiro

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    I have a feeling that most people nowadays encourage the use of software and other tools to do calculations.

    Some of my statistics teachers in the past have told me about how their own coursework was full of doing manual calculations, and because of this, couldn't focus on doing the kinds of projects and work that we do on a regular basis in modern statistics courses like the one I took.

    These professors certainly had no problem with the new curriculum, but what was surprising was that even though this was only say 30 years ago, this was the nature of things.

    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?
     
  18. Jun 29, 2012 #17

    Mentallic

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    And what kids that're just beginning to do math are required to make such calculations?
     
  19. Jun 29, 2012 #18

    lurflurf

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    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.

    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.
     
  20. Jun 29, 2012 #19

    Mentallic

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    Actually I'd prefer to think of doing arithmetic on a calculator as opposed to doing it by hand as turning on the cruise control while driving down the highway.

    And I haven't heard of any Learners that've been encouraged to use cruise control.
     
  21. Jun 29, 2012 #20
    Unfortunately that is what leads to basic drug errors and the administration of 10 times too much drug.
     
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