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My AP calculus teacher allowed us to use calculators on our tests. Why? Because he knew exactly how to design questions such that the calculator would switch

My AP calculus teacher allowed us to use calculators on our tests. Why? Because he knew exactly how to design questions such that the calculator would switch from exact to approximation mode. So you could enter any problem on the test into the calculator, and all it would spit out is a useless answer with as many decimal places as it could handle. Of course the calculator worked fine on every homework question. But you better have still learned the material if you wanted to make it through the test.

sonograph 5y ago
I don't follow. Do you mean to say that the calculator would produce .333333333 repeating but the student was expected to write 1/3 ?
- azalemeth 5y ago
  I suspect think more along the lines of spitting out a numerical answer instead of sqrt(pi) when fed with \int_-\infty^\infty exp(-x^2) dx...
- VLM 5y ago
  Those reciprocals are too small. Lets see if the kids know how to multiply fractions: factorial(256) times ( 1 divided by factorial(256) ) equals ? And yes, there will unfortunately be kids trying to brute force it by typing it in instead of cancelling the factorial(256).
  - voxic11 5y ago
    The TI-89 comes with a excellent symbolic solver that can do solve this or any calc problem and give the proper symbolic result. It can even do things like equation simplification and give the results in terms of the variables. Looks like this https://imgur.com/a/FmdCyYU https://imgur.com/a/FmdCyYU
    - deleted 5y ago
      [deleted]
    - mmcgaha 5y ago
      Saying any calc problem is a stretch. Just pull up the MIT integration bee and see how many the 89 can get symbolic results for. I think the 89 is awesome for algebra because typing in an equation and doing an ans(1) with an operation will let you do the algebra process without making stupid arithmetic mistakes. I wish someone made a calculator that does this only and not one that does all the other CAS tricks for integration and derivatives. Oh and I wish they would make it RPN but that is a whole other story.
- jdmichal 5y ago
  Yes, except not obvious and usually involving irrationals, so good luck figuring it out.
Workaccount2 5y ago
Calculators are generally useless in Calculus. Or at least they should be. Calculus is a process, and normally you are graded on that process, not on the answer. We were allowed calculators too, but the problems were designed that anyone even mildly good at mental math didn't need them. In theory you could teach all of calculus without ever even using numbers (perhaps except 0).
- cbsks 5y ago
  It's been a while since I took calculus, but I seem to remember that a TI-89 calculator could show its steps when solving a problem.
  - voxic11 5y ago
    Yeah I also had a TI-89 and you could directly type in most calc problem and get a great step by step answer. The symbolic solver on that thing was great.
  - jdmichal 5y ago
    Yep. We all had either TI-89 or -92. I used it to check myself after doing practice problems.
- titanomachy 5y ago
  I think you need more numbers than that. At least 1, pi, and e. Definitely don’t need any numbers bigger than 4.
- astura 5y ago
  >Calculators are generally useless in Calculus. Or at least they should be. Calculus is a process, and normally you are graded on that process, not on the answer. Yes. It's been so long since I took calculus but that's the reason why we weren't allowed calculators in my Calculus class. All the formulas needed for the test were also provided (as we weren't being graded on our memorization skills either) My professor also said don't bother doing simple arithmetic just to simplify an answer - leave it at 12/56 or whatever. Turns out, it was a really, really great system.

sonograph 5y ago

I don't follow. Do you mean to say that the calculator would produce .333333333 repeating but the student was expected to write 1/3 ?

azalemeth 5y ago
I suspect think more along the lines of spitting out a numerical answer instead of sqrt(pi) when fed with \int_-\infty^\infty exp(-x^2) dx...
VLM 5y ago
Those reciprocals are too small. Lets see if the kids know how to multiply fractions: factorial(256) times ( 1 divided by factorial(256) ) equals ? And yes, there will unfortunately be kids trying to brute force it by typing it in instead of cancelling the factorial(256).
- voxic11 5y ago
  The TI-89 comes with a excellent symbolic solver that can do solve this or any calc problem and give the proper symbolic result. It can even do things like equation simplification and give the results in terms of the variables. Looks like this https://imgur.com/a/FmdCyYU https://imgur.com/a/FmdCyYU
  - deleted 5y ago
    [deleted]
  - mmcgaha 5y ago
    Saying any calc problem is a stretch. Just pull up the MIT integration bee and see how many the 89 can get symbolic results for. I think the 89 is awesome for algebra because typing in an equation and doing an ans(1) with an operation will let you do the algebra process without making stupid arithmetic mistakes. I wish someone made a calculator that does this only and not one that does all the other CAS tricks for integration and derivatives. Oh and I wish they would make it RPN but that is a whole other story.
jdmichal 5y ago
Yes, except not obvious and usually involving irrationals, so good luck figuring it out.

Workaccount2 5y ago

Calculators are generally useless in Calculus. Or at least they should be. Calculus is a process, and normally you are graded on that process, not on the answer. We were allowed calculators too, but the problems were designed that anyone even mildly good at mental math didn't need them. In theory you could teach all of calculus without ever even using numbers (perhaps except 0).

cbsks 5y ago
It's been a while since I took calculus, but I seem to remember that a TI-89 calculator could show its steps when solving a problem.
- voxic11 5y ago
  Yeah I also had a TI-89 and you could directly type in most calc problem and get a great step by step answer. The symbolic solver on that thing was great.
- jdmichal 5y ago
  Yep. We all had either TI-89 or -92. I used it to check myself after doing practice problems.
titanomachy 5y ago
I think you need more numbers than that. At least 1, pi, and e. Definitely don’t need any numbers bigger than 4.
astura 5y ago
>Calculators are generally useless in Calculus. Or at least they should be. Calculus is a process, and normally you are graded on that process, not on the answer. Yes. It's been so long since I took calculus but that's the reason why we weren't allowed calculators in my Calculus class. All the formulas needed for the test were also provided (as we weren't being graded on our memorization skills either) My professor also said don't bother doing simple arithmetic just to simplify an answer - leave it at 12/56 or whatever. Turns out, it was a really, really great system.