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Ideally, wouldn't math classes teach students how to solve the parts of problems that computers aren't as good at? I mean, I'm happy that I can use memorized m

by khafra 15y ago

Ideally, wouldn't math classes teach students how to solve the parts of problems that computers aren't as good at? I mean, I'm happy that I can use memorized multiplication tables to make my quick estimates of various quantities accurate to two orders of magnitude instead of one, but that's about all they're good for. Anything more, and I pull out my phone or head over to wolframalpha. And I'd much rather have spent those years of brute-force arithmetic practice advancing to higher, more interesting math.

sliverstorm 15y ago
The point of a math education is to understand what's going on. If you can't work problems, you don't really know what's happening, and you will have trouble applying the concepts outside of strictly defined problem spaces from classrooms. Learning to use computing to do the heavy lifting is great, but I often see learning to use the sin() function used as a proxy for learning what sin() is, for example.
- derleth 15y ago
  > If you can't work problems, you don't really know what's happening On the contrary: If all your 'work' can be done even faster by a machine, you don't know any more than the machine does and your skills are worthless once your wages are more expensive than just buying and maintaining the machine. Real mathematicians use software like R and Matlab and so on, because their real skill lies in knowing what to do with the software and how to interpret the results it gives.
  - sliverstorm 15y ago
    Real mathematicians use software like R and Matlab and so on, because their real skill lies in knowing what to do with the software and how to interpret the results it gives. Of course! But what I would contest is that (at least in my humble experience) knowing what to do with the software and how to interpret the results comes with learning about how those results are produced. When I want to analyze a complicated circuit, I don't use a pencil and paper, I use pspice. But I would not be able to create a useful model, run useful tests, or make sense of the output if I was not able to (at least once upon a time) do it on paper.
    - derleth 15y ago
      This post seems to contradict what you said above: > It seems like more and more, math classes are teaching students how to use a graphing calculator to avoid solving problems. This is, simply, wrong: Calculators are banned for as long as students are learning to calculate. Once they are actually solving problems, as opposed to grinding through numbers (which isn't something they need to be doing anyway), they're thinking in ways calculators cannot match. A calculator can only do the most mechanical, least problem-solving-like parts of solving a problem.

by khafra 15y ago

sliverstorm 15y ago

The point of a math education is to understand what's going on. If you can't work problems, you don't really know what's happening, and you will have trouble applying the concepts outside of strictly defined problem spaces from classrooms. Learning to use computing to do the heavy lifting is great, but I often see learning to use the sin() function used as a proxy for learning what sin() is, for example.

derleth 15y ago
> If you can't work problems, you don't really know what's happening On the contrary: If all your 'work' can be done even faster by a machine, you don't know any more than the machine does and your skills are worthless once your wages are more expensive than just buying and maintaining the machine. Real mathematicians use software like R and Matlab and so on, because their real skill lies in knowing what to do with the software and how to interpret the results it gives.
- sliverstorm 15y ago
  Real mathematicians use software like R and Matlab and so on, because their real skill lies in knowing what to do with the software and how to interpret the results it gives. Of course! But what I would contest is that (at least in my humble experience) knowing what to do with the software and how to interpret the results comes with learning about how those results are produced. When I want to analyze a complicated circuit, I don't use a pencil and paper, I use pspice. But I would not be able to create a useful model, run useful tests, or make sense of the output if I was not able to (at least once upon a time) do it on paper.
  - derleth 15y ago
    This post seems to contradict what you said above: > It seems like more and more, math classes are teaching students how to use a graphing calculator to avoid solving problems. This is, simply, wrong: Calculators are banned for as long as students are learning to calculate. Once they are actually solving problems, as opposed to grinding through numbers (which isn't something they need to be doing anyway), they're thinking in ways calculators cannot match. A calculator can only do the most mechanical, least problem-solving-like parts of solving a problem.