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Apr 19, 2015 at 20:08 comment added Kyle Strand Your comment about the "big picture" value of math courses should really be expanded somewhat and added to the answer itself.
Apr 18, 2015 at 6:06 comment added jpmc26 @Mehrdad Agreed. Show them the limits of the technology. That's when you absolutely have to know what you're doing, or you won't even realize the computer is wrong. I had a professor who liked to point out that calculators would give you a rounded answer when doing special relativity math, making it look like the relativistic equations made absolutely no difference in the answer, when really it was a very minute difference. Then he would go on to show them how they could transform the answer into pieces the calculator could handle individually and that you could add up in your head.
Apr 17, 2015 at 12:04 review Suggested edits
Apr 17, 2015 at 12:37
Apr 17, 2015 at 8:58 comment added user541686 You should also show them when Wolfram Alpha is outright wrong and self-contradictory.
Apr 17, 2015 at 3:50 comment added AaronLS "Having gotten their attention, I now have a good opportunity to make my case for the value of a math education." This seems like an incomplete thought. Everything you said supports the opposite argument.
Apr 16, 2015 at 20:43 review Suggested edits
Apr 16, 2015 at 22:18
Apr 16, 2015 at 7:49 comment added PLL @DavidRicherby: an important part of making a robust case for something is to honestly acknowledge (things that might appear to be) points against it. If a course is really only teaching obsolete skills, then the course needs to be changed. More commonly, if the motivation we give the students sounds like the skills are obsolete, then we need to be giving the students a better explanation/motivation.
Apr 16, 2015 at 5:09 comment added Chris Cirefice @Anonymous Computers have become really good at solving all sorts of repetitive, trivial problems that could be done by hand, but (imo) really shouldn't once concepts are understood. Especially in mathematics. Take for example multiplication of triple-digit numbers, or decimal numbers. Why would we have students waste time writing out the solution when they know the process? There are drawbacks, as you've mentioned; students can (and some will) cheat and never bother to learn the concepts. They're hurting themselves, and I don't think that responsibility lies with the instructor...
Apr 15, 2015 at 21:59 comment added AaronD @KSmarts: Nailed it! +1 (That's actually true for a lot of things - they don't cause or solve anything, they just amplify what's already there.)
Apr 15, 2015 at 15:42 comment added KSmarts So, basically, better computation tools help good teachers and hurt poor teachers.
Apr 15, 2015 at 11:34 vote accept Miguelgondu
Apr 15, 2015 at 11:16 comment added Anonymous The point I make is that, Wolfram Alpha or no, just being able to mechanically compute derivatives and integrals for its own sake is of questionable value. Rather, the point of a calculus course lies in the big picture and appreciation for concepts which students subliminally develop, in the problem-solving muscles which get exercised, and in the good habits of precision which get refined.
Apr 15, 2015 at 9:45 comment added Sean ^ It's not a point for the value of a math education, but against. They said that by using that, they were able to essentially confirm / recognize an opposing argument that students may have in order to (presumably) present a strong counter-argument which supports the program.
Apr 15, 2015 at 7:11 comment added David Richerby "This website can solve your math problem in 0.05s" seems like a terrible case for the value of a math education. It makes it sound like any other obsolete thing that we used to teach people but which are now done by computers or machines.
Apr 15, 2015 at 5:47 comment added user32344 What you say about Wolfram Alpha being able to solve the problem in about 0.05 seconds, when I took differential equations, I learned to solve problems that Wolfram Alpha couldn't directly solve (I had to make clever substitutions to another form before it could handle it, then substitute back). This was the first time I encountered a computational problem that I could solve and Wolfram Alpha could not.
Apr 15, 2015 at 3:08 history answered Anonymous CC BY-SA 3.0