Are we wasting our time on computation?

[maroonblazer]

There's an interesting talk and discussion (in the comments) over on TED:

http://www.ted.com/talks/conrad_wolfram ... uters.html

The speaker's thesis is that math education boils down to the following 4 steps:


He posits that our existing math education spends far too much time on step #3 at the expense of the other steps. Indeed, he argues that computers can handle step #3 just fine and given that step is the most boring and tedious part of learning math it's no wonder we struggle to get students excited about the subject.

This line of thinking accords with my own observation over the last several months as I've attempted to remedy my lack of math education (I'm an adult, 20 yrs post college). Specifically, in parallel with learning Algebra and Pre-Calculus, I've discovered tools like Maple, MatLab and Mathematica. These tools seem to be to Algebra, Trig and Calculus what a calculator is to basic math.

Which makes me wonder if it's worth my while drilling myself on the computation and calculation (by hand)? Or rather should I invest just enough effort to understand the underlying concept and then move on(?)

Would love to hear the community's thoughts on this topic, esp those with advanced math backgrounds.

Thanks in advance,
mb

[stapel_eliz]

I think it kinda depends on what computations you're talking about.

For instance, it's amazing how helpless many students are when it comes to simple fractions. I was tutoring a high-school senior once and asked him, in the course of working through an exercise, to multiply one hundred by one-fourth; he looked at me like I was nuts and said, "But this calculator doesn't have a fraction key!"

On the other hand, I taught a matrix-algebra course in which, on the first day, I told the students that I would be assuming that they all had graphing calculators ("so go beg, borrow, or steal one, if you don't already have one"), because there was no way I was going to waste their (and my) time with working five-by-five determinants by hand. Sure, I'd show them how it could be done by hand, but then I'd show them how to do it with the calculators.

Sometimes the computations are meaningfull, conceptually. Students who've never worked with fractions or done long division can have real problems with the concepts related to rational functions. On the other hand, the graph of a sine wave can be more meaningful than trying to do trig from trig tables, so a calculator can usefully speed things up.

So my answer is, "It depends."