Learning in a digital world

Maxima is a piece of software that can solve problems symbolically as well as numerically. I downloaded it last week and have played with it for two days. Yesterday I gave it a test my students struggled with earlier this week. Click here to see how it did.

I found lots of help at this forum.

The questions it raises are: Why train the students to solve problems the computer can solve faster and better? It is similar to the question, Why teach students algorithms for square roots or long division when calculators do it better?

The second question I find more interesting: How may students be trained to solve problems the computer is not good at? There is no algorithm for discovering problems, for setting up a model that fits a situation, for interpreting the result the model gives you, for discussing the weaknesses of a model, … When will we train students to be more than second hand calculators?