Using Wolfram|Alpha in a math class

As Maria Andersen convincingly argues in her blog Teaching College Mathematics, the introduction of Wolfram|Alpha will have a significant impact on our math classrooms.

We are not going to make Wolfram|Alpha go away, so we need to learn how to make the best use of it.

Both Maria and Robert Talbert provide interesting examples of what Wolfram|Alpha can do. But how do we take advantage of its power (and weaknesses)?

If we assume that our students will be using Wolfram|Alpha with or without our encouragement, we should at least help them get past some of the things Wolfram|Alpha does that are not appropriate for a given class.

If we ask it to "graph y=3x+5" we get two graphs, the first of which seems to have a negative y-intercept and a positive x-intercept. We can show this to our beginning algebra students, discuss why this graph should surprise us, and, after examining the scale on the horizontal axis, resolve the apparent error.

If we ask it to "solve 2^x = 5" we get an answer that involves complex numbers. We can still show this to our intermediate algebra class, and discuss what appears when we click on the "Show steps" button.