How does the author determine what the first equation should be? What about the second equation? How are these examples similar? How are they different?
2 answers
Author of what? These sound like followup questions to some reading assignment.
Well, when I taught callucus, I told my students to use Wolfram Alpha whenever they couldn't figure out how to do the problem by hand. I told them to try figuring out the steps on the website, then write the solution in their own words, then write with help from WA next to their answer. They seemed happy to do that, and they seemed to instinctively know that if WA did it for them, they weren't exactly on top of things.Homework was not a big part of the grade, though, and if it were I think there would have been more motivation to use WA as a way to fake-it. Not sure what I would have done in that case. I'm also not sure what to do in the cases where the students view the whole class as an obstacle (like remedial math classes), except to say that I can tell when you've done all your homework by computer (the steps are often overly detailed or technically awkward).