Head in the clouds

Abstract

Once upon a time I was a boy in high school who listened to the Firesign Theatre Group and wondered what one of their phrases meant: "How can you be in two places at once when you're not anywhere at all." Today I am thinking of a similar phrase, one I think may apply to many of our introductory courses: "How can we teach problem-solving when we're not solving real problems at all." Of course I have something in mind when I use the phrase real problem . Before I describe what I have in mind I'll take a liberty and describe what I don't have in mind: I don't have in mind Towers of Hanoi to illustrate recursion; I don't have in mind a program printing the verses of 'Old MacDonald had a Farm' to illustrate methods and parameters; I don't have in mind employees, hourly employees, and salaried employees to illustrate inheritance. I confess, however, to having used all these examples at some point, but I've abandoned them for a higher cause: the cause of using real problems. My bias is that the real problems we use should come from the academic disciplines our students know about and are close to. For my students these include computer science, biology, economics, sociology, physics, and mathematics. But I am biased even further and I'm staying away from number theory, combinatorics, and inclined planes. That doesn't mean we shouldn't use songs to illustrate parameter passing or employees to illustrate inheritance. We should use these as metaphors and analogies to ground the concepts in terms the students understand. However, these examples should not be the ultimate goal in what we want our students to understand --- they should be tools we use in explaining the concepts we need to understand real problems.