Many instructors realize the value of teaching students fundamental concepts rather than focusing on details. A certain number of basic facts may have to be memorized, but beyond that it is generally more important to have students learn how to apply those facts to solve problems. A considerable amount of research suggests that active learning is an effective way for students to understand and retain information. Accordingly, I like to illustrate a concept and then have the students work with that principle through group problem-solving, subsequently answering a series of questions to demonstrate that they understand how to apply facts to solve a particular problem. This approach appears to work reasonably well, with one significant caveat—if I make a relatively minor change in the group problem, many of the students cannot apply what they just learned. Why not? One reason is that the context is critical. Even though the problem might be similar to the one they just solved, if the context changes, students do not realize that what they have already learned still applies.
