By Joe Pickett, OCW Publication Director
“Why do we solve problems?” asks Professor Wit Busza in the first of his Instructor Insights on the This Course at MIT page for RES.8-005 Vibrations and Waves Problem Solving. “We don’t often explain to students why we solve problems. But shouldn’t we? After all, when you really stop to think about it, the answer to this question is not at all trivial.”
Professor Busza has thought about this question a lot, having taught physics at MIT for many years. In fact, he was honored for his exceptional teaching ability by being made a MacVicar Fellow. His 10 problem-solving videos cover a full range of topics from harmonic oscillators to electromagnetic waves for the course Physics III Vibrations and Waves. Along with each video, Professor Busza has included two sample problems for users to solve. Hints and correct answers are provided, but not full solutions showing all the steps.
In Professor Busza’s view, “The primary reason we solve problems is to experience one of the greatest mysteries of science.” That mystery is twofold: our ability to describe physical situations as mathematical equations, and in solving those equations, to be able to predict what will happen in situations we have never seen before.
So one of his goals as a teacher is to help students learn to “take a given situation, convert it into mathematics, solve it, and predict what will happen. We call that problem solving.”
But students, even at MIT, are often ill-prepared for this challenge, since they “have the preconceived idea that problem solving is the same thing as memorizing equations.” Students tend to get hung up on the mathematics, but in Professor Busza’s experience, it’s the physics that really trips them up:
“Although most students think setting up the problem is trivial, it is actually the hardest part of solving a problem . . . The first thing I do . . . is to ask the student to tell me what the problem is in words. You would be amazed how often the student has not understood what the problem is actually asking. So that’s the first thing. It’s very useful for the student to draw sketches at this point, then articulate the situation and explain the question being asked.”
And then? “The next step is to ask the student to explain in plain English what he or she would expect to happen. At each step in his or her explanation, [I] ask him or her to state the laws of nature that are playing key roles.” And so are revealed the key areas of misunderstanding.
Of course, the usefulness of problem-solving extends to other areas of physics. In an ideal world, students would be able to pursue the scientific mystery to their heart’s content in whatever courses they choose: “Even at the university level, I think students do not have enough opportunities to come full circle in problem solving—that is, to implement experiments to test the accuracy of the predictions they derive from their equations.”
No mystery there!