In this section, Wit Busza shares his strategies for supporting students who encounter difficulties when trying to solve problems.
Stepping into Students’ Shoes
I’ve come to the conclusion that the most important thing when teaching problem solving is to be able to get into the shoes of the students. You’ve got to discern how students’ experiences and knowledge are shaping how they are hearing what you are telling them. The teacher must realize that what is obvious or trivial to the teacher is not to the students.
Sometimes what students ask is actually not obvious—it’s nontrivial and profound. But the teacher does not realize it because he or she thinks it is something trivial that the students have asked. There’s an interesting story that captures this kind of typical interaction between professors and students. Apparently, the famous physicist, Wolfgang Pauli, was once giving a lecture, and halfway through someone interrupted and asked him, “How did you go from A to B in this proof?” He looked at it, stared at it, and left the room. He returned 10 minutes later and said, “Oh, it’s trivial!”
Making Sure Students Understand What the Problem is Asking
"I end at the very spot they asked me to begin."
If a student is having a difficult time solving a problem and asks you what formula to use, the last thing you want to do is tell him or her what formula to use. Rather, you want to help students separate the problem into its component two parts: the physics and the mathematics.
The first thing I do, under these circumstances, 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.
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, ask him or her to state the laws of nature that are playing key roles. Although students think translating the physical situation into mathematical equations is the easiest part of problem solving, as I have stated before, it’s actually the hardest part, and this is where I spend most of my time when I help students. Once they’ve written the equations, I then say, now go to a book of mathematics and solve them. I end at the very spot they asked me to begin.
