When You Have to: Model the Skills, not the Problem-Solving

In our ongoing pilot of revised algebra-based physics curriculum, we have been trying to get away from worked examples. See, in the old curriculum, everyday the instructor showed a worked example of whatever topic students were learning about. Then students would work collaboratively on similar problems (“white-boarding”). Most of you are probably aware of the pitfalls of this–students copy what you do and try to emulate exactly what you did on their problem. The result is this: If the problems students get are superficially similar enough to yours, most can do it. If the problems are not superficially similar, many students will flounder.

The issue at hand is that problem-solving is not learned via “monkey see, monkey do”. However, by teaching problem-solving this way, we give students a false impression that it is. When students were adopting this view of problem-solving, it was our own fault really. We were the ones that were organizing our classroom to make it seem like problem-solving should be learned via, “monkey see, monkey do”.

So if we aren’t doing worked examples now, what are we doing? This has been what’s working for us lately:

1. Use some combinations of labs, demos, and discussions around clicker questions to (i) give familiarity with phenomena, (ii) motivate some new concepts, (iii) and provide instruction and practice with reasoning about new concept (e.g., before learning about Torque, students did a lab exploration to see what effect forces at different distances had on how hard it was to balance a rod.)
2. Then, if needed, carefully model a specific skill involved in problem-solving (e.g., we carefully modeled how to find the torque do to different forces about a pivot, emphasizing how to make good diagrams and tables to organize one’s work). This is most like doing worked examples.
3. Immediately after modeling the skill, provide students with multiple and varied practice with the skill (e.g., students worked mini-whiteboard problems that involved calculating torque for different scenarios.) This part is mostly “monkey see, monkey do”. Students try to closely follow what you did, but that’s OK, because that’s the point right now.
4. But then, give them problems to solve that embed that skill without ever explicitly showing them an example of how to work those problems (e.g., students had several problems of varied difficulty finding the angular acceleration of objects). At this point, students have to figure out how to solve the problems and how to make use of the new skill.

With this particular example of torque and angular acceleration, we also had demos and clicker question discussions around moment of inertia and Newton’s 2nd Law of rotation. We reasoned with the ideas, but didn’t do any formal calculations.

I know that this is certainly not the ideal model for inquiry learning… that is, students in our class are not doing a lot of discovering or inventing. In our class, they are encountering. Our constraints and pacing make it difficult to invest the time in having students deeply explore a phenomena in ways that allow discovery and invention. However, this method is working a lot better than doing worked examples of problems. The reason why I suspect is that certain skills (like finding torque) benefit from following carefully the moves of an expert. Problem-solving however is not about “following”… it’s about “figuring”. We’ve been giving students practice in following along when its helpful, but leaving them to figure things out when that’s what needs to be learned. Striking the right balance between letting them “follow” and encouraging them to “figure” isn’t always easy. Some days we’ve done a great job. Other day, it wasn’t quite right.

All and all, though, it’s been a good experience to see our students figure their way through problems, rather than trying to emulate their way through problems. The good part of the skill modeling and practice we do has been that students enter the problem-solving phase not “frustrated novices”. They aren’t perfect at the skills yet, but they’ve gotten enough practice that they can focus their thinking on the “figuring” of the problem, with some confidence that they know how to use the skills well enough.