worked examples etc.

I received a very well written email from a student arguing for worked examples, similar to but not identical with the complex problems I write. Here an excerpt of my reply:

If the primary goal is to have you learn content such as Gauss’ law, then I agree with you, the complex psets would be structured differently. However, let me ask you to consider having your primary goal to develop your ability to analyze novel problems.

Let’s take three scenarios

1) students, such as yourself, working on complex problems that are similar to what you describe, with hints, or a possible similar worked example. Then you are correct you might learn more about, e.g., Gauss law. But since you are using prior examples, or hints, the challenge on confronting a novel problem is much less.

2) students working on the current problem sets who ask the question “how do I do this problem”, then make no progress, and get frustrated. Then I agree little learning takes place, either on problem-solving skills or on, e.g., Gauss Law.

3) students working on the current problem sets who ask a more open question “what is going on in this problem”, sketch, analyze the key stages of the scenario, ask what ideas are involved, and hence start to build a frame or structure around a problem. I think these students, even if they make no further progress in the solution, have grown tremendously in earning how to tackle novel situations.