In my last post, I wrote at length about Dan Schwartz’s work about teaching students how to learn by having them create a solution to a problem before you give them the standard lecture about how to solve that kind of problem. I wanted to give you an example of this kind of “Preparation for Future Learning” activity, in addition to the batting machine example in the previous post. The full article is “Practicing versus inventing with contrasting cases:Â The effects of telling first on learning and transfer, J. Educ. Pysch. — downloadable via Dan Schwartz at AAA Lab.

This one is to help students learn about density. The task is below.

And here are the graphics for the task.

The key to notice here (and in the previous batting example, though I only showed you one example of the batting machines) is that he uses **contrasting cases** to teach this concept. There are different buses with different amounts of clowns. These cases are chosen carefully so that the student must come up with a solution that satisfies all these different cases. For example, the number of clowns in the bus does not distinguish between the very first and very last cases shown on this sheet (for which the answer would be “2” for both cases, which are clearly different).

He found that those students who first invented this density ratio were better able to then use this knowledge to understand spring constants (another ratio) than those were were just told the formulas for density. That data is shown below.

More on how to write your own preparation for future learning activities in the next post….