Last lesson, we talked about the role of prior knowledge in learning. This lesson tackles a closely related topic: analogies.
Analogies map the structure of one situation onto the structure of another: Blood vessels are like highways for blood; the immune system is like an army that defends the body from attack. Analogies are helpful because they help students learn about the boundaries of a principle.
We talked about how experts have organized knowledge structures in their brains. There’s another important aspect of expertise: being able to apply a principle to new situations. Experts can recognize that even though two situations look very different, they share an underlying principle. Learning scientists usually call this underlying principle, the “deep structure,” and the superficial appearances, the “surface features.”
Remember the expert and novice students who categorized physics problems? The experts categorized problems according to the deep structure: Conservation of Energy or Newton’s Second Law. They understood the deep structure behind the problems.
Life is full of cases where things that look very different share a deep structure. Gas engines all work in essentially the same way, but they can look very different. All mammals share certain underlying traits, even though the largest living mammal is 200 tons and the smallest around 10 grams. Understanding the deep structure gives you a powerful resource for understanding a wide variety of situations. Analogies are a powerful way of learning that deep structure.
A common educational approach is to give students an example and the principle that explains this example. This is not a very effective way of learning the target principle. It’s far better to give students at least two examples that superficially appear different but share the same deep structure. In other words, “two is better than one.”
Consider the following study. Researchers taught students about two important concepts in probability: permutations and combinations. With one group of students, they taught combinations with problems involving cars and permutations with problems involving dice. As a result, these students tended to think that “cars means combination problem” and that “dice means permutation problem.” They didn’t appreciate the deep structure of these concepts and performed poorly on a test. When students learned each concept with both kinds of examples (cars and dice), they were far better at applying the right concept on the test. By using multiple kinds of examples, students learn the deep structure more effectively.
Analogies can also be dangerous. Yes, the immune system behaves like a defending army in some ways, but in other ways, it does not. No analogy is perfect. When thinking about analogies, it’s best to identify which parts of the analogy are accurate and which parts are not. This helps prevent learning misconceptions, which can be difficult to overcome.
How Can These Ideas Help?
First, analogies can be powerful learning tools. They help us think about new situations. They help us grasp the deep structure behind a concept or problem. But coming up with a good analogy takes considerable effort. When learning a new concept, try coming up with several analogies and determining which ones best explain the concept, which do not, and why. This helps prevent developing misconceptions because of a bad analogy.
Rushing to read the “correct solution” or the canonical principle is not usually the best learning approach. It’s better to take example cases to understand the variation—and explicitly look for situations that the principle can apply to and when it breaks down.
For my Chinese studying, it’s helpful to push the structures I’m learning to the limit: Can they be used in this situation? What about that situation? How different can the context be for a word or sentence structure to be appropriate?
Next lesson, we look at the flip-side of analogies: contrasting cases.
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