Verbalizing how you solved a math problem can help you understand what you did, as well as helping others.
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Do you ever think you understand something, but then when someone asks you "why?" you realize you can't explain it? Do you launch nervously into a explanation, feeling as if you're flying by the seat of your pants, only to have an internal "eureka!" moment that crystallizes the answer in your mind?
If so, you're like most people. Verbally explaining a concept really does help you to better grasp it, according to work by psychologists at the University of California at Berkeley. That's because we all have an intuitive sense of what makes a thorough explanation, but we often neglect to generate one for ourselves. The query of an outsider forces us to replace our false feeling of understanding with actual reasoning.
"We have pretty systematic intuitions about what makes a satisfactory explanation, and it is if the explanation invokes some kind of underlying principle," Berkeley's Joseph Williams told Life's Little Mysteries. We aren't satisfied by a reason that applies only to the specific person, fact or circumstance in question, he said; we want one that "describes it as an instance of some broader framework or pattern."
When we ask someone why, we're acutely aware of whether or not their answer satisfies that requirement. When someone asks us why, we're equally as aware of whether we can explain it in terms of a broader pattern or principle. "You intuitively search for these principles," Williams said. [The Surprising Origins of 9 Common Superstitions]
For example, imagine if someone asked you why monkeys have four limbs. "If I just said, 'oh, because monkeys a long time ago had four limbs, and so now they do as well,' it doesn't explain it, right? It only applies to the monkeys, rather than telling you something broader about the world," he said. "Whereas, if I said, 'it's because it allows them to move more easily in the environment, both to run on the ground and climb in trees,' that is a better generalization because it applies also to other animals, and invokes the underlying relationship between environment and body structure."
In a 2010 study, Williams and his colleague Tania Lombrozo demonstrated that people are much better at latching onto these deeper explanations when they are forced to produce them for others. Given a collection of robot figurines of various shapes and sizes, students in the study who were asked to explain the group of robots were much more likely to discover the (rather subtle) common thread between the figurines than students who were asked merely to describe the group of robots. "We were able to show directly that explaining helps you find the underlying principle," he said.
In the classroom, or in the course of our day-to-day lives, we often overlook deeper explanations in favor of mere observations, or even mistake the latter for the former. Being asked "why" forces us to reassess our knowledge.
In yet-to-be-published work, Williams and Lombrozo have investigated differences in people's ideas of a good explanation. "People's knowledge about the world influences this," Williams said. "An example is to what extent you think people in an unfamiliar group are all similar."
If you're young, you and your friends might think all old people are the same. "If your friend asks you, 'why does your grandma donate to charity?' you might say, 'because she's old' — and that might satisfy your friend," Williams said. "But an old person will think that's a bad generalization because they don't think all old people are the same."