Dr. Suri is a professor of mathematics at the University of Maryland, Baltimore County.
Does studying mathematics enhance your overall mental prowess?
Abraham Lincoln certainly believed so, embarking on the arduous task of mastering Euclid’s treatises on geometry to increase his cognitive capacities, in particular his linguistic and logical abilities. This idea — that mathematics strengthens your mind much as physical exercise strengthens your body, helping you negotiate a variety of mental challenges — goes all the way back to Plato. Alive and well in today’s world, it is one reason popularly given for why everyone should study mathematics.
So it can come as a surprise to learn that cognitive psychologists have a different take on the issue. Various studies point to the conclusion that subjecting the mind to formal discipline — as when studying geometry or Latin — does not, in general, engender a broad transfer of learning. There is no sweeping increase of a general capacity for tasks like writing a speech or balancing a checkbook.
But surely a narrower claim is true: that mathematics, so systematically built as it is on inference, must develop logical thinking. Right?
By “logical,” I mean the kind of thinking needed to solve the following problem:
Four cards are laid in front of you, each of which, it is explained, has a letter on one side and a number on the other. The sides that you see read E, 2, 5 and F. Your task is to turn over only those cards that could decisively prove the truth or falsity of the following rule: “If there is an E on one side, the number on the other side must be a 5.” Which ones do you turn over?
Clearly, the E should be turned over, since if the other side is not a 5, the rule is untrue. And the only other card that should be flipped is the 2, since an E on the other side would again disprove the rule. Turning over the 5 or the F doesn’t help, since anything on the other side would be consistent with the rule — but not prove it to be true.
This innocuous-looking puzzle, a variation of which was introduced by the British psychologist Peter Wason in 1966, has been called “the single most investigated paradigm in the psychology of reasoning.” If you answered E and 2, congratulations: You are among the roughly 10 percent of the public able to solve the puzzle. Many reasons have been advanced for this poor showing, including the lack of relevance of such an abstract exercise to people’s daily lives.
Most people reflexively eliminate the cards not explicitly specified in the rule (the F and the 2) and then continue with slower, more analytic processing only for the E and the 5. In this, they rely on an initial snap judgment about superficial similarity, a tendency that some scholars speculate evolved in humans because in most real-world contexts, quickly detecting such similarities is a good strategy for survival.
Interestingly, though, it turns out that if the puzzle’s abstract rule is translated into terms that are logically equivalent but grounded in real-world experience — as in, “If someone is drinking beer at a bar, she must be at least 21 years of age” — then the success rate jumps to 75 percent or more.
I learned about the Wason selection task and its intricacies from a fascinating recent book, “Does Mathematical Study Develop Logical Thinking?” by the education and cognition researchers Matthew Inglis and Nina Attridge. They conducted experiments that found that university students studying mathematics were just as likely as those studying history to quickly reject the F and the 2 cards. But differences emerged in the slower, more effortful cogitative phase that followed, leading to divergent success rates in the end: 18 percent for the mathematics students versus 6 percent for the history students.
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