When I interviewed one of the mathematicians in the study, he asked me if I knew how to define a function. I confessed that my knowledge was a little rusty, and that the definition I remembered memorizing in college didn’t spring immediately to mind, something about variables being related to the values of other variables. “But can you explain the basic concept in your own words?” he persisted. I stammered and began looking for the nearest exit. At that point, he tossed a pen in my direction, which I instinctively reached out to catch. “How did you catch that?” he asked. “I opened my hand and then closed it around the pen at the right moment.” “But how did you know when to open your hand and when to close it?” he pressed. After a little struggling, and some additional questioning from the mathematician, I stumbled to the conclusion that I predicted where the pen would be by observing its flight. “That’s a function,” he exploded. “You took information about where it was at this point, this point, and this point, and predicted when it would arrive in your hand.” He then turned to the board and wrote a formula. “I could have explained it this way, and that’s the way it’s ordinarily done. But when we do it that way, students just memorize formulas or definitions and really don’t grasp what’s involved in the concept.

Autore: Ken Bain