Good math students use rote memory

Students who excel at math use rote memory to solve simple arithmetic problems, while weak students calculate, concludes a new study, Why Mental Arithmetic Counts, published in the Journal of Neuroscience.

Researchers scanned students’ brains while they were solving problems.

Higher-level mathematical skills are built on “arithmetic fluency, the speed and efficiency with which correct solutions to numerical computations are generated,” researchers wrote.

This “buttresses the Common Core’s call for ‘automaticity‘ of math facts in the early grades, writes Education Gadfly.

Drill, student, drill

Despite the education world’s rejection of “drill and kill, rote learning has its uses, writes Virginia Heffernan in the New York Times Magazine.

By e-mail, E. D. Hirsch Jr., the distinguished literary critic and education reformer, told me that far from rejecting drilling, he considers “distributed practice,” the official term for drilling, essential. A distributed practice system, Hirsch explained, “is helpful in making the procedures second nature, which allows you to focus on the structural elements of the problem.”

For knowledge that must be automatic, like multiplication tables, “you need something like drilling,” adds Dan Willingham, a cognitive scientist.

“Colorful, happy apps” can make drilling less boring, Heffernan writes.

Apps devoted to specific subjects always have the right answers in reserve. They unfailingly know stuff that might elude more fallible human drillers, like atomic weights, the order of cranial nerves and African geography. And they can make almost any exercise feel like a video game.

. . . even as they profess reluctance about drilling schoolchildren, adults who themselves are looking to learn something new — from foreign languages to bar-exam material — increasingly turn to apps that animate some version of a multiple-choice or flashcard narrative.

I tutored a girl in algebra who hadn’t memorized the multiplication tables. She had to slog through the arithmetic on every problem, which made it hard to “focus on the structural elements.”

Ten years ago, I tutored a sixth grader who was an excellent phonetic reader with poor comprehension because of her limited English vocabulary. She asked me for the definition of every word she didn’t know and memorized the definitions. I just found her high school-era web page, which lists her favorite books, including The Scarlet Letter.