Its relevance to math, however, is particularly intriguing – and somewhat unsettling in light of the fact that most of us still think in behaviorist terms.
Mathematics is the subject in which practice homework seems to be most commonly prescribed, so this is as good a place as any to understand the limits of the whole idea. An emphasis on practice to reinforce skills proceeds naturally from the assumption that kids primarily need to learn “math facts”: the ability to say “42” as soon as they hear the stimulus “6 x 7,” and a familiarity with step-by-step procedures (sometimes called algorithms) for all kinds of problems — carrying numbers while subtracting, subtracting while dividing, reducing fractions to the lowest common denominator, and so forth.
The more they’re given algorithms and told exactly what to do, the farther behind they fall in terms of grasping these concepts.
“Mindless mimicry mathematics,” as the National Research Council calls it, is the norm in our schools, from single-digit addition in first grade to trigonometry in high school.
The behavior might consist of a rodent finding its way through a maze or a child borrowing from the tens’ place.
For a behaviorist, these actions are different only in degree, and the same theory applies equally well to both.
Thus, to justify sending students home with a worksheet full of practice problems on the grounds that it reinforces skills is to say that what matters is not understanding but behavior.
In the 1920s and ‘30s, when Watson was formulating his theory that would come to dominate the way we teach students (not to mention the way we raise children and manage employees), a much less famous researcher named William Brownell was challenging the drill-and-practice approach to mathematics that had already taken root.
“If one is to be successful in quantitative thinking, one needs a fund of meanings, not a myriad of ‘automatic responses,’” he wrote. Repetition does not lead to understandings.” In fact, if “arithmetic becomes meaningful, it becomes so drill.” An emphasis on making meaning is directly opposed to the view that learning consists of the acquisition of a collection of behaviors.
Brownell’s insights about math instruction have been expanded and enriched by a long line of experts who have come to realize that the behaviorist model is, if you’ll excuse the expression, deeply superficial.