In the 1970s and the 1980s, cognitive scientists studied a population known as the unschooled, people with little or no formal education. Observing workers at a Baltimore dairy factory in the 80s, the psychologist Sylvia Scribner noted that even basic tasks required an extensive amount of math. For instance, many of the workers charged with loading quarts and gallons of milk into crates had no more than a sixth-grade education. But they were able to do math, in order to assemble their loads efficiently, that was “equivalent to shifting between different base systems of numbers.” Throughout these mental calculations, errors were “virtually nonexistent.” And yet when these workers were out sick and the dairy’s better-educated office workers filled in for them, productivity declined.So that's math education in America: destroying children's native ability in math. A few years ago I watched my youngest daughter descend into cognitive paralysis in the face of her math homework, too confused to even count along a number line correctly. Over the course of the first grade she only got worse. These days she is performing at grade level, but I don't think she can do math at all; I think she memorizes the answers to all the likely questions. I shudder to think what happens when she encounters long division.
The unschooled may have been more capable of complex math than people who were specifically taught it, but in the context of school, they were stymied by math they already knew. Studies of children in Brazil, who helped support their families by roaming the streets selling roasted peanuts and coconuts, showed that the children routinely solved complex problems in their heads to calculate a bill or make change. When cognitive scientists presented the children with the very same problem, however, this time with pen and paper, they stumbled. A 12-year-old boy who accurately computed the price of four coconuts at 35 cruzeiros each was later given the problem on paper. Incorrectly using the multiplication method he was taught in school, he came up with the wrong answer. Similarly, when Scribner gave her dairy workers tests using the language of math class, their scores averaged around 64 percent. The cognitive-science research suggested a startling cause of Americans’ innumeracy: school.
The stumbling block that wrecks all math reform efforts is the training of teachers. According to Green, teachers in states moving to Common Core are being asked to radically change their teaching methods with only two days of instruction and no chance to practice. In class they try to convey what they only half understand using completely unfamiliar methods, with predictable results. At a deeper level, says Green, we simply don't give teachers enough training to overcome their biggest experience of teaching, the way they were taught themselves. (I was personally told, when I started teaching, to remember what my most effective teachers did and copy it.) Since the way teachers were taught is precisely the problem with math education, it is extremely different to make any change work. And since we know that for many people the way we teach math damages their understanding rather than helping, many of our teachers don't understand math well enough to teach it conceptually anyway. Not to mention that the attention span of the American system is too short to ever enact a reform that takes a generation to pay off; the Japanese experts interviewed by Green all emphasized persistence as the key to education, and here we switch fads every few years.
All this is why I think Common Core math is doomed. Americans who understand math conceptually have too many career options for many to be drawn into the modestly paid, low prestige profession of elementary school teaching. For practical purposes we are stuck with the teachers we have, and they are not going to throw themselves into learning a very difficult to master new way of teaching, especially when they all assume (correctly) that the fad will pass and in a few years they will be back to what they were doing before.