Elizabeth Green’s Why do Americans Stink at Math? didn’t go far enough, writes Dan Willingham. Improving math instruction is even harder than she thinks.
The nub of her argument is this. American stink at math because the methods used to teach it are rote, don’t lead to transfer to the real world, and lead to shallow understanding. There are pedagogical methods that lead to much deeper understanding. U.S. researchers pioneered these methods and Japanese student achievement took off when the Japanese educational system adopted them.
. . . Traditional classrooms are characterized by the phrase “I, We, You.” The teacher models a new mathematical procedure (“I”), the whole class practices it (“We”), and then individual students try it on their own (“You”). That’s the method that leads to rote, shallow knowledge. More desirable is “You, Y’all, We.” The teacher presents a problem which students try to solve on their own (“You”). Then they meet in small groups to compare and discuss the solutions they’ve devised (Y’all). Finally, the groups share their ideas as a whole class (“We”).
Reform math comes around every 30 years, but never gains traction, writes Willingham. Green blames “lack of support for teachers, and the fact that teachers must understand math better to use these methods.”
Green’s take is that if you hand down a mandate from on high “teach this way” with little training, and hand it to people with a shaky grasp of the foundations of math, the result is predictable; you get the fuzzy crap in classrooms that’s probably worse than the mindless memorization that characterizes the worst of the “I, We, You” method.
True enough, writes Willingham. But there’s more.
Green’s preferred method requires teachers to make quick decisions in class when a group gets on the wrong track. “Do you try to get the class to see where it went wrong right away, or do you let them continue, and play out the consequences of the their solution? Once you’ve decided that, what exactly will you say to try to nudge them in that direction?”
Japanese teachers discuss individual lessons in detail to prepare for this. They agree on the best way to teach each lesson down to what numbers are best for examples. And they expect all students to learn the same content with no regard for individual differences.
U.S. teachers are used to teaching autonomy.