It’s hard to forget Donovon. He sat in the far right corner of his sixth-grade math classroom facing the wall. He was quiet and listened to the teacher’s class discussions and lectures, even though he could not actually see her or engage with her. He was deemed too far behind to work with the other kids and was assigned computation problems out of an old fourth-grade textbook. Published in 1968, Donovon’s tattered textbook was older than I was. On occasion, I would sit next to him and encourage him to work on the problems assigned to his classmates. Like the equation x+3= 7. I gave him a series of simpler problems, talking about all the ways one could arrive at seven when adding, and I discussed for what seemed to be the entire class period why the letter x was in the problem in the first place. And then the light went on. He realized not only what x meant, but also why it must equal four. Through mathematics instructional practices centered on student thinking and sense-making versus rule-giving and recall, Donovon was able to understand the equation.
Donovon’s experience in math class may have been substandard and uninspiring, but he was not missing out on much. Though they worked from a sixth-grade textbook, his classmates often copied long columns of problems from the board, solving them with predetermined steps. On this day they were told to subtract three from each side of the equation. No explanation was given for why the method worked, and students spent the entire class session completing nearly identical problems by rote. We have all heard the argument that repetition is essential to math success. Yet, only 2 percent of the sixth-graders at Donovon’s school were scoring at or above proficiency on their state math exams.
Things were not much different in the Southeast Los Angeles community next to Donovon’s. Driving on the freeway, I couldn’t help noticing that most of the cars were going in the opposite direction. Happy as I was to drive on a virtually empty freeway, I understood that the lack of cars going my way signaled something disturbing about the nature of life and opportunities in these communities. On the route between my freeway exit and the school, the men (both young and old) standing around on sidewalks, wandering the streets, and sometimes stretched out on bus stop benches told the story all too well. Unemployment in this community was among the highest in the nation, and the often resultant ills of poverty, incarceration, and drug abuse had taken their toll.
In a school similar to Donovon’s, students sat in rows, faced with computation problems written on their white board. A column of fractions with like-denominators, another column with unlike-denominators, a column of triple digit by double digit multiplication, and a column of long division problems—with and without decimals. After the work session, students would be called one by one to give their solutions. When a student g...
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