Samuel G. Freedman:

*Ms. Dempsey circled all those numbers on her own chart, which was being projected onto the blackboard. Now, she said, everyone in the class should color in all the multiples of two on his or her page. The students uncapped their yellow markers and set about filling in the appropriate boxes, noting the patterns they formed.*

“Wonderful,” Ms. Dempsey said, looking over one child’s completed worksheet. “Just awesome.”

At one particular desk, though, Jimmy was solving a different problem. He had just transferred to Claremont from a nearby Catholic school, and during the lesson he had whispered to an educator who happened to be visiting the room, “I know all my facts,” by which he meant his multiplication tables.

So that educator, Ferzeen Bhana, the math coordinator for Ossining’s elementary schools, gave him a problem to try: 23 times 16. Within a minute, Jimmy delivered 368, the correct answer. Ms. Bhana asked him how he had gotten it. Jimmy offered her a shy, yearning face and said nothing.

That brief moment, one moment in one school in one middle-income town, described the divide of the math wars in America. It was evident to Ms. Bhana that Jimmy had learned multiplication the old-fashioned way, with drills, algorithms and concepts like place-value. The rest of the students were using a curriculum called Investigations, one of the new constructivist models, which teaches reasoning out a solution.