NEW YORK—Teacher John Garuccio wrote a multiplication problem on a digital whiteboard in a corner of an unusually large classroom at David A. Boody Intermediate School in Brooklyn.

About 150 sixth-graders are in this math class—yes, 150—but Garuccio’s task was to help just 20 of them, with a lesson tailored to their needs. He asked, “Where does the decimal point go in the product?” After several minutes of false starts, a boy offered the correct answer. Garuccio praised him, but did not stop there.

“Come on, you know the answer, tell me why,” Garuccio said. “It’s good to have the right answer, but you need to know why.”
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