Other mathematicians called the findings interesting but warned against overgeneralizing. “One size can’t fit all,” said Douglas H. Clements, a professor of learning and instruction at the University of Buffalo. “That’s not denying what these guys have found, whatsoever.”

“The motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning,” said Jennifer A. Kaminski, a research scientist at the Center for Cognitive Science at Ohio State. “It was really just that, a belief.”