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"Singapore, the land of many math geniuses, may have discovered the secret to learning mathematics (pdf). It employs a teaching method called productive failure (pdf), pioneered by Manu Kapur, head of the Learning Sciences Lab at the National Institute of Education of Singapore." according to Jenny Anderson, reporter in our London bureau for Quartz.
Students who are presented with unfamiliar concepts, asked to work through them, and then taught the solution significantly outperform those who are taught through formal instruction and problem-solving. The approach is both utterly intuitive—we learn from mistakes—and completely counter-intuitive: letting kids flail around with unfamiliar math concepts seems both inefficient and potentially damaging to their confidence.
Kapur believes that struggle activates parts of the brain that trigger deeper learning. Students have to figure out three critical things: what they know, the limits of what they know, and exactly what they do not know. Floundering first elevates the learning from knowing a formula to understanding it, and applying it in unfamiliar contexts.
The education ministry in Singapore has given Kapur over $1 million to explore productive failure, including a $460,0000 grant to train teachers for 11th and 12th grade statistics.
He learned the approach firsthand as a student at the National University in Singapore. He spent four months trying to solve a non-linear differential equation in fluid dynamics. His teacher finally let on that the problem was unsolvable with math alone (it required computation). Frustrated, he asked why he had allowed him to waste so much time. It wasn’t wasted, the teacher explained; Kapur now truly understood the problem he was trying to solve. As a teacher himself, Kapur wondered whether this method could be more broadly applied.