Failing "productively" might be the best way to learn math

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Direct instruction might be limiting students' ability to see the possibility of other creative approaches and solutions.

According to Quartz, Singapore (the land of many math geniuses), may have discovered the secret to learning mathematics. It uses a teaching method called productive failure, initiated by Manu Kapur, head of the Learning Sciences Lab at the National Institute of Education of Singapore.

The approach finds students who were first given unfamiliar concepts and then given time to work on them before being taught the solutions significantly outperformed students taught through formal instruction.

An approach that lets kids fumble around with unfamiliar math concepts seems inefficient and potentially damaging to their self-confidence. Yet, intuitively we learn from our mistakes.

Kapur believes that struggle activates parts of the brain that trigger deeper learning. During this process, students have to figure out three critical things: what they know, the limits of what they know, and exactly what they do not know.

Struggling with the problem advances learning a formula, to knowing it and eventually understanding which allows application to unfamiliar situations and contexts.

“We are taking the science of human cognition and learning and designing failure-based experiences to help kids learn better,” Kapur tells Quartz.

Kapur uses the research to make his case. Students get a more in-depth learning for the same number of hours of instruction, which presents another issue: teachers have to get out of the way.

“They [teachers] say it’s stressful to teach this way,” he says. “It’s easier to tell them [students] what you know.”

Effective teachers prepare students for the experience, he explains. They are told, “we know you don’t know this, we want you to generate as many ideas right or wrong and the more you generate the more you will learn.”

Kapur theorizes in one of his studies that direct instruction might limit students' ability to see the possibility of other creative approaches and solutions.

“We are saying persist, be resilient, struggle a bit,” Kapur says.