FIT FOR FAILURE
The best way to learn math is
to learn how to fail productively
Quarz,
10/29/2015
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.
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.
He soon designed studies to test it.
In one, written up in Cognitive Science, researchers presented 9th grade
students in an Indian private school with the following math problem. The
concept is standard deviation, but the kids—who have never been exposed to it
before—don’t know that.
One group is asked to figure out how
to solve the problem in as many ways as possible. They are given 30-45 minutes
and teachers cannot help. After that, the teacher discusses 3-4 of the most
common approaches. The teacher then shows the class the standard solution.
A control group is taught standard
deviation the traditional way and then asked to do problems. Both groups are
then tested.
On procedural knowledge, or applying
the formula, there was no difference between productive failure and direct
instruction. But on conceptual understanding—understanding what it means and
possessing the ability to adapt the information—the productive failure students
dramatically outperform their direct instruction peers.
“We are taking the science of human
cognition and learning and designing failure-based experiences to help kids
learn better,” Kapur tells Quartz.
Kapur started to design
quasi-experimental and randomized-controlled studies to test his theories in
2003. The work has been replicated by researchers in the US, Germany, and Australia.
So far, teachers have mixed
reactions. They recognize that the approach is good but they worry about
efficiency and standardized tests: will kids fall on high-stakes national and
international tests?
Kapur uses the research to make his
case. Students get more output (deeper learning) for the same input (hours of
instruction), which presents another problem: 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.”
In fact, Kapur theorizes in one of
his studies that direct instruction might close students’ minds. Once a teacher
presents a solution, students may no longer see the possibility of other
solutions, or more creative approaches.
“We are saying persist, be
resilient, struggle a bit,” Kapur says.
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