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Learning Is Optimized When We Fail 15% of the Time

To learn new things, we must sometimes fail. But what’s the right amount of failure? Research led by the University of Arizona proposes a mathematical answer to that question.

A “sweet spot” for learning

Educators and educational scholars have long recognized that there is something of a “sweet spot” for learning. That is, we learn best when we are challenged to grasp something just outside the bounds of our existing knowledge.

When a challenge is too simple, we don’t learn anything new; conversely, we don’t enhance our knowledge when a challenge is so complex that we fail entirely or give up.

Sweet spot is failing 15% of the time

So, where does the sweet spot lie? According to a study published in the journal Nature Communications, it’s when failure occurs 15 percent of the time. Put another way, it’s when the correct answer is given 85 percent of the time.

“We’ve put the idea that there is a ‘zone of proximal difficulty’ in which you ought to be maximizing your learning on a mathematical footing,” said UArizona assistant professor of psychology and cognitive science Robert Wilson, lead author of the study, titled “The Eighty Five Percent Rule for Optimal Learning.”

Machine-learning experiments

Wilson and his collaborators at Brown University, the University of California, Los Angeles, and Princeton came up with the so-called “85% Rule” after conducting a series of machine-learning experiments. The researchers taught computers simple tasks, such as classifying different patterns into one of two categories or classifying photographs of handwritten digits as odd versus even numbers, or low versus high numbers.

The computers learned fastest in situations where the difficulty was such that they responded with 85 percent accuracy.

“If you have an error rate of 15 percent or accuracy of 85 percent, you are always maximizing your learning rate in these two-choice tasks,” Wilson said.

When researchers looked at previous studies of animal learning, they found that the 85% Rule held true in those instances as well.

Applied to humans

When we think about how humans learn, the 85% Rule would most likely apply to perceptual learning, in which we gradually learn through experience and examples, Wilson said. Imagine, for instance, a radiologist learning to tell the difference between images of tumors and non-tumors.

“You get better at figuring out there’s a tumor in an image over time, and you need experience and examples to get better,” Wilson said. “I can imagine giving easy examples and giving difficult examples, and giving intermediate examples. If I give really easy examples, you get 100 percent right all the time, and there’s nothing left to learn. If I give really hard examples, you’ll be 50 percent correct and still not learn anything new. If I give you something in between, you can be at this sweet spot where you get the most information from each particular example.”

Lessons for education

Since Wilson and his collaborators were looking only at simple tasks in which there was a clear correct and incorrect answer, Wilson won’t go so far as to say that students should aim for a B average in school. However, he does think there might be some lessons for education that are worth further exploration.

“If you are taking classes that are too easy and acing them all the time, then you probably aren’t getting as much out of a class as someone who’s struggling but managing to keep up,” he said. “The hope is we can expand this work and start to talk about more complicated forms of learning.”

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