Studying Wrong Answers Helps Learn the Right Ones

With teaching as with baking, sometimes you should follow steps in a very particular order. If you don’t do this, and then that, and then the other, you don’t get the best results.

Two researchers in Germany wanted to know if, and when, and how, students should study incorrect answers.

To explore this question, they worked with 5th graders learning about fractions. Specifically, they taught a lesson about comparing fractions with different denominators.

(When studying this topic, students can’t rely on their instincts about whole numbers. For that reason, it’s a good subject to understand how students update conceptual models.)

They followed three different recipes.

One group of 5th graders saw only correct answers.

A second group saw both correct and incorrect answers.

A third group saw correct and incorrect answers, and were specifically instructed to compare correct and incorrect ones.

Which recipe produced the best results?

The Judges Have Made Their Decision

As the researchers predicted, the third group learned the most. That is: they made the most progress in updating their conceptual models.

In fact: the group prompted to compare right and wrong answers learned more than the group that saw only the right answers. AND they learned more than the group that saw (but were not prompted to compare) right and wrong answers.

In other words: the recipe is very specific. For this technique to work, students should first get both kinds of information, and second be instructed to compare them.

Important Context

I’ve held off on mentioning an important part of this research: it comes in the context of problem-based learning.  Before these 5th graders got these three kinds of feedback, they first wrestled with some fraction problems on their own.

In fact, those problems had been specifically designed to go well beyond the students’ mathematical understanding.

The goal of this strategy: to make students curious about the real-world benefits of learning about fractions with different denominators in the first place.

If they want to know the answer, and can’t figure it out on their own, presumably they’ll be more curious about learning when they start seeing all those correct (and incorrect) answers.

As we’ve discussed before, debates about direct instruction and problem-based learning (or inquiry learning) often turn heated.

Advocates of both methods can point to successes in “their own” pedagogy, and failures in the “opposing” method.

My own inclination: teachers should focus the on relevant specifics. 

In the link above, for example, one study shows that PBL helps 8th graders think about deep structures of ratio. And, another study shows that it doesn’t help 4th graders understand potential and kinetic energy.

These German researchers add another important twist: giving the right kind of instruction and feedback after the inquiry phase might also influence the lesson’s success.

Rather than conclude one method always works and the other never does, we should ask: which approach best helps my particular students learn this particular lesson? And: how can I execute that approach most effectively?

By keeping our focus narrow and specific, we can stay out of the heated debates that ask us to take sides.

And: we can help our students learn more.

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