Wrong answers are more interesting
What is going on here, anyway? (A page from Victrola Book of the Opera)
In the midst of a quick lesson on Figaro’s Aria from Rossini’s The Barber of Seville, we asked the middle schoolers, “Where is Seville?”
Just a simple, boring question, meant to establish some context.
However, the answer was interesting. It was not incorrect per se, but demonstrated intriguingly faulty reasoning.
“Well,” one seventh grader mused, “They’re singing in Italian, so it must be somewhere in Europe?”
Seville is indeed in Europe, and the student can certainly be forgiven for not knowing exactly where. If a major goal of education is to expand a student’s perspective, however, she just gave us an opening. There are so many follow-up questions we could ask from here in order to deepen her understanding of the world: Must an Italian-language opera take place in Europe? Must a French novelist confine himself to French settings? (Jules Verne didn’t think so.) If English-speaking Americans can set their works anywhere, might we not imagine that others can do the same?
The student’s wrong answer gave us a fascinating window into her thinking and provided an opportunity for a mind-expanding lesson. And this is why wrong answers are more valuable and interesting than right ones: There’s only one right answer, but each of the infinite array of wrong ones can tell us far more about what a student knows and understands.
The exhortation to “show your work” in mathematics classes is not about proving the student didn’t cheat (at least, it shouldn’t be) — it’s so that, if she gets the problem wrong, we can figure out how it was wrong. What is the gap in the student’s understanding? If we can identify it, we can help her with not only this problem, but many future ones.
When we become experts at something, we risk losing the ability to see things from the perspective of a beginner. Wrong answers help us to return to that mindset and question concepts that we have come to take for granted. Guided by errors both common and unexpected, we discover new ways of breaking down knowledge and skills in order to better serve our students.
So many of us are ashamed of our own wrong answers because of the way they expose our ignorance. On the other hand, each one provides an opportunity for growth and learning. And if we are guided by someone we trust, these wrong answers can even help us to resolve problems we weren’t even aware of.
Teachers sometimes crave right answers as much as the students do, navigating through the classroom from correct guess to correct guess. But delving into the fallacies and misconceptions provides a much richer discussion that can address the needs of the students more directly and lead to real, immediate learning.
Wrong answers are not to be feared. They are to be appreciated and even sought after for the light they shine into the unexamined places in our minds.