The value of being wrong is often underrated in the mathematics classroom. You may or may not be familiar with the internet meme “Wrong Answers Only” where you are presented with a question prompting you to reply with the “best answer”. The twist is that the best answer has to be completely wrong, often resulting in hilarious and unexpected responses. 

In the fall, the Upper School Math Department attended the National Council of Teachers of Mathematics Annual Meeting and Exposition in Los Angeles. We were all excited to be able to return to in-person collaboration and conferences after a long spell of non-attendance and virtual conferences. Each of us left with new ideas and inspiration for our classrooms. Some of the ideas will take longer to implement and research, but I always try to leave with one idea that I can start using immediately. 

I attended a talk given by Dan Meyer, the current director of Research at Desmos (if your child has me as their teacher, they will probably make a joke about how much I love Desmos). During the presentation called “Math Without Mistakes,” he made the argument that there is more to learn from wrong answers than we usually assume. One of the great teaching strategies that I took away was “Wrong Answers Only”. Let me give you an example of how it might be used on a word problem:

“Two cars start 100 miles apart on the same road. One car is traveling east at 50 miles per hour, the other is traveling west at 60 miles per hour. How long will it take for them to reach each other?”

There are two camps of readers right now: Those who have shut down and given up, and those who have already tried to start solving the problem. But I’d like to suggest a third approach: “Wrong Answers Only”. Try to think of a solution that you know is absolutely wrong. Like so wrong that it’s ridiculous. How about 1,000,000 hours? That’s obviously wrong.  Even the most reluctant student can come up with a wrong answer. But why would we want a deliberate wrong answer? There are two main reasons: it encourages participation from a broader population of students and it gives the teacher insight into what students do understand about the problem. The biggest mistake that most students make when trying to solve a word problem is immediately trying to write an equation before they really understand the situation. Wrong Answer Only slows down the problem solving process intentionally. 

Now, there is obviously a difference between deliberate wrong answers and unintentional wrong answers. There are right answers and wrong answers, but there is a lot of gray area in between. There are wrong answers with great logic and reasoning and there are “right” answers with incorrect logic, bad reasoning, or just a bit of luck. The ability to recognize that an answer is wrong is an important step to understanding the problem and a skill that should be highlighted and valued. The next time your child is stuck on a math problem, try asking them for “Wrong Answers Only” and have them explain to you why their answer is wrong. 

In case you were wondering, there are lots of fantastic wrong answers to the question I posed: 0 hours, 200 hours, 500 miles, or 700 pancakes. The right answer was approximately 54 minutes and 32.7 seconds.