This was the title of the best talk I went to at the MathFest last week. It was given by Kathryn Leonard of California State University Channel Islands, who was one of the winners of an award for early-career mathematics teachers.
Leonard’s main point was that as a society, we overdramatize failure and simultaneously deprive students of the opportunity to learn how to deal with it. “We currently live in a society of extreme failure avoidance,” she commented. Because we think that giving a student an F will scar him or her for life, we never do.
We also do not discriminate between failure and “capital-F” FAILURE, she argued. One need not look farther than the recent headlines about the Penn State football program (though this is not the example she used). Losing a football game is a small-f failure. Letting a sexual predator remain on campus for a decade is a big-F FAILURE. When we overestimate the importance of the first kind of failure, we become blind to the second kind.
She said that it’s especially important for mathematicians to cope with failure, because “we spend 99 percent of our time in a state of failure.” I had never thought about it in quite this way, but it’s true. When you’re doing research, if you’re doing it right, you’re working by definition on a problem you do not know how to solve. That means that the great majority of the time you will be trying ideas that don’t work. If you do not have the courage to fail, to try those 99 ideas that don’t work, you will never get to the one idea that does. I’m sure that the same thing is true in many other academic disciplines and non-academic pursuits. Every successful entrepreneur, for example, has probably had his or her share of failures.
One of the purposes of education is to give students a chance to experience those small-f failures and learn to overcome them. Ironically, in mathematics education (even though math has a reputation for being difficult) we really don’t do enough of this. The problems served up in math courses and on math exams are of the pre-digested type, where once the student knows how to play the game, success is almost guaranteed. No failure there. For example, I didn’t seriously fail to understand a math course until I hit graduate school.
In fact, at my last college reunion one of my classmates made an interesting comment that has stuck with me. “You know, Dana, I never thought that you really had the full Swarthmore experience,” he told me. He explained that almost every student at Swarthmore eventually runs into a student smarter than them, or a course they can’t get. He didn’t think that had ever happened to me, and though it may sound immodest I think he was right. So I was completely unprepared for grad school and for my later academic career. I didn’t even learn the first and most elementary lesson about failure, which is when you can’t do something, you ask for help. I saw academia as one big competition, me against the world, and so I never learned to collaborate, never learned to share ideas, never learned the value of a mentor. It’s no wonder that my growth as a mathematician was stunted.
Eventually I did fail in a big way. I was denied tenure and had to change careers. My college classmate was shocked that this happened to me, of all people. I think it was inevitable.
So, getting back to Kathryn Leonard, I really liked the conclusion of her talk. She said, “I’m making a pledge to…”
- Talk about failure neutrally, and accept other people’s failures. If a student gets an F, don’t act as if it’s the end of the world. No one died. She also said it’s important to be open about your own failures, and so she told us about how she dropped out of high school as a senior. That could have turned into a big-F FAILURE, and she said that to some extent she was just lucky that it didn’t.
- Take risks and be open about it.
- Offer the cookies. This was a reference to a psychological experiment she had discussed, where the subjects were given a task with one subject as the leader. While they worked on it, the experimenters brought around a plate of cookies, and the students who had been given the leadership role (even though they had done nothing to earn it) voluntarily took more cookies. I think her point here was that you should not feel entitled to more just because society says that you are a “success” and another person is a “failure.”
Why do I write about this in a chess blog? Well, first of all, chess is a tremendous way to learn about small-f failure. In fact, the French word for “chess” is échecs, which also means “failures.” Just don’t ever confuse losing a chess game with a big-F FAILURE.
Also, I think that many chess players would be wise to learn from her last point. Some people think they are entitled to more cookies just because they have more rating points or more titles. An even larger number of players probably feel that they are entitled to fewer cookies because they don’t yet have a high rating or a title. So, if you haven’t gotten to the level you want to reach, and you’re feeling frustrated by your failures, ask for help. And if you are one of the lucky ones who has gotten to a high level, be willing to share and encourage the ones who haven’t.