I had lunch a couple of weeks ago with a group of about 20 math faculty, all of whom teach at a community college. The lunch was good but the discussion was even better.

We talked about what makes math so hard for students and covered the usual suspects—students haven’t had enough rigorous math in high school; they aren’t willing to work hard enough; at the first sign of trouble, they bail concluding there’s no way they’ll ever be able to figure it. But then one of the teachers said, “Sometimes I just can’t figure how why they don’t get it. It’s not that hard or confusing.” “But math was easy for you—that’s why you’re a math teacher,” one of his colleagues observed.

So maybe the best math teachers would be those who struggled with the content, and maybe this is true of all fields. When you understand something, when it’s crystal clear and makes perfect sense, it is hard to figure out how or why it’s so confusing to somebody else. It’s easy to imagine that they have a problem—that maybe they just aren’t smart enough. But teaching is pretty much a lost cause once a teacher starts believing the students can’t learn.

“I really don’t like to have students work problems on the board,” another of the teachers commented. “I just hated that when I was a student. You know the kid at the board doesn’t know what he’s doing, and seeing him make a mess of a problem is such a waste of time.” But learning how to solve problems is a messy process for some people—just like learning to write, to draw, to dance, or to run a CAD program. It’s so easy for us to project our learning preferences on our students, quickly forgeting that not all learners are like us. Does seeing other students working problems on the board help students to learn? Does reading other students’ papers help students write better? The best way to answer these questions to ask students.

I don’t really think we want people who aren’t all that good in math teaching math, but I would have to say one of the best math instructors I have ever seen was a woman who dropped out of high school. She later earned a master’s degree, but she starts her classes by telling students, “There was a time in my life when I hated math. I failed the first several math courses I took.” Students wait semesters to take her math courses.