Whether it be a small arithmetic error, or correcting a student when they were actually doing something right, we always make mistakes in class. The other day, I wrote the parametrization of the unit circle as x=cos(t) and y=sin(t) and took the derivatives as dx/dt=sin(t) and dy/dt=cos(t). It wasn’t until a student humbly interrupted me saying, “Um, Ms. Schettino, don’t you mean -sin(t)?” and I looked at it for a little while, trying to figure out what she was saying, and then I realized what I had just done. I knew I was calculating the arclength, using the arclength formula, and that I was going to square it anyway, so I just left off the sign, but they didn’t know that – skipping steps in my head is a really bad habit. So I said, “Yes, oh yes, sorry – thanks so much for fixing that for me.”

I do things like this all the time, and hopefully, I am a big enough person to admit my mistakes and give students credit for finding mine, especially if it might affect some students’ understanding. I was talking to a colleague about this with respect to PBL the other day. I asked her why it’s so important to her to admit to students when she makes mistakes and to fix them in front of the students. She told me that she likes to “model proper mistake-making” for her classes so that when they do it, they can see what she does and use the same humor, self-confidence, risk-taking and humility to fix their own mistakes, learn something and move on. I actually see this in her classes and have heard her students say that they do this too. I believe that without this attribute students do not fully take advantage of a problem-based curriculum because they cannot find the way to learn from their mistakes. I even heard a student once say that “There was one time during class that I put a problem up at the board and got the entire thing correct. I was actually, in a way, disappointed because I feel like I learn better from my mistakes.” I was amazed that a student could see that in her own learning, that the growth happened for her when she was wrong, as opposed to when she was right.

Clearly, being wrong in front of students can be somewhat embarrassing, but for me, it allows me to have bit of solidarity with my students, if even for a moment. It allows me to feel, what I ask them to do every day, to move out of their comfort zone and attempt a problem that they cannot do, and perhaps not live up to their expectations of themselves. It reveals my human side, which I do end up feeling the relational part of my teaching is all about.