As some of you know, I'm entering a transition in the day job. This involves a lot of interviews, some where I'm the interviewee and some where I'm on the panel of interviewers. It makes for an interesting dual perspective.
My current school includes something extra in the interview process—candidates have to teach a brief mock-lesson. For me, that's the make-or-break portion of the interview. I can forgive a few weak answers on the standard interview questions, but if the math teaching isn't up to snuff, I'm not recommending.
Since we're nearing the end of the school year, I'm also leading my classes through reviews to prepare for their final exams. This includes going through problems we haven't discussed in-depth since last fall. Most of the time, it's fine. But a couple of times last week (in calculus, naturally), I had some ridiculous cerebral failures.
That's fine, too. I make a point of emphasizing to my students early on that I can make mistakes, and if they catch me at it, good for them. Seeing me make mistakes without falling apart seems to help them be more willing to take risks even though they might be wrong.
I got to thinking about the two situations. Where's the line between "Oops, the teacher's human and makes mistakes" and, "No, this interviewee doesn't have what it takes"?
My guess is that the line is in awareness. When I screwed up in calculus, I either knew right away or within moments. I immediately 'fessed up to the students and set about figuring out what I'd done wrong. With interviewees who aren't cutting it, they generally seem to think what they're doing is fine. Top interviewees often have more to criticize about themselves. There's a question in the interview about what they think they need to work on most. It's always interesting to correlate their answer to this question with their performance in the mock-lesson.
So, everyone, let's aspire to make mistakes. Own them, learn from them. But never let it cross into incompetence. If we are incompetent in an area, let's be aware of it, and work to correct it.