I’m demonstrating a number string for a group of staff members (including some who are joining virtually via webcam/phone) who support secondary math teachers, many of whom I’ve never met before but would be working with for a full school year. These staff members have never taught or seen number strings before even though many of them are former math teachers—this is part of their initial learning experience. In addition to creating a mental image for these staff members of what a number string is, I also wanted to demonstrate the type of learning experience we should be providing for teachers; in contrast to the typical “I lecture about a strategy and give examples/non-examples and then you apply it” professional development session, this is a demonstrate-then-debrief approach. One more layer: I wanted our work together over the full year to gradually chip away at the cult(ure) of correctness that often pervades math classrooms (fishing for or steering people towards the right answer, treating wrong answers as dangerous, only valuing people who give right answers), especially because I knew that many of these staff members—despite having taught math themselves—still didn't see themselves as “math people” and still saw the discipline of mathematics as a difficult-to-access temple that not everyone could enter.
Prior to the clip below, we've worked through finding the speed when traveling a distance of 36 miles in 2 hours and in 3 hours, and I've asked whether we'd be going faster or slower if we traveled that same distance in 1.5 hours. Someone has explained why we're going faster, and now I'm asking for a calculation of the speed. Here's what's on the board:
During the demonstration, a staff member acting as student gave a strategy for finding speed that wasn't mathematically viable, thinking it was a viable strategy (not trying to throw me off or test me). Making an actual mathematical mistake can be embarrassing for an adult who obviously knows how to calculate speed, and it could be particularly embarrassing because she was trying to not just give me the standard algorithm; she was trying to offer an alternative. I wanted to respect her contribution and validate what was there, but not spend a ton of time digging into the exact misunderstanding both because I wasn't sure in the moment exactly what she was thinking (“she’s confusing rates with numbers and we can’t operate on rates the way we can on numbers, like the classic miles per gallon vs. gallons per mile calculation!” was about as far as I got; this is an area of growth for me because I think a teacher more fluent in talking about rate and ratio would have been able to understand this more quickly and handle it more adeptly), and because I suspected she’d quickly recognize and be embarrassed by her error. So the approach I took was to identify something that made sense about what she had said—the idea of a unit rate—and move forward to consider another strategy. However, you can hear her laughing and being embarrassed and whispering as she tries to figure out why her method doesn't work… for the next several minutes. And she brings it up in the debrief later. Take a look:
Why does this feel like a dilemma? The most superficial response here is that she and her seat-partner were now distracted and not paying attention to what I’m trying to demonstrate, but more importantly, I've allowed her to reinforce the cult of correctness. Hearing her be so vocal about her embarrassment could (hypothetically—I can’t prove this is how anyone actually experienced this particular moment, but it seems worth discussing nonetheless) reinforce for someone else that being wrong is embarrassing (rather than an important and inevitable part of learning) or that being right is more important than contributing mathematical thinking to the conversation. Someone who shared her inaccurate idea but hasn't yet figured out the flaw might feel even more embarrassed; I’m stupid both for being wrong and for not figuring out why it’s wrong. And, while she’s being vulnerable in public, it’s not exactly by choice; admitting an error because it’s been made visible is very different from exploring possible errors or areas for growth that others haven’t seen, and in fact can sometimes be a defensive posture: If I tell you what I did wrong before you tell me what I did wrong, then you can’t really criticize me.
What to do instead?
There are two places I think I could have handled this differently: a) when she actually made the error and b) in the debrief. In the moment of the error, I could have stopped to dig in further, even though it would have taken us away from the number string, because it would have allowed us to engage in some important mathematical conversations. In the debrief, I could have explicitly addressed her reaction and used it to make a broader point about the type of culture we want to create in a professional learning community and why that culture is important. I don’t know if I necessarily should have done the former, and I’m not sure I know how I would have approached the latter. That’s why I’m curious for your feedback; how would you have addressed this in a room of teachers? When would you have said/done something, and what would you have said/done?