So I’m the kind of nerd that puts in three 11 hour days and comes home and starts brainstorming about math ideas. My only solace is that I know the majority of people reading this are the same kind of nerd.
I was sitting here trying to help Julie work through some issues she was having with lopsided quiz scores. Lots of As, but too many Fs at the same time. So I suggested a number of error analysis techniques I’ve used in the past, but then something popped into my head (further developed by Sam).
Full disclaimer I have not yet tried this in my classes, but I think it has some serious potential. Also I’m slightly punch-drunk from exhaustion after my first two days.
Basically the goal of this activity is to get everyone in the classroom to agree on an idea. The teacher puts some problem on the board, then a set of multiple choice answers. Students discuss the problem in small groups, and then everyone votes anonymously. If the results are not unanimous, then groups shuffle and discuss the problem in their new groups. Students vote again, and again if ideas are not unanimous then they shuffle and start over.
Here is the example I have in my head right now:
After a test, put an example of a common student error on the board. Maybe number each step the student took. Then ask the class “Is the error in step 2, step 3, step 5, or step 7?” Students discuss at their table. Then they use Plickers to vote. The key here is that the teacher can’t show the bar graph of responses. The teacher just looks at their mobile device and says whether the results are unanimous or not. If they are not unanimous, then have groups shuffle (visual random groupings? Jigsaw of some sort?) and have another short discussion. Then students vote again. If everyone agrees, then you can move on to the next problem. Otherwise shuffle again.
The whole class is working together towards a common goal, but in small groups. They’re practicing talking about math and making arguments and analyzing the arguments of others. But the votes are still anonymous so no one has to feel like they’re being called out.
In my dream world it would be like 12 Angry Men where one student dissents, then sticks to their argument, and eventually everyone comes around and sees that they were right.
And think how crazy interesting it would be if everyone was unanimous, but they were all WRONG?!** The discussion after that could be so interesting. Sam suggested giving them a seemingly-easy hard problem and having one of the answers being seemingly easy. I have no idea what this would look like because I’m not smart enough for that, but I think it could be so cool (I’m envisioning the situation as saying “You all listened to the smart kid in the room, but he’s wrong, so start over”)
The biggest (non-logistical) challenge I see is that it moves away from the idea that there are multiple ways to do math. So I don’t think the question should be something like “What’s the best way to solve this problem?”. I think it’s better for things where there is only one right answer, but it’s not immediately obvious what that one right answer is.
I think there are still logistical issues to iron out here, this idea is by no means fully formed and I’m in no place to try it out for a couple weeks. If anyone is inspired and tries it, let me know!
** It occurs to me the analogy of 12 Angry Men followed by a unanimous-but-wrong vote parallels just a little too closely to falsely imprisoned people. But hey, that’s something to talk to kids about!