I tried my #LessonClose a couple of times this week in my 3D geometry class. The first time I used the Collaboration poll and the second time I used a new Learning from Mistakes poll. Both polls were given while working on the question: “Which Platonic solids can tessellate space?” It was clear that cubes would work, but there was some disagreement about the tetrahedron.
Student comments about how they collaborated included:
- I was part of the conversation when we were brainstorming answers
- I participated but did not lead
- I argued about shapes that would or wouldn’t work
- Everyone’s voice was heard
Student comments about Learning from Mistakes included:
- I assumed an angle stayed that same when rotated on the plane. This turned out to be false, and I had to later revise my answer.
- I forgot Trig, and I may have messed up a little bit with the answer of #1
- A few times, we started to follow a faulty train of logic, based on angle assumptions, that messed us up until we figured it out.
- I wasn’t exactly wrong just wasn’t very sure. My group had made a prediction that was actually true.
I’m finding it difficult to decide on the specific poll to give. I might create a new poll that let’s the student select which aspect they would like to give me some information about. This is the heart of the PDSA cycle – learning quickly and making changes to improve.
Earlier this week, Dan Meyer wrote this post about explanations and mathematical zombies using z-scores as an example. In the comments I shared an activity that I’ve used, one that I posted about last year. It so happened, that it was time for that activity again this week. In both classes, students were able to develop the reasoning behind the formula through discussion. One student even described what we were doing as a transformation to the standard normal distribution. Never once did we write a formula.
Once again my Flex Friday work connects me with students who are new to Baxter Academy. This year we are teaching them skills through workshops. This Friday’s morning workshop employed design thinking: asking and answering “How Might We … ” (HMW) questions. (For more about this approach check out The Teachers Guild or the d.school at Stanford.) Once you have a bunch of HMW questions, you attempt to answer each one in as many ways as you can think of. My colleague called this “thinking around the question” and illustrated it with the question, “What’s half of thirteen (or 13)?” And here’s what we came up with.