The first part of the Hills walk was steeper than I remembered. I had dressed for standing in the car park, apparently, and was too warm within fifteen minutes. Stopped to put the jacket in my pack and noticed I was holding my jaw tight, a school habit transported several kilometres at my own expense. The next stretch was easier. My breathing settled into the pace of my steps, and I stopped checking how far remained. By the car my calves were tired and my face felt gritty with dried sweat. Pleasant enough. The bath was considerably more persuasive than the marking table tonight.

I am revising a lesson on probability because the class can calculate the answers and still argue that a long run of one outcome makes the opposite overdue. Repeating the rule has not helped. I could let them predict a sequence first and keep their predictions visible while we test it. The difficulty is arranging a useful disagreement without making the students who are wrong feel displayed. I spend enough time avoiding that position myself. A written prediction collected before discussion might work. It also means thirty fewer hands waving while I try to distinguish confidence from understanding.

A Year 8 student waited until everyone else had left to show me a correct answer. He had erased most of the working and wanted to know whether it still counted. I said it counted, but I wanted to see how he got there. He reconstructed it slowly, with three false starts, then grinned at the page rather than at me. I was pleased in a way the whole-class results rarely manage. Later a colleague asked why I was late to the meeting and I said a student had needed help. That was accurate, though it left out the part I would have preferred to keep doing.