Journal-writing time for my class, and by that I mean, “hmm I’m three weeks behind now … wait, 1, 1, 2, 3 … dang it I’m turning into a Fibonacci sequence, this is bad!”
First, an update on how my math classes are going.
I’ve been sticking with (what I know of) Thinking Classroom strategies pretty consistently since the last update. I’m less overwhelmed than 1st semester, but still a lot of last-minute decision making as class is about to start. (I keep reminding myself that someday my kids will be old enough to, you know, just go to bed without requiring two hours of policing in the evenings and maybe I’ll be able to actually prep everything in advance …)
Students are functioning pretty well with group work at the whiteboards & windows, and I’m doing an okay job adapting the textbook concepts into Decent Problems. (Not “Good Problems”, but they’re getting there.) I’m still wrapping my mind around how to identify a good *extensible* problem – something that you can add more interest to for groups who get to the goalpost sooner. Right now this feels like A Problem To Work On: what are the strategies we can use to extend a mediocre problem into something with more to think about? What are the requirements? Which starting points should we just throw out immediately (if any)?
However, since this is going sort-of-okay, I’m not putting my full attention on that this week. On Thursday I wrote down a four-day plan for myself that would give me some structure for getting course assessments in gear. It went something like this:
Day 1: Work on a Good Problem, talk about <mathematical competency>, get students to share good vs bad examples.
Day 2: Work on a Good Problem, then have groups self-assess with rubric made from their examples.
Day 3: (because I need to get content assessment going as well) Group quiz on <content assessment topic>.
Day 4: Individual quiz on <content assessment topic>, then work on something else (either intro to next unit, or just something for fun).
I’m currently just done Day 2 of said plan. I forgot to do the “walk around with a clipboard and assess three groups myself” step, so they didn’t drastically improve, but I decided to assess on Reasoning & Analyzing (a heading in our “competencies” doc which amounts to stuff you to do start working on a new problem) and that wasn’t something I needed to see drastic improvement on anyway.
Our two-weeks-ago reading was Mathematical Fluency: The Nature of Practice and the Role of Subordination by Dave Hewitt. We’d talked about the basic idea in class already: that rather than having kids do a repetitive set of practice tasks to master a skill, you can instead give them a larger task that requires using that skill as part of the process.
I was already pretty on-board with the idea just for the sake of making the practice less tedious and to give room for more creative and puzzle-solving sorts of thinking. But when I finally read the article (today) I found out it goes deeper than this. What Hewitt is suggesting is not just that this allows us to skip the tedium. Instead he’s saying that focusing beyond the basic skill onto something else actually helps us learn more deeply and with more knowledge retention.
His example was with learning to sail. If your attention is constantly jumping between rudder, rope and body position, you’re so focused on the immediate action that you lose track of how the other two are affecting the goal. Instead, his teacher had him look at the sail itself – to watch it and see how control of the rudder, rope and body position affect it.
The idea made me rethink my own university learning (where I first found myself frequently behind the learning curve in mathematics). During my undergrad, I noticed that when I was learning a new topic or course it would often feel hazy and I’d have trouble with it, but when I took a later course that used those skills I found them getting comfortable quickly. I’d attributed this to the way that knowledge and skill sort of ‘settle in’ after that initial struggle to learn, and there’s probably still something to that. But perhaps I was actually getting a better learning experience for my 2nd year courses when I was assumed to know them already in 3rd year …?
The whole paper is worth a read, and if I understand correctly you can grab a free read at jstor via that link above.
More readings to come, and at some point I’ll go back over the whole list and see which ones I’ve missed!