You can be trained to … prepare an organized “lesson plan” (which, by the way, insures that your lesson will be planned and therefore false).
-Paul Lockhart, A Mathematician’s Lament (p. 11)
I remember reading that phrase of Lockhart’s in my first year of teaching and sneering a bit. Yea, Lockhart has some good ideas, but not lesson planning is absurd. Maybe you can wing it some days and things fall into place, but that’s a recipe for disaster in the long run.
But I’m starting to change perspective, in one specific way.
I’ve shifted away from thinking about lessons as objects of teaching that have to act as coherent wholes. Part of this is my move to 90 minute blocks this last year. But more broadly, I no longer think of planning a lesson; instead, I think about planning tasks. A task could be anywhere from 5 to 120 minutes, though the majority fall in the 10-20 minute range. Some are one problem, some are a set of problems, often leading to some discussion. Delivering explicit instruction doesn’t fit neatly under the umbrella of “task”, but explicating for a few minutes fits in here as well. I might show up to a lesson on polynomials with a few Illustrative Mathematics tasks, some questions prepped for whiteboarding practice, an error analysis task, a Which One Doesn’t Belong, a Desmos Activity Builder lesson, a Shell Centre formative assessment lesson, and few bits of explicit instruction and neat examples prepared.
For a typical class, I try to come prepared with a set of tasks (in addition to a warmup, homework review, assessment, etc) that, altogether, I expect will take one and a half to two times the length of the class. I also come with an order and flow I expect to teach them. There are lots of types — tasks that are useful for introducing a new concept, diving deeper or introducing a new perspective on an idea students have seen, a piece of explicit instruction that will be helpful for students, practice to reinforce skills, formative assessment to see what students do and don’t understand, extension to assess how well a concept transfers to a new context, and more.
Most days, I teach the tasks I prepared in the order I planned them. The extra tasks I keep on the shelf until the next day. But I’ve found thinking at the grain size of the task really useful when I need to respond to different needs that come up during class.
The single most common change I make is around engagement — I love Illustrative Mathematics tasks, but they don’t quite have the fun factor that a Desmos lesson does. If student engagement is falling off a cliff, I can swap for something else, and save that task for tomorrow. No big deal, and the fact that I don’t have grand plans for the lesson as a whole helps me make that change.
I’ve also found myself making more and more changes based on formative assessment. I try to come in with more practice tasks than I think I will need, so that if I’m planning to introduce a new concept but kids aren’t quite there, we can step back and consolidate some big ideas before moving up a level. On the flip side, there are times when I underestimate what students can do — practice is too easy, or they’re just ready to move on. I can get rid of something that’s unnecessary, and jump to a more challenging task that might have been planned for the next day, but I’m happy to have on the shelf ready to go. And I can plug and play explicit instruction on demand, and move it forward or put it off when I need to.
I’m not trying to endorse Lockhart’s idea. I do think it’s foolhardy to walk into a classroom without a plan. Maybe he’s at a point where he just has so many things up his sleeve that he can do a great job without one. I’m not. But there’s a great deal of value in building in deliberate flexibility on an everyday basis. And I can see myself becoming more and more flexible by planning at the grain size of a task, and building in moments of formative assessment that allow me to make those deliberate changes as the need arises.