In my maths department, all teachers use the same detailed lesson plan and resources. Each plan contains examples and problems, as well as worked solutions to these examples and problems. The solutions are necessary because maths teachers often use surprisingly diverse approaches.
We meet as a cohort team once we have some assessment data. We then trawl through it, looking for anomalies. If groups are evenly matched, we might look for questions where one class seemed to do much better than the others. In cohorts that are ability grouped, we might look for questions where a less advanced group outperformed a more advanced group.
We then ask the teacher whose group performed well to try to account for this difference. Even with a detailed plan, there will always been slight differences in how a teacher interprets something or improvises in response to a student’s question, for instance. Given that we have locked down everything else, once we surface these differences, we can make reasonable, if not scientific, inferences about the effect of these differences. Sometimes this process is hard because the teacher will insist they ‘just taught the lesson plan’. But there’s pretty much always something there, hiding. We often have the lesson plan documents open in the meeting so that we can make adjustments for next time, based on what we have learnt.
This approach to improvement is not a genius idea. It is a simple idea. But it is an idea that you would struggle to apply in many maths departments due to notions of teacher autonomy. I don’t want to be autonomous. If my colleague is teaching something better than I am then I want to start doing it her way.
And that’s what has happened this year.
A colleague of mine, a fine teacher, has moved into one of the cohorts that I teach and I have learnt lots.
I have used mini-whiteboards for many years. I think they work well because you can collect feedback from the entire class. My routine involves posing the question, giving the students enough time to complete the question – an essential point – and then going ‘3, 2, 1 and show’. At this point, I expect them all to hold up their boards, even if they are not finished or not sure they have the right answer. I train them on this routine early in the year to ensure that it is slick.
However, my colleague doesn’t do this with multipart questions. For instance, if the problem involves solving a trigonometric equation, she might ask the students to rearrange the equation – the first step – then immediately hold up their mini-whiteboards as soon as they have done this. After this step, and once any errors have been corrected, she will ask them to do the same for the reference angle – the second step – and so on. Only later will students complete all steps independently.
When I heard about this, I wondered why I had not thought of it. It makes a lot of sense. There is little point continuing with a multipart problem if you’ve messed up the very first step. My colleague’s approach is entirely consistent with Rosenshine’s Principles of Instruction; a key document we use to aid our planning.
So I have started doing this too. I cannot prove that it has made me more effective, but I reckon it probably has.
As an aside, I used to accept the idea that mini-whiteboards are a maths and science thing. They work well in these subjects, but they don’t lend themselves to writing whole paragraphs, let alone essays, and so they are of limited use in English or history.
I’m not so sure any more because I have started to think we neglect sentence-level work, and sentences do lend themselves to mini-whiteboards. A paragraph is essentially a multipart problem made up of sentences. Why move on to the second sentence if the first one sucks?