Slow motion problems: a teaching method I have learnt this year

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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?

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12 thoughts on “Slow motion problems: a teaching method I have learnt this year

  1. I would love the mini-whiteboard idea to work in English. I’d be willing to give it a try. These are some of the problems I anticipate.

    1. When sentences don’t work, they usually don’t work in a really wide variety of ways. It would probably be quite time consuming to look at each individual whiteboard to determine all the particular things they’re getting wrong. It’s then quite time consuming to explain why each of these individual things is wrong and what they need to do to correct it. In the meantime, you have students who have got it right the first time just sitting there.

    2. In Maths, it seems to me (I could be wrong) that if all your students end up solving the problem in the same way and arrive at the same answer, you have succeeded. In English, with the exception of grammar work, if all your students end up answering the question in the same way, this is treated with suspicion by colleagues.

    Would happily give the mini-whiteboards a go, though. Are English teachers using them at your school? If so, how are they working out?

    1. for discrete language features for language learners, i.e., If the answer is “He is going to Perth,” what is the first word in the question?

    2. You would need to narrow the scope of what they are doing in order to make it more of a closed question, so you would have to focus in on a topic sentence with two clauses that identifies… you get the picture and I’m not an English teacher. Of course, this grates on a lot of English teachers because they feel it stifles self expression. My view is that by learning lots of ways to express your thoughts, you enhance self expression.

    3. The variety of sentences created can themselves be the source of some interesting peer and teacher feedback – “yes it’s wrong, but can anyone say why it is wrong? / Suggest ideas to improve it?” You develop other students’ analytical skills. If it’s really complicated, then save the feedback for another part of the lesson – give that student another whiteboard and then give them the detailed feedback later on. If it’s a hinge-point question – checking that everyone has got it – you could write a wrong sentence and ask for correction, or be very specific with the task to limit the possible answers. Word level is far easier, of course, and I would never go more than a sentence with this.

  2. I have worked in departments where having to teach the Head’s way would have made me a worse teacher. Not all Heads are capable of accepting that other teachers do something better than them. Even when results clearly show that (I was once told to cease doing comparative box-and-whisker plots of our Year 9 classes — the truth can be ugly).

    My current Head is awesome, and we do align much of our teaching. But then he is capable, humble and secure in his position, which is not that common.

    So I have sympathy for those who wish to do things their own way.

    1. That clearly could be an issue. How about a rule about experimentation to see if another way worked better? “Hey, your class did really well. But if we … might that be better?”. “Ok, let’s try that and see.”

      1. Yes, that would be good. But these people were never going to try things another person’s way, because it might show how bad their way was.

        Heads tend to older and more experienced. Younger staff can find it very hard to persuade a person who is senior and can fall back on “experience” to block novel ways. It’s not a teacher thing, just a human one.

        And while I obviously think my ideas are worth a try, I also had fellow staff at those schools who proposed ideas that were never going to work, so I wasn’t that unhappy when experimenting was blocked in those cases.

        The key is to try out techniques that are *shown* to work. And to be shown the powers that be must collect and release the data. If they won’t do that, you’re open to stupid as well as good ideas.

    2. I think individual teachers in poor departments are in a bind, but that’s not really what I’m talking about. Heart surgeons don’t do things their own ways. Bridge engineers don’t do things their own way. We will mature as a profession when we all seek to do our jobs in the most effective way.

  3. Hi Greg,
    It seems to me that the point you are making here is that mastery learning (and good understanding) is promoted by taking the complexities of a task in small steps. So, actually, the technology – in this case – small whiteboards – isn’t the issue (although small whiteboards can be very useful). The key is showing everyone the small steps involved in working through a learning task.
    In the case you use as an example, I should imagine you are also able to hold the attention of the class as they compare how far they’ve got with how far others have got and then there’s the opportunity for error correction of broader discussion of the detail.
    The approach can also be used in any subject and at all levels. The pedagogical point is that taking small steps should enable everyone to keep up, and anything that aids that process is to be recommended.

  4. How do you account for sampling error, “class personality” and other sources of noise? When I was a TA, I often had sections that responded very differently to instruction that was extremely similar.

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