One of the neatest ways of describing approaches to teaching that I’ve heard recently came from Jo Morgan on one of Craig’s podcasts: Maths teachers usually operate in on of three modes: I do, we do, you do.
It’s an oversimplification, but I like the way you can categorise approaches with this terminology. You might say that discovery is ‘you do, we do’, whereas ‘I do, you do’ is the lecture model and the Socratic method, that I was trained to use in my first school, is perhaps ‘we do, you do’.
Jo had been working with an inexperienced teacher who was struggling with a ‘we do, you do’ approach. Her suggestion was that the teacher should first show the pupils – employ the ‘I do’ mode, before moving on to involving pupils in a problem. Unsurprisingly, I disagree.
I’ve tried out ‘Silent Teacher’, traditional lecture and had a fairly substantial craze on discovery after my GTP, but I always come back to the Socratic method. Why do I like ‘we do’ so much?
Firstly, it ensures that you build up the mathematics in small steps that the pupils understand. In other words, it helps you to avoid the curse of knowledge. In the ‘I do’ mode, you may be making logical leaps that are too large but you won’t find out until it is too late.
Secondly, it emphasises to the pupils that maths is an interrelated web of ideas which can be developed from each other, and encourages the teacher to carefully consider how they will introduce a topic in a way which the pupils can make the steps.
Finally, it forces you to check that all pupils are listening to and understanding what you are saying. If pupils know that they may be called upon at any moment, then they have to be listening. Of course, it’s not perfect: they may not be listening, but at least you’ll find out and correct that.
That said, I empathise with new teachers’ struggle. It takes time and experience to deploy this approach effectively and at Highgate we spent a lot of time training people to do so. Some key strategies:
- Hands-down questioning with no opt-out: My mentor used to say “You have to have an idea. It can be a terrible idea, but you have to have one.” This way you find out what the pupils are thinking, and any misconceptions they may have.
- Back a step: If a pupil gives an incorrect answer, ask them an easier question to help build up to the original question. This requires good understanding of the prerequisite knowledge on the part of the teacher, and is easier if you have a clear Scheme of Work.
- Bounce-back: Another option is to pass the question, or a simpler one, on to another pupil, then come back to the original intended target.
- Differentiation: I’m not a huge fan of this, but I do sometimes differentiate my questioning; I’m looking for a balance between not asking too much patience of the high-attainers, whilst making sure the lower-attainers understand.
You can see (or at least hear) me employing ‘we do’ as the initial approach to instruction in this video:
Overall, I feel that ‘we do’ strikes a good balance between discovery and direct instruction: The teacher uses their expertise to guide the learning, but still gives the pupils a stake in making decisions and the experience of creating new mathematics.
Indeed, when I was speaking to my old HoD about this last week, he told me about the most consistent positive feedback his pupils give in surveys: Compared to their previous schools, they enjoy taking part of the development of new techniques, rather than just being shown how to apply them. (ps. they also get probably the best A-level results in the UK)
What do you think? I would love any feedback on the specific lesson or the idea in general.