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.
Very interesting. We have also been employing an I do, we do, you do model. I’m still not really clear, however, on what “we do” means. I don’t see “I do” as a pure lecture style. I think you have to have no opt-out questioning when you are explaining to the class even if it is just to keep them listening. So I think I would call what you described as “I do”. With “we do”, I suppose the question is, what are each of us actually doing? I tend to see this more as mini whiteboard where they are doing, but getting immediate feedback on a few seconds of work. The way these questions build is a critical part of the lesson that then leads them to being successful in a longer, more independent “you do” task.
It seems like you’re using ‘we do’ in a slightly different context from how Jo did on the podcast. – more like Craig’s ‘your turn’ approach. I definitely think this is a good idea, after the initial whole-class introduction to an idea.
I also see that sometimes, even though the class are doing each step of a problem, the teacher can be guiding and doing the key developmental steps, in which case it’s more like ‘I do’.
Did you watch the video? It’s not the best topic to demonstrate this. A better example would be if I’m teaching how to solve an equation, I would ask a pupil what we should do first and go with it, even if it’s not the most efficient strategy… it may lead to messy solution and then I’d ask for another suggestion and we’d solve the equation again.
I think I have tended to do less of that type of questioning this year, although it depends on reading the class at the time. To me, there is a balance to be struck.
The Socratic approach that you describe gives pupils agency in what is going on, they know that they may need to describe a step at any given moment so there is a strong impact of no hands-up, no opt-out. It can also lead to some really interesting discussion points that the teacher hadn’t thought of.
On the other hand their explanations may be confusing to the rest of the class or just plain wrong. Also it can take a long time which can lead to frustration on the part of the pupils. I wonder how many of them are sitting there thinking “I wish Sir would just tell us how to do it!”.
Teaching is HARD!
Ha yes it is.
I agree that confusing explanations can be a problem – you have to be clear when they’re wrong. Asking questions in very small steps helps to reduce the chance of this happening.
The frustration issue is a bigger one, and not something I have ever solved effectively. Although I’d say this comes more from the pupils who are thinking “I have done this in my head already”, rather than wanting to be told how to do it! Generally, I try to differentiate the questions sufficiently to make those pupils feel challenged, but inevitably they have to show some patience. For this reason, I think the approach generally works best with setted classes, but I’m currently doing it with mixed ability and it’s working fine.
I watched a lesson by @DanielPearcy recently on a visit to his school and he encouraged the pupils to have a go at the problem individually, but then started solving in himself on the board after a while, so pupils could follow if they wanted to. This produced a nice balance and worked well with a small year 12 class, but I worry that many pupils in a less motivated class would just not do the thinking on their own.
Just to clarify, I think the lessons I observed went something like this:
Teacher puts standard question on the board on previously unseen topic, or one they have seen before but totally forgotten (this was not problem solving, it was basic techniques).
Teachers asks students how to do it. She either allows them to put their hands up, or she cold calls.
Students answer with a load of stuff that’s totally wrong. They’re not thinking at all, they’re just saying things. Seriously, they just say random numbers sometimes because they think it’s funny.
Teacher says ‘good suggestion but not quite’ numerous times.
Everyone stops listening because the questioning and guessing goes on for ages and they still don’t know how to do it.
Behaviour falls apart. They’re all confused. No one learnt anything.
This is a *very* different classroom/school culture to what you’re referring to here! I think in this particular classroom it would have been beneficial if she’d modelled a few examples. I certainly wasn’t saying that gradual release starting with direct instruction is *the* way to teach in every classroom for every topic. I have no idea what works in classrooms that I haven’t been in.
Sounds like your approach is working really well for you. Good stuff!
Cheers Jo.
I can definitely understand that in the context you describe – it reminds me of my first year of teaching! I had a terrible year 9 class who I couldn’t control at all. When an Economics teacher from my school came to observe, her advice was to show them how to do the maths, but my maths mentors held out!
Maybe I would have got to the same point in the end with less pain for that particular class, but I feel that being forced to teach socratically made me get better at it.
My understanding of ‘no-opt-out’ as a technique described in Teach Like a Champion is that if a child is unable to answer a question the exchange should end with the child giving the correct answer. At one point Sven was unable to give an answer and Carla helped but we never heard back from Sven.
I only mention it because you specifically mentioned no-opt-out in your description and this was the only instance at which a child was unable to give an answer, so the only time it would apply.
Thanks for sharing, it is very useful to read and even see how other people are teaching, I got a lot out of it and it has made me reflect on whether I use enough of the ‘we-do’ in my teaching.
Thanks Marc – I agree that it’s definitely best to go back to a student if they can’t answer a question, but obviously you’ve noticed that I’m not perfect on this! I wish my working memory was a bit larger – I question largely at random so it’s sometimes hard to remember exactly who I asked originally.