- Dr Huw Humphreys
Peer modelling as a way of encouraging maths proficiency: an example from a primary PGCE placement
This is Huw Humphreys talking to Sidra Saeed, having a conversation about Sidra’s great work from the first Master's level assignment from the UEL primary PGCE, entitled Active Enquiry and Intervention. Sidra did this work whilst teaching a Y6 class locally. My first question is: what prompted you to think about investigating peer modelling?
I was thinking for ages about what was missing in the class; what did I need to do to push them on? Since there were high levels of maths attainment in this Y6 class, I thought, I'm going to use this maths lesson for my assignment. And one day, I said to one of them ‘Do you want to come up and show us how you worked out your answer?’ And this wasn’t me thinking of my assignment; this was just in a lesson. He came up and did it. And the class were in absolute awe: they were all mesmerized by him…. so I went home and thought ‘how do I put it into a research question?’ So that's where it came from. I had already had over a month with them and started to get to know them. So once I had my research question, I thought, let's give it a go.
What did the lesson look like, when doing it in that formal way? And how did you deploy peer modelling, in order to get what you wanted from it?
I started as I normally did, and at the beginning of the lesson, I said to them, ‘Right, we're just going to try this for a few lessons, and I'm going to have the same children modelling for us, who are going to show us how we're going to do this maths.’ And then it was ‘Can I do it, can I do it…?’ from the class. So I told them, ‘We all get a chance, but just for a couple of lessons, let's give it a go like I’ve told you.’ In my mind, I knew which two children I wanted to model, and I had a third child who was observing and learning from them, to test it worked. So I knew which children I’d be watching doing the modelling, but for the third child, I wasn't making it obvious that I was observing him observing those doing the modelling.
So the third child was learning from the modellers?
Yes, I monitored his responses – how he responded to the actual mathematical learning. He was right up front near the class, where I could see him, clearly. He was in my actual class, not just my maths set, so I knew him well.
So, you did the teaching to start with. Then what role did the children play? Obviously, the modelling bit of the presentation was done by the children?
As it was a new topic, on fractions, I modelled one problem formally, and then let them have a go at the work. I would usually model the maths, then let them have a go. Of course, there would be always some that were still struggling. So, for the two children that I was going to choose to model, I asked them to check their work to see if they got it right. And then for the class, I'd say ‘let's stop, see who's got it right, let's have a look, how did you do it?’ I’d bring one of the ‘modellers’ up, allow him to be the teacher, and the children then learnt from the model and did their independent work. And that's how we began with it. I did the instruction, checked the modellers’ work, then they took over.
Obviously, impact for you as a student teacher is really important, both the impact on you as a teacher and on the children’s learning. Have you been able to reflect on what this means for you in your practice, having used this peer modelling in a Y6 class?
I used it because it worked. Children felt engaged, they had a bit of power, and knew that they had to work. There was that bit of ‘Oh, we need to do it right so then maybe we could go to the front of the class and show it to everyone.’ So it pushed them and kept them engaged. They knew that they could be asked to have the privilege of going up and showing the rest of the class. Personally, I felt like I fell upon it accidentally, but I would definitely carry on using it.
When you finished those three lessons, what happened then?
They didn't want to stop! In the lesson after the lesson study, one of the children said ‘Could I have a go at doing it - it might be interesting.’ And whilst collecting feedback from the whole class, I noticed on some of their notes that ‘it might be really nice if such-and-such a child could try modelling…’
So the children were choosing one another as possible modellers?
Absolutely. So one child wrote, ‘Oh, so and so's really clever, I would like him to model it for me.’ They were picking out other children, which I saw on their little feedback sheets, that were meant to be anonymous. So I carried on, as my mentor had said, ‘It's fine. Go with it, if it works, and you're happy with it. The children are making really good progress.’ So we carried on. It was a high attaining class, but I gave modelling opportunities to the ones who were not so able, to give them that confidence. I like to make space in the classroom where we can make mistakes, maybe someone else can help us, and so on. But I carried on with it until the Christmas holidays. After that, other pressures took over a bit. But as much as I could, we carried on,
In terms of how you evaluated the impact from the children's point of view, how did you get feedback from the children to evaluate its effectiveness?
I gave them all a little slip of questions, depending on whether they actually modelled or didn't model. I told them ‘it’s anonymous; you just tell me how you feel about it.’ And then the ones that who had modelled, I asked them specific questions to see how they felt about it, to get their feedback. But for the general class, I gave them anonymous sheets to make them feel comfortable. They were like ‘Do we need to write names?’ ‘No, I don't even want to know your name… I just want to genuinely feel you guys actually feel about it, knowing that there's no pressure and Miss is not going to be upset with anybody, whoever says what, so feel the freedom to be able to speak freely.’
Sidra, you're teaching in Y2 now, obviously in a different school. What I saw in this morning's lesson was peer modelling. Was that deliberate, now that you’ve felt comfortable with it? How did you think about it when you came into this new setting?
When I first come into Y2 I wasn't quite sure. I thought, they’re not my Y6 - I can't carry on with that. But as I've got to know the children now, I feel more confident, not to the extent I did in year six, but definitely I've had children come up to the board and I'd say, ‘do you think you can show us that? That's amazing!’ And then even if it meant that she's doing some kind of number line or something, and the rest of the class might help her along with it, it really boosts them. I find that the class engages, and they’re going ‘Oh, we could be next – we could be going up to help.’ So even in Y2, they definitely are now used to it.
Thank you very much.
As a researcher and tutor, I found some of the children’s perspectives on the process fascinating. Whilst there was a lot to learn from those children who had done the peer modelling, here we list the learning from those who were learning from their peers’ modelling. For brevity, we have omitted the question on the panel above about feeling safe to make mistakes, although that is a crucial first step in encouraging the openness needed for peer modelling.
Have explanations from other students helped you with your understanding?
· Yes because it helps
· Sometimes because there are a few maths topics I need help with, and some like fractions are easy for me
· A little, depending on the calculation and the strategy
· Yes, because it gave me a better understanding
· Sometimes, because often I already know the answer
· Kind of, because I think sometimes I know what I’m doing
· Sometimes, because people are clear: sometimes not
· A lot, if I don’t understand something
· Yes, because then I know another strategy
· Yes, as I see how other people do things.
·Yes, exploring other students’ methods and explanations help me understand deeper, simpler ways to solve questions.
· Sometimes it is more clear than just doing it myself.
. Yes, the explanation helped with my understanding because they make me feel confident.
·No and yes, because when other students model on the board, it depends whether I know it or not already
Do you prefer explanations from a particular student? If so why
· No, because I like everybody
· I like a loud clear voice, with clear handwriting, because I understand more
· No! (no reason)
·No, I think everyone is good at explaining.
· Yes because ‘S’ is very clear and her explanations break it down.
. No because mostly everybody has good ideas.
· Yes, because they help me understand the question.
· No, because I like to see how other different people explain answers.
· I like answers and explanations from anyone, because they may have other really helpful methods to solve questions.
· Sometimes, but it depends on the topic. Really, anyone helps!
·No, because different methods can give a different prospect which sometimes helps.
·Yes because they’re your age, so you’ll understand them clearer.
· Nope, because I like many students to have a try!
·Yes and no, because when explained it makes a little sense, but I don’t know the strategies for some questions.
·Yes, if it is my friend, they would go into a lot of detail, because they are my friends. But sometimes others might not bother.
Do you find sharing strategies beneficial?
· Yes because it’s fun
· Yes, because it helps others
· Not always, because they share all the easy strategies not the ones I don’t understand
· Sometimes, depending on the clarity of explanation
· Yes, because I as a person want to use different strategies
· Yes, it helps you learn more techniques on how to solve things
·Yes, because I am helping other children.
· Yes, as I know other people use the same strategies as me.
· Not really, unless I can’t quite understand where I have gone wrong.
· No, because I can choose from a variety of strategies.
Has the idea of sharing your explanations with the class made you work any differently?
·Yes, it helps me a lot
·Yes, it made me work slowly and carefully
·Yes, it makes me feel more confident, but sometimes I’m topo shy to share.
· Not really
· Yes, because it has given me a really good understanding.
· Not really…a bit.
· Yes. If only I am correct, I would feel confident.
· No, because I work the same way.
·Yes, others have different opinions and explanations showing me I could have got a different answer if I used another method.
.Not a lot, sorry. But I have