29 March 2023

Join us as Emeritus Professor Peter Sullivan discusses strategies educators can use to improve students’ numeracy learning experience including the four types of maths lessons that should be delivered. Peter Sullivan is the Emeritus Professor of Education at Monash University and wrote the Australian Education Review publication ‘Teaching mathematics: using research-informed strategies’.

Show Notes

Transcript

Intro: Teach is produced on the traditional land of the Kaurna people. The South Australian Department for Education would like to acknowledge the traditional custodians of the land and pay our respects to all elders past, present, and emerging.

Dale Atkinson: Hello and welcome to Teach, a podcast about teaching and learning in South Australia. My name is Dale Atkinson from South Australia's Department for Education, and today we are talking about numeracy and mathematics with the Emeritus Professor of Education at Monash University. Peter Sullivan, welcome.

Peter Sullivan: Oh, thank you. I'm looking forward to the discussion.

Dale Atkinson: First things first. You're here at our Numeracy summit and have just presented to a group of 900 leaders and educators in in preschools and schools across the state. What's the one thing all educators could do straight away to improve a student's experience of learning numeracy?

Peter Sullivan: The main thing is to get students doing the thinking. Someone described it as the students holding the pen and finding ways to ask problems and exercises and tasks and experiences where the student is doing the thinking rather than following instructions from the teacher. And the more the students can take on that challenge of thinking for themselves, being curious, exploring possibilities, looking for patterns, the more likely they are to learn mathematics and to experience mathematics and to enjoy it.

Dale Atkinson: I think one of the ways you describe that in your presentation is a 'you do, we do, you do' approach. Can you unpack that a little bit more?

Peter Sullivan: One of the ways I describe it sometimes is experience before instruction. There's almost nothing that being told how to do it is helpful. Almost always. If you have an experience and then are told how to do it, then it makes sense. And I think that, that, if you're like metaphor is that if we always have the students do something before they have an opportunity to formalise it, then it's more likely to be resilient or to be persistent, to be retained by the student, to be able to use it again in the.

Dale Atkinson: You represented this in a very entertaining way actually, in that you gave all the educators who were there a simple problem that I think you would've given to, I think you said year three or four age students in, in that context, you engaged them in that problem, came back to them and spoke them through the techniques and the opportunities that existed to solve that particular problem, and then extended it to the next step.

And I think one of the things that you observed from the stage, but was really obvious participating in it on the floor, was just how much more engaged those teachers and educators were once they had to revisit that subject.

Peter Sullivan: And it's called consolidation. And the idea with the first task was, that it was what we described as low floor, high ceiling. Now, what that means is without it varying the task at all, it's possible for some students to engage and get one or two correct answers, whereas other students might engage not only getting multiple answers, but actually seeing the pattern, seeing the possibilities, proving that they'd found all the possibilities.

Uh, the idea is that the students work on a task. They have an opportunity to discuss the task with each other. But then work on another task, which is a little bit the same and a little bit different. And it's the experience of the first task prepares them for the second task, and it's the second task we want them to know how to do.

Often I suggest to teachers that the goal is we ask students things they don't know how to do, but arrange the lessons in such a way as they finish the lesson knowing how to do. Because that's what learning is moving from not knowing to knowing. Sometimes we can do it in the reverse order, but if we set tasks up like that, followed up by productive discussion that between the students and the students and the teacher, and then follow up with another task that the students have now learned the skills to be able to solve because they've had an experience before the instruction. It's the second task that consolidates the learning and that's what's engaging for students.

Dale Atkinson: You've identified that there are four types of maths lessons that should be delivered to students. Can you describe what they are and what links them and how they can be effectively used?

Peter Sullivan: Okay. Well, it's like a balanced metaphor diet. Now, sometimes when I talk about this, I have a graphic from the hospitals and it actually says that one of the food groups is biscuits. It looks like it says that. So the idea of a balanced diet is important. Now I say there are four types of maths lessons. One type is called practical investigations. That's more or less anything that involves measurement. Anything that involves the students getting out of their seats. Anything the students involves gathering data, you know, measuring the size of containers, measuring the areas of basketball courts, designing car parks, whatever they're doing. That's an example of a practical experience and that should be happening regularly. Not necessarily frequently, but certainly regularly and maybe let's say once in every planned sequence that that we have, there should be an opportunity to do something practical that's connected the mathematics with the world.

Another one is games and activities. Now there are literally hundreds of games and activities on the web, and there was one session today that was on that topic from James Russo and utilising games so that it's not just game playing, but actually a learning experience that's engaging for students is an opportunity to create lessons.

And I would say in the same thing, there should be a game slash activity in every lesson sequence that we might play in the every unit of work. A third one is active. I call it active teaching only because explicit teaching sounds a little bit like giving the students rules in which that they follow, but often the interactive teaching where the teacher is, is drawing from the students their knowledge but progressively leading the learning, you know, through the course of the whole of the lesson. That's another effective way of teaching. And the model that I was using was structured inquiry where the students predominantly work on a task that's then discussed and then a further task as opposed to do that.

But having said that, I think there are some principles that guide each of those lessons. We still want the students thinking to be at the centre. We still want the learning to be inclusive of all students and the students to feel like they're part of the classroom community. And we also want the lesson, however it's structured, to build connections between ideas, between parts of mathematics, between other KLA's between meaning.

We want those things to be parts of all of the lessons, even though they may have different goals and different pedagogies. The learning goals, the experience of the students is still.

Dale Atkinson: I think one of the really interesting things that you referenced, and there actually has been a through line in a lot of the presentations to the Numeracy Summit, which the presentations were all available on plink and there'll be some show notes which link off to those plink sessions.

But one of the things that you kind of touched on was that you can approach. , any of these subjects matters or these problems for all children altogether, and it's not necessary to stream them into different capability areas, but rather it's about the time that you give them to engage with and process some of these problems.

Peter Sullivan: Yeah. Some students if given a problem can just start work straight away. Other students just need 10 minutes to get their pen out. It's the amount of time that they take to get ready and sometimes the time getting their pen out is actually productive time. They're still considering the task. But what can happen is if the task is such that the, the students who have worked quickly and work efficiently get the task finished, we can then be stuck by saying, well, we've got to move forward. Some students sitting there and doing nothing. That's why I always say that teachers should always consider that there may be some students for whom the challenge is, is too great, and how do we support them? Well, maybe we need an enabling prompt that's specially designed to give them a, a leg up, a scaffold that they can get on back onto the main task.

But the more important thing in this context is we need to be able to extend the thinking of the students who are finished and give them something that's meaningful and relevant and extends their thinking. But is actually a, a meaningful challenge that they'll take on the challenge. Oh, that's an interesting challenge. I'll do that. And if we can do that, it actually allows us to have more time for those students, if you like, in the middle, who just need more time to engage with the task, to see the patterns, to build the connections.

Dale Atkinson: And of course sitting behind all of that is an awful lot of planning and preparation for teachers and, and for the leadership. Can you talk us through how that should be approached to the school level in terms of really enacting high quality numeracy education practice in the school?

Peter Sullivan: One of the things I believe in strongly is that we should have formal structures for our planning meetings. A lot of countries, teachers don't have time to plan, so having time to plan is a real privilege, and so we should really structure that time so it works effectively.

Now, I think the first item on the agenda should be what, why, how. That is, what do we want the students to learn? Why do we want them to learn it, and how can we bring that learning about, what experiences can we choose? The next stage is how would we know if they've learned it? You know, if you like it, formulating and formalising the assessment.

The next thing is how do we anticipate the students will respond? And how are we going to support the students who might need additional support? How are we going to extend the student's thinking? Then what resources do we need in order to be able to teach the lesson? What other things do we need to think about?

So if we structure the planning experiences, you know, formally and deliberately, and maybe even have an agenda with minutes, it's actually going to facilitate that planning. In effect, the planning, it looks complicated, but because the teachers are just planning one set of experiences for the students, and a lot of the learning is generated by the students themselves, the planning is actually less onerous once the teachers become familiar with the process.

Dale Atkinson: One of the things you spoke about was the absolute central nature of evidence as a key to understanding impact, but not to suffer too deeply from, I think what you described as a data museum, which is an overload of information that's perhaps not useful to, to the teacher.

Peter Sullivan: Well, schools gather and are sent a lot of information about student progress, about cohort progress, about implementation of goals, and sometimes I suspect schools may well be overwhelmed by it, but I think that we should use evidence to help guide emphasis and priorities in our planning. Now, for example, what seems to be a current issue at the moment is that there's attention to the, what I call high potential, but underperforming students. Now that's actually evidence in the data it's in, in the growth data, the year three to year five, year seven to year nine data that are accessible for every school.

And for example, if the students are in the top two bands are falling backwards from year seven to year nine students in top two bands from falling back to the year, to three to five, then I think it, it means that it warrants our attention to look at what might be the causes of that decline. But we need to think about, well, there should be improvement from seven to nine in, in everything.

And if teachers are teaching in a particular way and they, they're convinced that this is the right way, well, is that improvement what they're hoping to achieve? You know, are there enough students, for example, proceeding all the way to the elective areas of, of mathematics study and they need to use the data of their own school, because all policy implementation is context specific.

There's no one size fits all for educational programs. And so trying to find what's the data that we have access to, what are the resources we have, including the teacher resources, you know, including their enthusiasm and their knowledge, and how can we utilize those resources in the best interest of improving the experience of the students when learning.

Dale Atkinson: Could I touch a little bit on artificial intelligence, which has received a lot of media coverage recently. It strikes me that mathematical disciplines within all the academic areas are probably the area that has been most influenced and adaptable to technology, presumably since the invention of the Abacus coming forwards. So what can you see as the impact going forward on teaching practice, but also the learning experience for kids?

Peter Sullivan: Look, it's a difficult question to answer. I'll come back to answering the question, but what my interest at the moment is to try and create mathematics questions that are suitable for, let's say, year three students that the artificial intelligence can't answer.

So ones where, if you like, the sort of brain type of flexibility that's necessary to answer the question just isn't available to artificial intelligence. So my interest is trying to, uh, formulate questions of that sort. And I think that if we can come to understand what artificial intelligence does do and what it doesn't do and, and in fact how it does, what it does do, that would be useful.

I was actually out of school and they used artificial intelligence to create my introduction and it was quite accurate. Now, I assume it probably searched my bio at Monash, but it was interesting that something, a task like that, that would be able to create it for an individual in a place would be able to be done.

I actually applaud the South Australian Department for Education for its openness to exploring the possibilities of artificial intelligence, and I think it's an interesting challenge for, well, for everyone. Particularly for educators, uh, such as myself to say, yeah, well, what are the implications for teacher education, for classroom practice, for task design, for the design of experiences, now that we have access to artificial intelligence and that can influence not only the design of the task, but the design of the experience as well.

Dale Atkinson: And how do we unlock those unique human capabilities that hopefully remain unique. I guess we'll find out soon enough. So thank you very much for your time today. If you had one final message to provide to educators, for those who are at the front of the classrooms, what would it be?

Peter Sullivan: Well, look, if I can answer that with two messages. The first message, and probably the most important one, I'm often asked that question in, uh, when I'm doing professional learning sessions. If you had just two words of advice for us, what would those two words be?

And my thinking is, shut up. That you probably, if you are a teacher, you probably talk too much and you could probably afford to talk less, to encourage the students to talk more, to create more space for the students to talk. But the other thing is just connects to something that happened in my house. I hid some Easter eggs one time. And the grandchildren came into the room with the Easter eggs, and then something happened. It was a bit unfortunate. There were two people there and I, I won't name them, let's just call them the mother, and the grandmother, wanted to show the children where the eggs were, but it was an Easter egg hunt. The whole point is to hunt for the eggs.

It's sort of a metaphor for teaching. Sometimes we can be like the mother and the grandmother and we lose confidence that the students will be able to find the eggs. And so we say, oh, here's an egg. Now you've got an egg. But in fact, the more that we can encourage the students to hunt, the more we can be patient, the more we can trust them, the more likely they are to find and create their own knowledge. And so it sort of becomes like a metaphor for teaching. Let the students find their own eggs.

Dale Atkinson: I think that is the perfect summary and conclusion. Peter Sullivan, Emeritus Professor of Education at Monash University. Thank you very much for your time.

Peter Sullivan: Thank you. It's a pleasure.