Engaging all students in Mathematics
Dr Bobbie Hunter and Dr Jodie Hunter share their strengths-based culturally responsive pedagogy for deep learning in mathematics through collaborative problem-solving.
Hunter and Hunter are redefining teacher education, hoping to help raise the academic achievement for children of all cultures in New Zealand. They believe the New Zealand curriculum can build on the richness that children bring to school, especially for Maori and Pasifika pupils.
This talk was a part of Taking the Lead - Celebrating the Curricula in Wellington on 9, March, 2018
Resources from the presentation
- School leadership for improvement in primary mathematics education: Russell School best evidence in action implementation exemplar
As you watch the presentations, think about these questions:
- How do we get this right for our children?
- How will we enable all children to be ‘confident, connected, actively involved’ lifelong learners?
- How will we uphold the values and principles of a world leading curriculum, in the best interests of our children and our society?
- How will this start, from today?
You can also download these questions as a discussion sheet to use as a group. (Word doc, 0.15MB)
A dream I have and I voice lots of times, is that the day that we no longer have a Minister of Education who drives how schools are run or how schooling policy is run. The dream is that we have thirty years of deliberate policy thought up by educators and other people in the community, about schooling that is not changed when the government is changed. That’s the dream. So what we did was we looked at the proposed government work plan which was released just recently, and we thought: how does what we’ve been doing for the past fifteen years – so it’s gone through two different sets of governments and we’ve persistently carried on doing what we do despite the political shift that has come and despite lots of barriers really.
The video displays the proposed Government’s work plan.
So if we look at this proposed government work plan and you look at what’s up there you’ll see that learners are at the centre. This is the newest one out. We have barrier free access, quality teaching, quality public education and 21st century learning. Not bad. You know, could be a thirty year ideal.
How do we put that into place? What have we been doing, doggedly, despite the sudden shift from National Standards to suddenly there was a digital - and then every child had to learn a language despite the fact that we’ve got loads of children in our schools who already speak lots of languages that aren’t honoured – then we had digital. Yes, now there’s some millions going into digital which comes straight out of priority learners. We have CoLs, we have all sorts of barriers, so what we’re going to do is just look at some of the things that as teachers and educators we can just keep doing.
So our work really begins thinking about learners at the centre and when we’re working in schools and in classrooms and in the community we take a strength based culturally sustaining approach. So we in some ways problematise the overuse of culturally responsive teaching because we think that’s a term that’s been used and used again but not necessarily unpacked and yes, it’s about relationships but it’s more than that. What we want is a culturally sustaining approach so that the students – our learners – are at the centre of our work, have their culture – they can be their culture – they can succeed. And their culture is seen as a strength. So what we like to do in schools and with teachers is to really work alongside teachers in schools so that they can see the different cultures that their children come from, the ethnicities that they have, as a strength rather than a barrier. As Bronwyn referred to in her little talk, for a lot of learners and for teachers, culture is seen as a barrier. You know, ‘these children come to school with nothing’… the children themselves position culture as a deficit. ‘We’re from a culture that doesn’t do mathematics’. But instead we’re working to say: All culture, everybody has mathematics. You have mathematics in your culture, you have mathematics in your home. Our job as educators is to see the mathematics that is happening and to be able to build on that. So in that way your culture becomes a strength.
We take a similar approach with language. So I’ve had teachers and RTLBs unfortunately as well, and parents talking about their experiences where they’re told: Don’t speak to your child in Tongan at home. Speak to them in English, they need to learn English. If you speak to them in Tongan you’re disadvantaging them because they need to know English and that’s interfering with them. So we take the opposite view that language should be a strength. Children should be able to speak in the language that they are comfortable in in the classroom and use trans-languaging where they are moving between languages and learning mathematics with language as a strength. And teachers celebrate that. Celebrate that we have learners who have that capacity.
We also think about children’s current understanding, so we want to move away from labelling children. We had the numeracy project in New Zealand and an outcome of that is that labels were put on children: “These are my stage 4s, they’re going to do this because they’re a stage 5, these are my stage 4s and they’ll do this. I can’t teach them that because they’re a stage 4.” Only two weeks ago I heard a teacher talking about their children as ‘my overs/aboves and my unders… I couldn’t use that task with my unders because they wouldn’t be able to do it.” So instead, as educators we need to turn that around and say: what strengths do these children have? What are their current understandings that we can build on? Instead of as a barrier.
I can give you a little example thinking about culture. I do a lot of work in algebra and patterning so if you think about how can we make the culture of the children at the centre – I’ll take my grandmother as an example – and I was working in a school with a teacher looking at how could we use culturally based tasks, patterning tasks which were algebraic, and I looked at the tivaevae that my grandmother makes and when I started looking at it I thought: that’s got growing patterns in it - It was a different eye that I was looking at it with – so I saw that growing pattern and thought how can we take that into a mathematics classroom and get these little Year 2 children, you know six year olds, to look at that and generalise that pattern. And their understanding and knowledge of that aspect of their culture then became a strength to grow their mathematical understanding and to generalise. And we ended up looking at a whole lot of different things and thinking… Sasa for example is a repeating pattern that you could use and the children could draw on that knowledge, that expertise that they had from their culture and use that as an impetus to develop their mathematical understanding.
One of the things that we always have to thinks about is we’re actually putting up a lot of expectations on teachers. So if we don’t take a deficit view on students. We talk about what strengths the students bring, we also need to talk about the strengths the teachers bring and grow them from there. So this has to be transformative for them, it has to be generative. We talk about this as a long journey. For the first, maybe a year it’s all about you, it’s not about your students, because we’ve got to get you to grow to a point where things like one of the first activities we do is look at your values in terms of how you grew up, and then you might be able to understand from the perspective of somebody else who comes from a different value system, their values. But until you know your values you can’t possibly understand why they might be different. And we've learnt this over time, that this is what we need to be able to do with teachers, because at first we just used to put up Māori values, Pasifika values and we got lots of arguments from teachers saying: But we have the same values, and that was because we hadn’t explored theirs first.
So what are some of those values? Quite often a lot of teachers they always go back to ‘work hard and you will succeed’. Not different in any culture. Right? Be kind to other people – relationships, family. All of those. But when you start to dig under those. When you start to say to teachers: “But when you talk about family are you talking about your brothers and sisters or are you talking about all the other children in your street and your cousins and they’re all called your brother or your sister.” Suddenly they see that’s different.
So what we do, is we use a smart tool. And we use this thing called a communication and participation framework because ultimately we want the students to be reasoning and communicating so that teachers can assess where the student is at and where they’re going to next. The 20% that Mere (Berryman) talked about and in our situation, I would say in most of the schools that we work in, 50% of the children are sitting in that group – or even 60% of the children. You’ve got a lot of doctored national standards data coming out of lots of schools, so we know the reality when we go into schools.
So we use this communication and participation framework to give the teachers a scaffold with positive actions they can take to get their students talking. Recognising that for some students that their home values are quite different from what they’re being asked to do at school. So they need to be carefully given another alternative voice used only, maybe in mathematics, maybe right through the whole day, because most teachers start to say: if we’re doing this in maths why aren’t we doing it right through the curriculum?
We also have a focus on mixed-ability grouping and we’ve taken out the word ‘ability’. I’ve got it up there but we’ve actually started to talk to people and say: is there such a thing as ability? Because as soon as you start to talk about ability you get these low/high and so on. We say: “every single person can learn, can learn mathematics. They’re just not going to learn the same.” That’s the difference. And so yes, when they all go in to a task some will come out with something different. Exactly the same as sitting in this room today, all of us are going to walk away with a different perspective. It’s the same thing. And so New Zealand and New Zealand teachers have been in love with grouping and that really suits management, organisation in your classroom, it just doesn’t suit the children.
Part of that is that smart tool and part of that is that ‘group worthy problems’. So a group worthy problem is a problem at a level where nobody can actually sit down and solve it. Nobody. Everybody has to come and they have to bring something that they contribute. Now we use metaphors like for instance Jodie talked about her grandmother making tivaevae and you know, my mum does make a lot of tivaevae and now we have to too because she’s passing it on, but nobody owns the final tivaevae, the final product, and that’s the sort of thing that we work with children to say: when you’re doing a problem, a high level challenging problem, together you can make a really good outcome. Alone you may well not succeed.
I was really heartened about two weeks ago to go into a school which we’d been working at for – I think it’s the fourth year we’d been working with them, a lot of teacher change but this is one of the original teachers and I was working with her doing a bit of research into some of her class things, and about halfway through the lesson she said: :which child in here to you think has high learning needs?: And I said to her: “Honestly I could not say. I have absolutely no idea.: And to me, that was success. Because this child was in there with high learning needs, he was working in an inclusive group of students. None of those students were treating him any different, they had the same expectations for his participation and he was rising to the challenge and participating. They had the same expectations for his participation as did the teacher and anybody else. And any of you who had walked into that room I can 100% say you would not have been able to identify that child. So that’s taking away the barriers for that child.
What we call this is ‘ambitious teaching’ because, as I said, it’s a journey. And it is a journey for teachers to get to a point where they can do this ‘ambitious teaching’. It’s on a continuum, so at this end of the continuum – and it is actually how international and nationally we seem to have gone politically, lately, and it follows our political pathway. So we’ve got down this end of the continuum: traditional, very right-wing, just sit the children down, tell them. And this can be done digitally as well you know, that’s a danger. And on this end we’ve got ambitious teaching which was called ‘reform teaching’ in mathematics I’m talking about but it is going across into science and so on. And people are on a continuum. You are going to do some of that traditional, you are going to do some of the ambitious but you should be on the, somewhere, moving in a day, in the classroom.
Now, we also use mentors in the classroom in our work and those mentors do something that we call co-constructing, because what we didn’t want to do was to keep the model that we’ve had for years in this country, where we have somebody, an advisor who goes in, does an observation, gives the teacher feedback and walks away. And we saw that, I know, as a teacher myself that I wasn’t particularly good about it when somebody did that to me. Normally I would be saying: “I’ve got thirty-five children in this class don’t tell me what I did wrong.” That was basically. So what we do here, is we have mentors which we call dynamic mentoring – so again, you’ve got mentors, you’ve got coaches. Coaches are hands-on, mentors are hands-off. So we’ve got in the moment coaching, they are in, alongside the teacher and they are working – and we use something called a pause, where you stop in the middle of a lesson, you have a conversation. Somebody might say: “pause,” the teacher and the mentor will have a conversation like: “Did you notice this? What do you think you might do with that thinking?” Likewise, the teacher will call a pause and say: “I’m not sure whether I should do this or I should do that.”
So interestingly, the students become really interested in those pauses. And in most schools that I’ve been in towards the end of the year, the students call the pauses. And they’ll say something like: “Can you pause? I think we’re all confused now.” But what they’re actually seeing is teachers as learners – we are lifelong learners.
As part of that we avoid modelling because we don’t want to disempower teachers. So our mentors and our team is only there for a short snippet so we’d rather the teachers work through those actions rather than us model for them. So I think it’s a big shift and I take my own personal story in modelling where when I was first teaching Year 5 and 6 and I asked my mother to come in and model a lesson for me and at the end of it I said: “Oh thanks very much, now you’ve made me feel completely useless because I could never do what you did then.” And I think you know, often you see that, it’s hard to unpack it so it’s better to be doing it in action.
Along with the mentoring we work with schools and classes and teachers for tailored professional learning and development. We’re learning alongside teachers so sometimes things don’t go as we plan them to. Sometimes a teacher’s shifts are not as great as we want them to be, so we need to stop ourselves and our team and reflect and think: “Why is that? What do we need to do differently when we’re working alongside this teacher to move them along in their journey and to take them on a journey with us as well?” And that can be whole schools as well. We’ve had examples of whole schools where we’ve worked with them for a year – the results haven’t been what we’ve wanted. We need to step back and think: How do we change what we’ve been doing? What’s a different model that we can use in this particular environment to actually shift practice and to take people along with us?
The other aspect of the work that’s been really important is giving teachers access to post-graduate study. So one of the things that became really apparent to me working at Massey University and even thinking about my own teaching experience, was that for a lot of teachers in South Auckland, if you go to a face-to-face lecture it’s an awful long way to go at the end of a day to drive all the way to Albany or to Auckland.
So instead we’ve taken post-graduate study to the schools. So around the country we run a Masters paper based on the work, looking at the theory and the research and we go to a local school for example Porirua, we go to Russell School in Porirua and the teachers from the local community come there to take sessions – face-to-face sessions with us. To give them access to post-graduate study in a supportive environment. Because distance learning isn’t for everybody as well.
The final part that we have in terms of our quality teaching. Our job’s not done if we can’t walk away from a school. You know, if we have to work with a school forever more, have we succeeded? So the model that we follow is using lesson study, and towards the end of our professional development learning journey we introduce the notion of lesson study which is really about teachers then undertaking critical reflection on their own practice and the practice of the other teachers in the school. So that’s a model where teachers are planning together, a lesson is taught and observed and then everybody engages in a critical discussion of that, in the group. And then, that’s a cycle and is re-planned, retaught again for the year.
If we look at the notion of quality and inclusive public education, I think for a long time we’ve had a notion of: we invite parents into the school and we tell them what we’re doing. What are we doing as a school? But instead we need to turn that on the head and have teachers learning from the parents and from the children. So all children come to school with funds of knowledge that they have from their home and their community and we need to work with parents to find out what it is. You know, where does mathematics take place in your home and your life and your community, and we’ve gained a lot of information and teachers are able to use that as a resource.
I’ve been at a number of parents’ evenings where we’ve said: Let’s have a parent, student and teacher meeting, mainly because we want the teachers to be able to write problems around the life of the children outside of the school. And so we want the teachers to learn about the students. I’ve been at a lot of these meetings where we’ve actually said to the parents: “With your student can you tell the teachers, like write down all the maths that you do that is not school maths and not homework maths.” And instantly in every area of New Zealand you get a different – I get: “wow, I didn’t realise that this happened in Christchurch.” So these are the sort of contexts that you could do.
But I remember very clearly a school in Porirua where quite a large group of parents came and they got talking about time. And why is time such an important feature in New Zealand classrooms? Because it isn’t in the Pacific. And they were talking about bus timetables and so on, and the difference. And that was a really interesting one because all the teachers were saying: oh, we didn’t realise that.
You know, I think about the Cook Islands and how the bus goes clockwise or anti-clockwise. You know, that’s it. And yes it does have time things but it might just go inland for a bit because someone’s Mum is sitting on there and she needs to be delivered. You know, that’s time. So that’s what we’re talking about in terms of teachers learning from parents. But there have also been other incidents where we were in a school in Auckland and one of the things that a lot of schools do to bring the parents in, is have like a door raffle, where they give out tickets. And at this particular one they had those big blue bags full of like, plain biscuits and cans and… like food. When this man won it he sat there and he gave cabin bread to that person… and he distributed widely around the people around him, and one of the teachers said to me: “they’re currently living in a car. That’s where they’re sleeping. Why is he doing that?” And I said: “He’s giving service.” So that was a lesson for everybody there. So this is your learning. You know, this is teachers learning from parents and children so that they can understand.
I’ve already talked about this – removing notions of ability (all children can learn mathematics) but that comes into the ‘quality inclusive public education’, because we have this thing in New Zealand where people are not proud to say they can’t read but they’re very proud to say they can’t do mathematics. We have got to turn that around and say: Everybody can learn both. And you need to have mathematics.
So part of that removing the notions of ability and then tying back to the strength based thing, is widening our view of what it means to do mathematics. So rather than just thinking - at one very basic level people often associate mathematics with numbers or basic facts. You’re good at mathematics if you know your basic facts and you can work them out really quickly. So what we try and do is try and think: “what are the different strengths that you can bring into mathematics and into the mathematics classroom?” So for example, asking questions about mathematics. That’s a strength. It’s not been something that’s been recognised, in fact my own experience as a high school student where I did very poorly in 6th form maths, and kept saying to my mother: “what should I do?” And she said: “ask questions.” So I kept asking questions and then finally my teacher turned to me one day and said: “Do you not listen or are you just stupid?” Hmm, exactly!
So instead, we want children to see asking questions, being able to ask questions, a good question, in mathematics is really a strength. Being able to look for patterns is a strength. Being able to listen to somebody else’s viewpoint and engage with that, think about it and then reflect on it – all of those are strengths. So it’s really widening the notion of what it means to do mathematics and if we start doing that, and key competencies perfectly fit into that, if we start thinking about how key competencies come into mathematics then we have a lot more people being successful, a lot more people can do mathematics. But at the same time at the heart of it is giving our children opportunities to really work on complex, challenging mathematical tasks as well. Ok, so we can’t let that go.
So that’s also why we take away this notion of ability. Because we don’t want to have teachers saying: “my children can’t do this. This group of children can’t do this.” We want teachers to say: “everybody can get something out of this complex, challenging mathematical task.” And walk away with some form of learning from that.
So, if you start to think about the 21st century learning then student voice has to be sitting there very firmly. We have to be thinking about these students and teachers following student voice, not teacher voice leading student. So it’s student voice.
We also need to think about learner led inquiry because if we’re going to engage these students then they have to want to do it and we have to be following what they want to do. Of course, good teachers can actually motivate or engage – I don’t like the word motivate – but they can engage students in worthwhile work going forward.
We also want our students to be flexible. To be able to do mathematics in the real world. To be able to apply what they’re doing in the maths classroom to other classrooms. So when we talk about our students being able to explain their reasoning, to be able to justify their reasoning, to be able to engage in mathematical argumentation about their reasoning, to generalise their reasoning. That’s not different than what they need to do in a literacy classroom. That’s not any different than what they need to be able to do in a social studies classroom. That’s not any different than what they need to be doing in a science classroom. Each discipline has its own particular model and mathematics is no different. But all these skills are transferable. And then into the real world we also want them to be able to engage in justifying their actions, applying some argumentation when something doesn’t look good or does look good to them. And generalising. That if I do this, then this is going to be an outcome. So these are flexible skills that they should be able to do.
And the last one is that mathematics is for life. And they need to know that they are going to need maths for the rest of their lives. And in fact, I recently heard a man called William Tait - who is really worth looking up and listening to – who talked about mapping when people disengage from mathematics, to life expectancy. And people who disengaged, children who disengage from mathematics at primary school level have fifteen years less life expectancy.
And so when you think about the statistics you start to think about who we in New Zealand have to, equitably deal with giving them their rights. And I think - I’m quite hot on this – I think that we’ve got to actually have a lot of our students thinking about white privilege. It’s social justice to start thinking about: “who is more privileged than who,” and actually talking and having some of these conversations in the classroom about this so that we don’t have this deficit thinking of particular groups of students about themselves.
More from this series
How do we take the opportunity to uphold the values and principles of our world-leading curricula, in the best interests of our children and our society? Curricula experts share their expertise in working with all the New Zealand curricula in Taking the Lead - Celebrating our Curricula.