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A method of teaching which encourages group problem solving in culturally centred contexts is improving engagement and outcomes in mathematics learning. Developing Mathematical Inquiry Communities (DMIC) takes maths out of textbooks and into the hearts of classrooms and communities.
In a Porirua classroom, Dr Jodie Hunter tells a class of Year 3 and 4 students that her grandmother wants to make a tivaevae using a pattern from a cushion cover and doesn’t know how to extend it. This is a glimpse of Developing Mathematical Inquiry Communities(external link) (DMIC) in action.
The children find that algebra can solve the problem – the equation they come up with is ‘m x 8 + 4’. Along the way they talk about Cook Islands’ culture, personal experiences and develop an understanding of the concepts of generalising linear growing patterns.
“I did the same problem with Year 2 students and they came up with the same generalisations,” Jodie told the Education Gazette.
The precursor of DMIC began in 2008, when Jodie’s mother, Prof Roberta (Bobbie) Hunter, a former schoolteacher, developed a participation and communication framework for teaching maths to Pasifika students as part of her PhD study.
The results were good and ‘Bobbie maths’, as it is widely known, was born. Bobbie’s dissertation received international recognition for demonstrating that mathematical reasoning and achievement can be accelerated significantly and meaningfully in a single year.
The DMIC approach grew from there and is now used in 140 schools throughout the country, with funding from Ministry of Education’s Professional Learning and Development budget.
From 2019, additional funding from the Government’s Pacific Well-being Budget will be used so the approach can be rolled out over the next four years to an additional 48 Auckland schools with the highest number of Pasifika students.
Bobbie and Jodie, who are based at Massey University, come from a Cook Islands’ background and were concerned that Pasifika students’ achievement is poor.
“A Ministry of Education report in 2014 showed that only 11 per cent of Year 8 Pasifika students are achieving at the appropriate curriculum level for maths,” says Jodie. “That is really concerning because mathematics is such a gatekeeper in terms of opportunities in work, further study and just your daily life.”
Jodie says the approach is about equity and social justice and raising the achievement of Pasifika and Māori students.
“DMIC is about culturally sustaining pedagogy and getting to know the students and their identities so they are enabled to succeed while maintaining their cultural identity in the classroom,” she says.
“One of the reasons we emphasise using culturally based tasks is because it’s not something that’s usually been done in the past, particularly for Pasifika children.
“We have a lot of interview data from schools and when we ask, ‘how do you feel being Samoan, Tokelauan, etc in the maths classroom?’ they will often position their culture as being completely free of mathematics.”
International research shows that ability grouping in maths has negative consequences in terms of children’s achievement and their attitudes towards maths.
“One of the problems with using ability grouping is that teachers will have lower expectations of children who are in the lower ability groups. But if you think about the Pacific values of collectivism, collaboration and reciprocity, you can say that in fact, ability grouping is not a practice that aligns with the children’s cultural heritage,” explains Jodie.
Children like getting their teeth into difficult and challenging maths problems if they are set up so they can support each other.
“We want teachers to be using problematic tasks all the time, which the children don’t know the answers to straight away, but which are going to be challenging for everybody. We should take away the notion of ability and give everybody the opportunity to work on challenging tasks. What it’s about is getting kids to work collaboratively in groups and structuring them so they can build off each other’s ideas,” Jodie says.
DMIC has 20 mentors (will increase to 30 next year) who work alongside teachers around New Zealand. The mentors are highly skilled classroom teachers themselves who work with teachers to help them plan problematic mathematics tasks and then anticipate what student solutions might be.
“This grows teacher knowledge. Teachers may have come from negative teaching experiences with maths and perceive themselves as not being very good at maths and so they become anxious about teaching it. A lot of people say,
‘I’m not very good at maths’, but I think we’ve got to stop saying that and start saying in fact it’s about the way that it’s taught,” Jodie says.
The DMIC approach was featured as a stand-out pedagogy in the first Best Evidence Synthesis (BES) Exemplar in 2012 because of its alignment with BES findings and impact on learning, belonging and wellbeing.
And thanks to two recent accolades, Jodie will have the chance to take her research to the next level.
In October, Jodie was awarded a prestigious 2019 Rutherford Discovery Fellowship to continue the development of the DMIC initiative. And hot on the heels of the Fellowship award, Jodie’s research project received $300,000 from the Royal Society Te Apārangi annual Marsden Fund.
These planned research projects include documenting the mathematical experiences of diverse learners outside of school, including home and community settings, through student and parent use of photography and video recording.
See Jodie and DMIC in action in the Education Counts BES – a best evidence in action demonstration exemplar: Ambitious Mathematics for Young Pacific Learners.(external link)
When second-year teacher Ta’ase Puleaga first saw DMIC in action, she thought, ‘why are they talking to each other in groups? Where are the maths books? They are drawing pictures!’
“I thought they were doing topic work. But as I got into it, I could see they were drawing pictures that represent numbers. I was quite blown away – it’s fun. For me personally, maths was never a strength and I was always scared of maths because of the way I was taught,” says the Year 1 teacher at Russell School in Porirua.
While DMIC was different from what Ta’ase had been taught at school and teachers’ training college, she says she is open to any pedagogy that benefits the learning of her students.
“It’s a good system. I have five-year-olds and we use contexts that are happening in their world – not just throwing up 2+2=4. It turns on a light for them and they enjoy maths. We come up with a big story and then I let them go away and they can draw or use counters and there’s a rich discussion with how they are solving it.
“We encourage everyone’s voices to be heard, whether it’s explaining what they have done or asking questions. We’re really focusing on the fact that it’s OK to ask questions in my class. That’s not usually how it works in Pacific culture, so we are teaching them that it’s safe to ask questions and sometimes be wrong,” Ta’ase says.
Russell School’s values fit well with DMIC’s approach. The school’s HEART values stand for Honesty, Empathy, Aroha, Respect and Teamwork, Ta’ase says.
“DMIC teaching impacts the class culture and our HEART values are now embodied in maths. For me maths was numbers and getting it right, but with DMIC, it’s about how you share and explain. And if some of the kids don’t understand, it gives other children an opportunity to explain their learning – not me!”
“I’m learning to zip it. Teachers want to rescue children, but we are not letting them take those risks. When I do step back, it’s amazing what happens,” Ta’ase says.
With more than 25 years’ teaching under her belt, Ta’ase’s colleague Anna Borrer says DMIC has also taught her to ‘zip it’.
“This is a big shift for teachers. You have to listen really carefully to the thinking that’s going on and to be honest some lessons you think, ‘oh my goodness, I don’t know where we’re going to take this because they’re not getting it’. That’s when you as a teacher are connecting some of the ideas so you can then go forward together,” says Anna, who teaches Years 3 and 4 at Russell School.
Anna has been teaching DMIC for the past year and completed a post-graduate paper in Developing Mathematical Inquiry Communities which Jodie and Bobbie Hunter run through Massey University.
“The theoretical background as well as the mentoring the course provides was great. The big thing for me is getting to know the cultural context these children come from. Giving the children’s cultures credibility is important because unfortunately, some people have a deficit view – that some Pasifika or Māori children are not good at maths. But actually, there’s a long lineage of maths involved in things like navigation and crafts,” she explains.
DMIC incorporates skills that will be required in the future such as working collaboratively, problem solving, critical and strategic thinking and communicating ideas, Anna says.
“The area where I have seen the biggest shift is they are thinking of themselves as mathematicians. They know it’s not about having an answer quickly, it’s about justifying your thinking and being able to explain your thinking so others can follow. It’s in line with future-focused thinking and scientific models of thinking as well.”
Russell School’s vision is about encouraging voice, agency, action and identity and DMIC ticks all the boxes as tamariki are encouraged to bring their identity and voices to be active mathematicians, she says.
“It can be challenging and confronting around your role as a teacher because you have to listen more, speak less, rescue less and think ahead. For many of us who have been teaching for a while, letting go of being ‘the holder of the knowledge’ is probably the hardest thing. But it’s a better way of teaching for everybody – it’s co-constructing together and raising the status of some children who don’t think of themselves as good mathematicians,” Anna says.
Russell School in Porirua East is a decile 1 school. Sose Annandale taught at the school before becoming principal in 2011 and says that for many years, maths professional learning and development had been on the backburner. She was keen to turn things around when she became principal.
“I said to the leadership team, ‘we keep doing the same things again and again and it’s not really giving us the huge difference that we really need to see. And our children and their families deserve the best’,” Sose says.
When she saw the first exemplar explaining ‘Bobbie maths’, published in 2012, she could see the approach would suit the children at Russell School. A trip to Auckland to meet Bobbie Hunter and see DMIC in action confirmed this and Russell School started full PLD in DMIC from 2015.
“The power of DMIC is in students unpacking and understanding the power of their deeper thinking and analysis of how the maths works. A well-designed problem that has multiple entry levels which caters for the children who aren’t quite there, but also challenges the child whose thinking is strong and who is articulate, is a really powerful resource,” she says.
Sose says that DMIC can be challenging for teachers as it is a totally different way of teaching. The framework encourages teachers to let children learn through making mistakes and group problem solving. “Teachers struggle with the silence sometimes, but sometimes you have to allow the children that processing time.
“The framework is very powerful because it does empower the child – it’s a communication framework which is transferable across the curriculum. The engagement comes when I see the kids communicating with each other in a really positive way and when I see kids who are struggling a little bit and other kids showing empathy and aroha for them and being really respectful and honest in their learning.”
Q: What do you like about DMIC maths?
When I work and share with my buddy.
Working as a team and sharing ideas. I like helping kids learn more.
There are many different ways to get the answers and there are a lot of ways that I can learn from the people in my group, including the mistakes we make.
I like the way we work together to go on a maths journey.
I like that you can take people on a maths journey and be in a group to solve the problems.
Q: What is the best thing you have learnt in DMIC maths?
Counting in 5s and counting to 100.
To give me some more strategies to solve problems and I like learning more.
I can make mistakes; I don’t need to hide anything because people will learn from the mistakes. I also enjoy working in a group because our ideas can connect with the question and each other.
To ask questions in maths so I know if what they are saying is right about the maths. I can also relate to others.
You don’t let your team down; you work together to solve the problem. You give maths reasons for your ideas. I like building on other people’s ideas.
Early change data on student bullying rates across the three Porirua East schools for the first year of DMIC implementation in 2015 showed marked improvement and a reduction in bullying associated with the DMIC intervention. From 23.5 per cent to 10.4 per cent of students reported they were made fun of or called names at least once a week, from 15.1 per cent to 5.5 per cent of students reported they were left out of activities at least once a week, and from 20.5 per cent to 7.4 per cent of students reported being hit, kicked or hurt by other students at least once a week.
There was change also for students’ sense of belonging at school. Baseline data for the three Porirua East schools indicated there were children who, in mathematics, ‘never’ or ‘hardly ever’ felt good to be Māori, or Samoan, or their own (other) culture. This started changing. For example, in the Year 1 post-testing, Māori, Samoan, Cambodian and Iraqi students in Porirua East explained:
“I feel proud in my maths lesson today by carrying my family with me.”
“I felt bad ‘cause people tease my culture... [in maths now] I feel normal.”
“To be Samoan today in maths was awesome.”
The percentage of students who never or hardly ever felt good to be their culture dropped from 8.6 per cent to 3.3 per cent over the seven-month early implementation period.
Rutherford Discovery Fellowships support the development of future research leaders, New Zealand’s talented early- to mid-career researchers. Ten prestigious five-year Fellowships are awarded annually for research based in a New Zealand host institution, with competitive funding for the research of up to $160,000 a year. Royal Society Te Apārangi has responsibility for administering the Fellowships.
Dr Jodie Hunter, a 2019 recipient, plans to do several nested projects during her five-year Fellowship. The first will look at how DMIC develops mentors to grow their expertise to work with teachers; the second will look at how student outcomes are evaluated and assessed, using a qualitative scale to measure a range of factors including the mathematical engagement of students.
Jodie and her team will research the productivity of the DMIC pedagogy, looking at schools new to DMIC and those they have worked with for longer periods of time.
They will also look at schools in relation to the level of fidelity with which DMIC is implemented and the outcomes for students in terms of achievement, engagement, wellbeing and cultural identity.
The final project will involve documenting the mathematics children and their whānau use outside school and in the community setting. Participants will be given a device to take photographs or videos of themselves doing maths whether it be while baking, fishing or preparing a hangi.
The Marsden Fund was established by the Government in 1994 to fund excellent fundamental research. It is a contestable fund administered by the Royal Society of New Zealand on behalf of the Marsden Fund Council. It operates under the Terms of Reference issued by the Minister of Science and Innovation.
This year, Jodie’s research received a funding grant of $300,000 to explore culturally embedded knowledge and successful mathematical experiences of Pāsifika learners in their everyday settings – at home and in the community. The aim of her project is to raise awareness of Pāsifika learners’ strengths and address current equity issues in education.
BY Education Gazette editors
Education Gazette | Tukutuku Kōrero, firstname.lastname@example.org
Posted: 9:20 am, 22 November 2019
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