DMIC and Inclusive Practices
Helen Collins shares stories – both personal and professional – about Developing Mathematical Inquiry Communities (DMIC), inclusion, and how DMIC supports, challenges, and provides enhancements to teaching and learning.
Collins is a teacher at Corinna School in Porirua. She is passionate about inclusive teaching and learning practices. Collins is a Practitioner of the Developing Mathematical Inquiry Communities pedagogy.
This talk was a part of Growing from Strong Foundations in Auckland on 5, June, 2018
- New Zealand Curriculum
- Te Marautanga o Aotearoa
- Te Marautanga o Aotearoa (English translation, pdf, 0.39MB)
- Te Whāriki (pdf, 4.4MB)
Best Evidence Syntheses
- School Leadership and Student Outcomes Best Evidence Synthesis: Chapter Seven (pdf, 0.7mb)
- Iterative Best Evidence Synthesis (BES) Hei Kete Raukura Resources
Developing Mathematical Inquiry Communities
- School leadership for improvement in primary mathematics education: Russell School best evidence in action implementation exemplar
- Improvement in Mathematics Education: Evidence in Action Hangaia te Urupounamu Pāngarau Mō Tātou
- Developing Mathematical Inquiry Communities
Hei Oranga Tika: Wellbeing Matters
- Hei Oranga Tika: Wellbeing Matters Emerging evidence of the impact of the Christchurch earthquakes on young children
Reading Together Te Pānui Ngātahi
- Reading Together Te Pānui Ngātahi: Implementation for impact and enduring, reciprocal high trust relationships between families, whānau and schools
- Poutama Pounamu
- Evaluation of Te Kotahitanga Phase 5 (2010-2012)
- Disciplined innovation for equity and excellence in education: Learning from Māori and Pasifika change expertise
- 'Walking the talk' matters in the use of evidence for transformative education (pdf, 0.7mb)
Writers in Schools
As you watch the presentations, think about these questions:
- What is something that has challenged or confirmed your thinking about the curricula?
- What can I do as a result?
Helen Collins: Ko Ngāti Kahungunu me Ngai Tamanuhiri tā rātou iwi
Ko Helen Collins toku ingoa
Nō Te Wai Pounamu ahau, engari e noho ana au i te riu o Porirua inaianei
Ko Corrina te kura
Nō reira, ngā mihi nui ki a tātou katoa
Kia Ora Koutou, I am Helen and I am not here today, as I quote, one of New Zealand’s leading experts discussing the potential of the curricula to support challenge and enhance children’s learning post-National Standards. I would like to be one of New Zealand’s experts at it, but I am not. We have all heard this morning from Jodie Hunter, who along with Bobby Hunter are the experts, meitaki maata to you both.
I feel very lucky that the tamariki I teach, my own children and I, are part of a way of learning that I really believe in. I am the proud mother of three children – aged 15, 12 and 11 – and I currently co-teach in a Year 6/7/8 class. I am not an expert practitioner in DMIC maths… yet. But as a teacher of 28ish years and a mum, I do feel qualified to talk about inclusion/engagement.
I would like today to share some stories – both personal and professional – about DMIC maths and inclusion and about how it enables all students to learn about how it supports, challenges and provides enhancements to teaching and learning. Three years ago, I joined Corinna School in Waitangirua in Porirua East and brought with me my younger two children. When we joined Corinna, they were six months into taking on DMIC maths. I did have some inside information however about what was in store for me. My sister Kate had been teaching for many years at Corinna before I arrived.
She is world famous within our family and our Corinna school whānau for her complete dedication and passion for teaching and learning and her commitment for doing what is best for our tamariki, their whānau and our community. So, DMIC maths was – despite being really challenging for her – right up her alley and I had been ear-bashed with every step of her journey. While we were out jogging, during family outings, extra long sessions in the school holidays, there were phone calls full of wonderings and theory, honest accounts of epic fails. All of this for most of the six months prior to joining Corinna. I actually felt that I knew Bobby and Jodie personally.
Despite all this, when I started in term three in 2015 with a new class of year 2/3s, it was all on. The best advice I had was to put my trust in DMIC – I actually think of your T-shirts now, in DMIC we trust, we could wear at Corinna – and also to throw myself in. Yep, that and get comfortable with being uncomfortable. Corinna School is a decile 1A school with around 78% Pasifika, 20% Māori and 2% Syrian, South East Asian and a couple of Pākeha students.
The video shows the statement: “There has been a failure to meet the needs of every learner, particularly Māori, Pasifika, students with special education needs and students from low socio-economic backgrounds.”
The last statement on this slide sums up for me how the DMIC model addresses the significant problem of not meeting many of our students needs in the past. The stories I will share today show how inclusion means that these students can have their learning needs met. They can be and are expected to be part of a learning community. For us at Corinna, inclusion has to acknowledge the complexity of diversity – that is the diversity even within the 78% Pasifika is huge.
In DMIC, for our practices to be inclusive, we need to create maths problems that include youth culture, sport which is hugely significant for our whānau, ethnicity of course and religion. What the DMIC model has helped me understand is that we need to really actively know our learners, their whānau and community to be genuinely culturally responsive and inclusive and not make assumptions. I think Jodie that you spoke to that when you talked about this being hard work. This is hard work.
I would like to share with you a story from my daughter’s maths learning last year that her teacher shared with me. Hinerangi is 11 years old. In our school – and especially in the DMIC model – she is encouraged and nurtured to bring her unique perspective and way of being a mathematician to the mixed ability group she works in. She is a Down’s Syndrome 11-year-old mathematician. Hine was in a group who were trying to figure out 3x4. One person said that 3x4 was 12 and Hine said – no, it’s 7, see. She showed her fingers – 3 and 4 – and showed that it equalled 7.
Another boy in the group said – no Hine, you are wrong, Promise is right. It is possible that because he didn’t want to listen to Hine and her status wasn’t high in that group and Promise’s status is higher. The teacher stopped the group and was able to raise Hine’s status because she was proving exactly why she thought 3 and 4 was 7. She was explaining and showing the group. So, then Faa’sa was able to change his mind; he saw her explanation and said, I change my mind. Hine, you are right.
We were then able to go back to Promise and for her to notice what Hine had done. She said – Hine, you plussed them, but I put a times symbol. So, when you times them, you need to count in 3’s four times. That’s what I meant. And Hine was able to say – oh, okay, I change my mind too. You were timesing them, not plussing them. Faa’sa was able to see that both people showed their thinking and proved why they were good mathematicians by showing HOW they knew what they thought. Explaining, showing, proving, noticing, persevering and changing my mind …. Hinerangi is expected to be part of this. And she intentionally has her status raised for her maths thinking and not just for a correct answer.
I have added on another little shorter story about Hinerangi again in a different maths group, just because I think it has a slightly more human side, shall we say. Okay, a group had made 23 on an abacus and Hine said it was 30. She kept saying, as she slid over each row – 10, 20, 30. Lipali and Daniel were very kindly trying to explain how it wasn’t 30 because the last row only had 3, but it would be 30 if there was a full row. I just need to add in here that Hinerangi is well-known for being sure when she is right. She can be very determined – that is a euphemism – when trying to convince you. Her aunty has long said the extra chromosome is a negotiating one.
Finally, Hine changed her mind but when I tried to get her to explain she wasn’t fully able to explain how she knew it, but she did change her mind. We are still not sure if she was convinced by the mathematical explanation or just worn down by so many people telling her.
This story, shared by another teacher, talks about how the DMIC model has seen a gorgeous wee man grow in front of our eyes. Mickey is an 8-year-old Māori boy with a speech impediment; it is quite serious. He has low status both academically and socially. He is beginning however to see himself as a learner and this means taking risks. Mickey was working in a group with three girls and they were working on a second part of a maths problem. They had already found the area of a Te Vivi and were working out how many 25cm squares they would need to make it. One girl had drawn a 1 metre square and then she was called out of the classroom. The group was now in the pit; they didn’t know what to do next. It goes on… the teacher that shared this with me about what Mickey decided to do which is really quite clever mathematically. In the end he, along with his group, semi-solved the problem.
When they were reporting back, the teacher said to him – well done Mackie. By splitting the square and then using your knowledge of making 100, you have worked out how many 25cm squares in a one metre square. You took a big risk sharing your ideas and working it through. Here the teacher assigned competence to raise the status of Mackie and he smiled and his eyes lit up. Others in the group looked surprised and suddenly they sat up and listened to him repeat what he had done.
Shortly afterwards the group were brought back together to discuss the problem. The teacher said that Mackie had a clever idea and had got his group out of the pit. Intentionally noticing and publicly praising the student encouraged a shift in his peers’ expectations of him and himself. Mackie proudly explained his ideas.
Who can be successful in maths? Mackie can and Hine can.
I am going to play a video clip that my sister Kate made for an assignment about DMIC and collaboration, but to me it illustrates inclusion just as much as collaboration. In this video, you will see a student from our class who is elective mute. He is required to contribute his maths thinking to his group and to share his groups thinking and problem solving back to the larger group. We often talk about ‘maths smarts’ as either status building or assigning status to aspects of maths learning other than just having quick recall.
Last week I reminded him of his ‘maths smart’ and that he is great at representing his group’s thinking mathematically – something he can do without speaking – and that he needed to come and take the whiteboard marker without being asked and record his own thinking or his group’s thinking on the board. This is actually aspirational as he is painfully aware of the effects of his choice not to speak and would rather chew razor blades than come forward voluntarily. However, our ethic of care means that we would not be showing him the love and respect we have for him if we didn’t have the expectation that he will participate. He is also required to show respect for his learning group by taking responsibility for contributing.
On the video clip you will also see and read the reflection of a student who could be classed as having special learning needs. He sees himself as a mathematician. He knows his strengths and what ‘maths smarts’ he brings to his group. I am hopeful – probably unrealistically – that this is still the case that he has moved to College and is no longer learning in the DMIC model. Visitors to our school couldn’t identify him as the member of his group for special learning needs.
At Corinna School, all students work in mixed ability groups to solve challenging maths problems embedded in culturally relevant contexts. For three years, we have been working with Dr. Roberta Hunter and Dr. Jodie Hunter to develop a mathematical enquiry community called DMIC. The students see these problems as worth solving and relevant to their lives. As a result, they are fully engaged in solving the problem.
The students are proud of the fact that they are the experts when we discuss the cultural context for the problem. The problems are challenging and require a range of strategies, skills and group norms to be used. There are no passengers on the waka. The work is inter-dependent as all students must participate in order for the team to succeed. Our year 6, 7 and 8 students collaborated to solve a level 1 NCEA problem that year 11 students struggled to solve. They did it!
The students have a clear understanding of their shared responsibility to solve the problem as a group. All have a role to play. These are the criteria they have decided they need to use to collaborate effectively and to reflect on how well they have collaborated. The students may be ‘in the pit’ which means that they are struggling to solve a problem, but they persevere and support each other because in the end, when the group succeeds their understanding is extended and their learning enhanced.
The group has to be prepared to share their conjecture in the way they chose to solve the problem with half the class. The responsibility for doing this is shared. All group members must explain what they did clearly and confidently – step by step – and justify the decisions they made. They must also share what the numbers they talk about represent in the context of the problem. The students observing and listening make connections to their own conjectures that also repeat, re-voice, ask for clarification, challenge, agree and disagree – which we call friendly arguing.
This is a Year 6 student’s learning blog. As a result of the collaboration, she can share how her group solved a problem. She can explain the process her group went through. She can reflect on her own ability to collaborate. Through collaboration, Corinna school students see themselves as competent mathematicians.
There was a lot of talk about the problem of educating our tamariki for a future that we can’t be sure of and the uncertainty of this. I think it is fair to say that we haven’t been doing the best job of this. What we have been doing hasn’t worked so well. My belief is that this uncertain future is going to need us to be collaborative problem solvers, for strong key competencies in group norms, not competing with each other and being assessed in a one-size-fits-all system.
We will need to foster teaching, learning, playing and working environments where there are the values of belonging and being invested. We often use the phrase – everyone is on the waka - which I think is really apt an in my mind there is a picture of everyone being valued for the strengths they bring to move their waka forward. This is me is inclusion and it is mirrored in the DMIC core beliefs. Valuing everyone’s strengths and genuinely believing that everyone can be a successful contributor is the bottom line.
He mihi nui kia koutou katoa
More from this series
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