Ambitious mathematics: Ratios, decimals, fractions and time for Ta’ovala
Learning from Pacific expertise in education


This feature highlights the approach taken by a non-Pacific teacher to learning from Pacific expertise in education. Year 8 teacher, David Ahlquist, demonstrates with humility in his learning journey towards culturally responsive teaching. David is using the Developing Mathematical Inquiry Communities (DMIC) teaching and learning approach with Year 8 students at Koru School in Mangere, South Auckland.

Photo: Matilda Ngaluafe Williams

The DMIC professional development is co-led by Cook Island Kiwi mathematics education experts, Professor Roberta Hunter and Dr Jodie Hunter. DMIC, well-implemented over time, builds children’s progressions in mathematical reasoning, participation and communication skills, as it builds teacher capability in culturally responsive ambitious education.

The co-leaders of the DMIC intervention have won a series of awards for this ground-breaking ‘re/invention’ of pedagogy. The Massey University Developing Mathematical Inquiry Communities team won the Mathematics Educational Research Group of Australasia Award for Māori and Pacific Success 2018. Professor Roberta Hunter received an Excellence Award from the Cook Islands Government. In 2019, the Royal Society awarded Dr Jodie Hunter a prestigious Rutherford Discovery Fellowship.

DMIC has brought expert support and a development opportunity to the teaching profession. NZEI Te Riu Roa has provided national leadership in supporting this intervention. Find out more in NZEI’s Professional Journal AKO 2018 - Stunning results from culturally responsive maths. See also the 2019 Gazette article Taking maths into the hearts of communities.

In an early DMIC feature, Hangaia Te Urupounamu Pāngarau Mō Tātou, Ryan Pearce reflects on how for Pākehā teachers, the best intentions for culturally responsive teaching can ‘miss the mark’. Ryan values the DMIC in-class mentoring that so powerfully challenges his thinking about how to connect to the knowledge and experiences of Pacific learners in his class. See: Geometry – Connections: Tapa, Siapo, Ngātu.

DMIC, well-implemented, accelerates achievement as the pedagogy combats bullying and racism, and builds wellbeing and belonging. This feature explains the pedagogical foundation for the acceleration of mathematics learning through ‘low floor, high ceiling’ mathematical tasks. Teachers learn to design tasks that make educationally powerful connections to the lives of every student to the benefit of the whole class.

Koru School is one of over 140 schools that have taken on the deep challenges of the DMIC pedagogy; including mixed ability grouping.

In the latest New Zealand National Monitoring Study of Student Achievement in Mathematics and Statistics, there is a significant lift in mathematics achievement nationally; with the largest achievement gains evident for Year 8 Pacific students between 2013 and 2018. This change matters.

In the 2013 National Monitoring Study of Student Achievement in Mathematics and Statistics, only 11% of Pacific students at Year 8 were achieving at curriculum level 4 or above. In the 2018 New Zealand report almost 24% of Pacific students at Year 8 were achieving at curriculum level 4 or above compared with almost 27% of Māori and 50% of New Zealand European students.

The Pacific Wellbeing Budget has provided $7.2 million over four years for evidence-based, targeted, intensive provision of the Developing Mathematical Inquiry Communities (DMIC) re/invention of practice to schools serving high numbers of Pacific learners so that effective professional learning is resourced using lessons learned from best evidence findings about what makes a bigger difference for diverse Pacific student success and wellbeing. The new funding is resourcing further research and development on learning from Pacific families and school holiday pilots to support mathematics learning. See an interview with Dr Jodie Hunter here.

In the videos that follow, Year 8 teacher, David Ahlquist and his students at Koru School demonstrate a step up in culturally responsive mathematics teaching and learning using a Tongan context for learning.


"It is definitely a symbol of Tonga. It’s made from the land here, and then you wrap that around yourself. So you’re wrapping a piece of Tonga around your waist everywhere you go." Ben Work, Tongan TV presenter

Koru School teacher, David Ahlquist, demonstrates the DMIC teaching approach using Ta’ovala weaving as a context for ambitious mathematics teaching and learning with Year 8 students.

Koru School is a large primary school in Mangere, South Auckland with 79% Pacific and 18% Māori students. As various sources of funding have been available, Principal Stan Whata and Deputy Principal Bronwyn Jones have led the implementation of the Developing Mathematical Inquiry Communities (DMIC) teaching approach since 2013.

Developing Mathematical Inquiry Communities (DMIC)...

When well-implemented, DMIC is an evidence-based teaching approach that:

  • maximises student engagement for ambitious mathematics reasoning and learning
  • is culturally responsive and inclusive in ways that address unconscious bias
  • supports teachers to de-stream in ways that advantage both low and high achievers
  • pro-actively builds students’ collaborative problem solving skills
  • develops mutually respectful relationships and communication skills.

DMIC achieves these outcomes with clear well-structured task design and cognitive activation with challenging and meaningful content, and a supportive student-oriented classroom climate in which children feel they are respected and belong.

A DMIC lesson begins with preparation and task design to ensure challenging mathematics problems, related to big mathematical ideas, make educationally powerful connections to the lives and identities of the students.

The first part of the lesson is a teacher-directedLaunchof the task, ensuring the students relate to and understand the context and cognitive demand of the problem. The second part isGroup Workwith students working in small mixed ability groups to solve group-worthy, high-level problems. Extensive training is required, especially in the first year of implementation, to build specific student competencies for collaborative problem solving.

The third stage of the lesson sequence isSharing Backby groups, where the teacher selects and facilitates a meaningful selection of group explanations followed by the final stage of the lessonThe Connect.The Connectis a teacher-directed whole class discussion in which the teacher makes the connections back to the big ideas in mathematics that are the focus of the lesson.

As you view these videos, note the ‘low floor, high ceiling’ nature of the problems the students are solving, with these Year 8 students (aiming to achieve at curriculum level 4 by the end of their Year 8 year) working up to a problem at curriculum level 5 and beyond.

Consider the teacher’s skill in using DMIC cognitive activation strategies to develop the students’ deeper thinking. Cognitive activation strategies include ‘asking students to solve mathematics problems that require them to think for an extended time, for which there is no immediately obvious solution or that can be solved in several different ways’. Echazarra et al. (2016).

An OECD paper explaining findings from PISA mathematics found‘cognitive activation’strategies, effectively used, to be most strongly related to mathematics achievement of any teaching strategy.

Source reference:

Echazarra, A., Salinas, D., Méndez, I., Denis, V., & Rech, G. (2016). How teachers teach and students learn: Successful strategies for school (OECD Education Working Papers, No. 130). OECD: Paris.

Follow-up individual practice opportunities enable students to review, further apply and remember new mathematical strategies.