1: Developing Mathematical Inquiry Communities

Ngāi Tahu kaumatua and educational psychologist Laurie Loper reflects on our education system and speaks of Developing Mathematical Inquiry Communities (DMIC) as a culturally responsive and evidence-based way forward.

Key Content

Associate Professor Bobbie Hunter explains how cultural reticence and ability grouping have had unfortunate consequences for Pasifika children. She advocates a collectivist ethos, de-emphasising speed, repositioning mistakes as a necessary and desirable part of learning, and teaching the skills of friendly arguing/respectful engagement.

Leaders from Otumoetai Intermediate, Southern Cross Campus, Koru School and Robertson Road School talk about how they have upgraded their expectations since embarking on the DMIC journey and realising that their children know a lot more and are capable of a lot more than they ever thought possible. They also discuss some of the changes that they have made to classroom and group dynamics, and how they now teach mathematics. It hasn’t been easy, but it has been worthwhile.

Children from these schools explain what it is like working in mixed ability groups, relishing the increased challenge, accepting mistakes as part of learning, enjoying the opportunity to learn from others as well as to share their own ideas, and enjoying increased agency in their own learning.

Evidence in Action

  • Children are often a lot more knowledgeable and capable than their teachers realise.
  • Effective links are created between school learning and children’s lives and identities
  • If we underestimate children’s abilities, we inevitably limit their opportunities to learn.
  • Pedagogical practices enable classes and groups to work as caring, inclusive, and cohesive learning communities.
  • Mixed-ability groups give children multiple opportunities to learn from each other.
  • For many children, a collectivist approach to learning (‘no-one gets left behind’) is more effective than a competitive approach.
  • Children appreciate having agency in their own learning.
  • Maths is about being able to explain how the answer has been arrived at as well as getting the answer.
  • Children need to be taught how to work productively and respectfully together.
  • Seeing outside expertise working with their own children can create dissonance in teachers, causing them to question existing theories and becoming a catalyst for substantive change.
  • Effective maths teaching involves careful preparation: to generate worthwhile problems that build on children’s proficiencies, to connect to big mathematical ideas, and to anticipate children’s mathematical thinking.
  • Teachers become students of their own students, learning to use children’s thinking as a springboard for further learning.
  • Teachers can find it beneficial to prepare collaboratively.

Key Evidence Informing Action – References

Specialist providers, principals and teachers working in New Zealand schools and early childhood services, as well as the New Zealand Ministry of Education and central government education agency staff, can contact the Ministry of Education Library for access to the key evidence. For anyone else requiring this material, you can contact your institution or local public library.

Alton-Lee, A. (2015, September). Disciplined innovation for equity and excellence in education: Learning from Māori and Pasifika change expertise.Invited paper for the World Educational Research Association Focal Session: Education of Diverse Students: A Multi Country Perspective. Budapest, Hungary.

Alton-Lee, A. (2012). The use of evidence to improve education and serve the public good. Paper prepared for the New Zealand Ministry of Education and the annual meeting of the American Educational Research Association. Wellington: New Zealand.

Alton-Lee, A. (2006). How teaching influences learning: Implications for educational researchers, teachers, teacher educators and policy makers. Teaching and Teacher Education: An International Journal of Research and Studies, 22(5), 612-626.

Alton-Lee, A. (2003). Quality teaching for diverse students in schooling: Best evidence synthesis. Wellington: Ministry of Education.

Alton-Lee, A., Hunter, R., Sinnema, C., & Pulegatoa-Diggins, C. (2012, April). BES Exemplar 1 Ngā Kete Raukura – He Tauira: Developing communities of mathematical inquiry. Wellington: Ministry of Education.

Alton-Lee, A.G., & Nuthall, G.A., with Patrick, J. (1995). In G. Capella Noya, K. Geismar & G. Nicoleau (Eds.). Shifting histories : Transforming Education for Social Change. Reframing classroom research: A lesson from the private world of children. Cambridge, MA,: Harvard Educational Review. Reprint series No. 26.

Anthony, G., & Walshaw, M. (2010). Te ako pāngarau whaihua: Educational practices series – 19. International Academy of Education, International Bureau of Education & UNESCO.

Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics: Educational practices series –19. International Academy of Education, International Bureau of Education & UNESCO.

Bills, T., & Hunter, R. (2015). The role of cultural capital in creating equity for Pāsifika learners in mathematics. In M. Marshman, V. Geiger, & A. Bennison (Eds.). Mathematics education in the margins (Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia), (pp. 109–116). Sunshine Coast: MERGA. 109-117. Cohen, E. & Lotan, R. (2014). Designing groupwork: Strategies for the heterogeneous Classroom, (3rd ed.). Teachers College Press: New York. Educational Assessment Research Unit & New Zealand Council for Educational Research. (2015). National monitoring study of student achievement, mathematics and statistics 2013. Ministry of Education: Wellington, New Zealand. Hanushek, E. & Woessman, L. (2011). The economics of international differences in educational achievement. In E. Hanushek, S. Machin & L. Woessman (Eds).Economics of education. Vol. 3, 89-200. Handbooks in economics. The Netherlands: Elsevier B.V., North-Holland. Hunter, R. (2012). Coming to ‘know’ mathematics through being scaffolded to ‘talk and do’ mathematics. International Journal for Mathematics Teaching and Learning, pp. 1-12. Hunter, R. (2008). Facilitating communities of mathematical inquiry. In M. Goos, R. Brown, & K. Makar (Eds.). Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 31–39). Brisbane: MERGA. Dr Bobbie Hunter’s 2008 publication received the Beth Southwell Practical Implications Award sponsored by the Australian Association of Mathematics Teachers (AAMT) and the National Key Centre for Teaching and Research in School Science and Mathematics, Curtin University, Perth, Western Australia. Hunter, R. (2007). Teachers developing communities of mathematical inquiry. Unpublished doctoral thesis, Massey University. Palmerston North. National Council of Teachers of Mathematics. (2014). From principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics. Nuthall, G. (2007). The hidden lives of learners. Wellington: New Zealand Council for Educational Research. Nuthall, G. (2002). The cultural myths and the realities of teaching and learning. New Zealand Annual Review of Education, 11, 5-30. Nuthall, G. (1999). Learning how to learn: The evolution of students’ minds through the social processes and culture of the classroom. International Journal of Educational Research, 31 (3), 141-256. OECD. (2012). PISA 2012 results: What students know and can do. Student performance in mathematics, reading and science, Volume 1. Chapters 2 & 3. Trend: p. 55. Organisation for Economic Co-operation and Development: Paris.