Developing Mathematical Inquiry Communities
Leaders from Otumoetai Intermediate, Southern Cross Campus Junior School and Koru School discuss what has been involved in creating new classroom norms that are more conducive to learning.
Creating new norms requires a lot of effort; children have to be explicitly taught how to engage in productive collaboration. The whānau is a familiar and extremely useful model: the children get that everyone has a role and a shared responsibility for the learning of all members of the group. It's for them to ensure that no-one gets left behind.
The 'talk moves' (wait time, revoicing, etc) have proven a powerful tool. Children come to understand them and use the terminology with each other. As they gain confidence to explain their own understanding they put high expectations on each other to actively engage and enjoy actually leading the learning.
Evidence in Action
- Creating new social norms for productive collaboration is a major endeavour
- A collaborative, respectful whānau model informs the values on which the group norms are based; teaching and learning practice consistently exemplifies these values
- Children need to be explicitly taught the 'how' of productively participating and contributing
- The 'talk moves' provide a framework for productive engagement that can be taught to, internalised, owned and propagated by children.
- Shared responsibility for each other's learning goes hand-in-hand with high expectations of each other: no passengers, everyone will explain clearly, no-one gets left behind
- The group is responsible for ensuring that each member can explain and justify the strategy used. A 'one pen per group' policy supports productive collaboration.
- When well-implemented, DMIC leads to accelerated improvement in literacy as well as mathematics.
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.
- Effective use of mixed-ability groups has equity and excellence effects
- Lower achieving students who get access to the thinking of higher achieving students benefit
- Both high and low achieving students who learn how to give elaborated explanations gain accelerated achievement benefit
- 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.
- Boaler, J. (2008). How Complex Instruction led to high and equitable achievement: The case of Railside School.
- Cohen, E. & Lotan, R. (2014). Designing groupwork: Strategies for the heterogeneous Classroom, (3rd ed.). Teachers College Press: New York.
- Cohen, E. G., & Lotan, R. (Eds.). (1997). Working for equity in heterogeneous classrooms: sociology theory in practice. New York: Teachers College Press.
- Cohen, E. G., & Lotan, R. A. (1997). Creating equal-status interaction in heterogeneous classrooms: Evidence from complex instruction. In R. Ben-Ari & Y. Rich (Eds.), Enhancing education in heterogeneous schools: theory and application; studies in memory of Yehuda Amir. Ramat-Gan, Israel: Bar-Ilan University Press. Pp. 249-280.
- Cohen. E. G., & Lotan, R. A. (1997). Raising expectations for competence: the effectiveness of status interventions. In E. G. Cohen & R. A Lotan, (Eds.), Working for equity in heterogeneous classrooms - sociology theory in practice. New York: Teachers College Press. pp 77-91.
- Hunter, J. (2009). Developing a productive discourse community in the mathematics classroom. In R. Hunter, B. Bicknell, & T. Burgess (Eds.) Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 249-256). Wellington, NZ: MERGA.
- Hunter, J. (2007). Developing early algebraic understanding in an inquiry classroom. Master's Thesis, Massey University, Palmerston North.
- Schleicher, A. (2014). Equity, excellence and inclusiveness in education: Policy lessons from around the world. Paris: OECD.
- Webb, N.M. (1991). Task-related verbal interaction and mathematics learning in small groups. Journal for Research in Mathematics Education, 22, 366-89.