Developing Mathematical Inquiry Communities

Introduction

The DMIC approach envisages a three-part structure to maths lessons: the ‘launch’ at the beginning, problem solving in mixed-ability groups, and the ‘connect’ at the end.


05 PROBLEM AND LAUNCH from BES Programme on Vimeo.

Key Content

In this video Associate Professor Bobbie Hunter explains the importance of coming up with problems that have genuine mathematical value, that connect to big, worthwhile mathematical ideas, that will lead to understandings that will set them up for success at high school.

Leaders from Otumoetai Intermediate discuss how they go about collaboratively devising such problems and then planning the 'launch'. The 'launch' is where the problem of the day is introduced to the children. It is crucial on two counts: the children must understand the problem and believe that it is worth applying themselves to.

This video does not discuss the 'connect', the concluding part of the lesson where the children share how they went about solving the problem and the teacher ties their learning into the big idea.

Evidence in Action

This video provides a window into these critical success factors …

  • Problems need to be carefully designed so that:
    • the children will understand what it is they are trying to solve
    • they connect to big, worthwhile maths ideas
    • they connect in some way to the lives/communities of the children
  • Devising good problems is best done collaboratively
    • pedagogical leaders 'talk the walk'
    • meetings optimise coherence, value and impact of pedagogical design
    • choice of problems is linked to the curriculum
    • exploration of possible misconceptions
  • An effective launch ensures that:
    • the problem makes sense to the students
    • the problem matters to the students
  • Pedagogical leadership.

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.

  1. Alton-Lee, A. (2003). Quality teaching for diverse students in schooling: Best Evidence Synthesis Iteration (BES). Wellington: Ministry of Education.
  2. 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.
  3. Anthony, G., & Hunter, R. (2010). Communities of mathematical inquiry to support engagement in rich tasks In B. Kaur (Ed.), Mathematics applications and modeling: Yearbook 2010 Association of Mathematics Educators (pp. 21-39). London: World Scientific.
  4. Anthony, G., & Walshaw, M. (2010). Te ako pāngarau whaihua: Educational practices series – 19. International Academy of Education, International Bureau of Education & UNESCO.
  5. Anthony, G., & Walshaw, M. (2009). Effective pedagogy in mathematics: Educational practices series –19. International Academy of Education, International Bureau of Education & UNESCO.
  6. Anthony, G., & Walshaw, M. (2007). Effective pedagogy in mathematics/pāngarau: Best evidence synthesis iteration. Wellington, New Zealand: Ministry of Education.Chapter 5: Mathematical Tasks, Activities and Tools.
  7. Hattie, J (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London, UK: Routledge. Effect size for teacher clarity = 0.75
  8. Leach, G., Hunter, R., & Hunter, J. (2014). Teachers repositioning culturally diverse students as doers and thinkers of mathematics. In J. Anderson, M. Cavanagh, A. Prescott (Eds.) Proceedings of the 37th Mathematics Education Research Group of Australasia (pp. 381–388). Sydney, NSW: MERGA.
  9. Robinson, V., Hohepa, M., & Lloyd C. (2009). School leadership and student outcomes: Identifying what works and why: Best evidence synthesis iteration. Wellington, New Zealand: Ministry of Education. Chapters 5, 6 and 7.
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