Developing Mathematical Inquiry Communities:
13 It’s a journey
Seeing Associate Professor Bobbie Hunter and her mentors in action with their own students has made them realise that they need to become much more ambitious in their teaching. While DMIC pedagogy asks a lot of them they have been well supported to make the necessary changes, and they have gone far enough to know that they don't want to go back.
Evidence in Action
- You have to become uncomfortable with how you are teaching before you can become a more effective teacher
- It is important that the level of discomfort is not so high that you give up
- Teachers come to understand how to better teach mathematics through developing their own content knowledge, understanding children's learning processes and anticipating children's misconceptions in mathematics
- Teaching maths effectively requires major investment in preparation time, particularly to construct problems that meet multiple criteria
- Challenge, in-class modelling and mentoring from external experts, managed in a safe and caring manner, are powerful tools for demonstrating what is possible, creating dissonance and supporting teacher change
- The DMIC lesson framework (launch, problem solving in groups, connect) imposes discipline on planning and teaching, but getting each phase right requires practice
- It is good for children to see their teachers as learners: taking risks, making mistakes, accepting feedback
- The move from teaching based on fragmentary learning intentions to learning that connects to big mathematical ideas is very important and can involve a major mind shift
- Uncertainty about what the big mathematical ideas are is stressful for teachers, especially those who are not secure in their content knowledge
- The 'connect' at the end is powerful because that is where the learning is consolidated
- Once children realise that mistakes are part of learning they are happy to take risks and to question and share
- Learning, whether by the children or teacher, thrives in a safe and supportive environment.
Key Evidence Informing Action - References
Specialist providers and 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.
- Anthony, G. & Hunter, J. (2008). Developing algebraic generalisation strategies. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd conference of the International group for the Psychology of Mathematics Education (Vol. 2, pp. 65-72). Morelia: PME.
- Anthony, G., Hunter, J., Hunter, R. & Duncan, S. (2015). How ambitious is "ambitious mathematics teaching". In J. Huria & J. Roberts (Eds.), Set: Research Information for Teachers. (pp. 45- 52). Wellington, New Zealand: About Print.
- Anthony, G., Hunter, R., & Thompson, Z. (2014). Expansive learning: lessons from one teacher's learning journey. ZDM – The International Journal on Mathematics Education, 46(2), 279-291.
- Anthony, G. & Hunter, J. (2010). Developing early algebraic reasoning. In R. Averill, & R. Harvey (Eds.) Teaching Primary School Mathematics and Statistics: Evidence-Based Practice (pp. 65-74). Wellington, NZ: NZCER.
- Bicknell, B., & Hunter, R. (2009). Explorations of year 6 to year 7 transition in numeracy. In Ministry of Education (Ed.) Findings from the New Zealand Numeracy Development Projects (pp. 98-109). Wellington, NZ: Learning Media Limited.
- Burghes, D., Szalontai, T., Koyama, M., Myllyntausta, S., Beston, Y., Hazell, M., Robinson, D., Pitman, P., Smith, R., Kellet, S., & Hunter, J. (2012). Enhancing primary mathematics teaching and learning. UK: CfBT Education Trust.
- Burghes, D., & Hunter, JM. (2012). Recommendations for good practice. Section 7 (pages 97104) in Burghes, D. Enhancing primary mathematics teaching and learning. UK: CfBT Education Trust.
- Hunter, J. (2015). Teacher actions to facilitate early algebraic reasoning. In M. Marshman, V. Geiger, & A. Bennison (Eds.) Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia (pp. 58-67.) Sunshine Coast: MERGA.
- Hunter, J. (2014). Developing early algebraic reasoning in a mathematical community of inquiry. Doctoral Thesis, Plymouth University, UK.
- Hunter, J. (2014). Developing learning environments which support early algebraic reasoning: A case from a New Zealand primary classroom. Mathematics Education Research Journal. 26:659–682.
- Hunter, J. (2012). Developing teacher understanding of early algebraic concepts using lesson study. In J. Dindyal, L.P. Cheng, & S.F. Ng (Eds.) Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 346-353). Adelaide, SA: MERGA.
- Hunter, J. (2010). Developing early algebraic reasoning through exploration of odd and even numbers. In B. Maj, E. Swoboda, & K. Tatsis (Eds.) Motivation via natural differentiation in mathematics (Proceedings of the 2010 Conference of Children's Mathematical Education (pp. 101-109).
- Hunter, J. (2010). Developing early algebraic reasoning through exploration of the commutative principle. In M. Joubert, & P. Andrews (Eds.) Proceedings of the British Congress of Mathematics Education, BCME-7. Vol. 30, pp. 105-112. Manchester, UK: BCME.
- Hunter, J. (2007). Developing early algebraic understanding in an inquiry classroom. Master's Thesis, Massey University, Palmerston North.
- Hunter, R, (2005). Reforming communication in the classroom: One teacher's journey of change. In P. Clarkson, A. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: Research, Theory and Practice. (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia. pp. 451-458). Sydney: MERGA.
- Hunter, R. (2010). Coming to 'know' mathematics through 'acting, talking and doing' mathematics. Proceedings of the 33rd Annual Conference of the Mathematics Educational Research Group of Australasia (pp. 264-271). Freemantle, WA: MERGA.
- Hunter, R. (2002). Constructing decimal concepts in an inquiry classroom. Master's Thesis, Massey University, Palmerston North, NZ.
- Hunter, R. & Anthony, G. (2003). 'Sensing': Supporting student understanding of decimal knowledge. In N.A. Pateman, B.J. Dougherty, & J.T. Zilliox (Eds.) International Group for the Psychology of Mathematics Education: Proceedings of the 2003 Joint Meeting of PME and PMENA. Vol. 2, pp. 41-48. Honolulu, HI.: PME.
- Hunter, R. & Anthony, G. (2003). Percentages: A foundation for supporting students' understanding of decimals. In L. Brogg, C. Campbell, G. Herbert, & J. Mousley (Eds.) Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australasia, (Vol. 2, pp. 452-459). Geelong, VIC: MERGA.
- Ormond, C. (2012). Developing "algebraic thinking": Two ways to establish some early algebraic ideas in primary classrooms. Australian Primary Mathematics Classroom 17 (4) (pp13-19).