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Shifting more than the goal posts: developing classroom norms of inquiry-based learning in mathematics

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Abstract

The 3-year study described in this paper aims to create new knowledge about inquiry norms in primary mathematics classrooms. Mathematical inquiry addresses complex problems that contain ambiguities, yet classroom environments often do not adopt norms that promote curiosity, risk-taking and negotiation needed to productively engage with complex problems. Little is known about how teachers and students initiate, develop and maintain norms of mathematical inquiry in primary classrooms. The research question guiding this study is, “How do classroom norms develop that facilitate student learning in primary classrooms which practice mathematical inquiry?” The project will (1) analyse a video archive of inquiry lessons to identify signature practices that enhance productive classroom norms of mathematical inquiry and facilitate learning, (2) engage expert inquiry teachers to collaborate to identify and design strategies for assisting teachers to develop and sustain norms over time that are conducive to mathematical inquiry and (3) support and study teachers new to mathematical inquiry adopting these practices in their classrooms. Anticipated outcomes include identification and illustration of classroom norms of mathematical inquiry, signature practices linked to these norms and case studies of primary teachers’ progressive development of classroom norms of mathematical inquiry and how they facilitate learning.

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References

  • Australian Academy of Science (AAS). (2015). Desktop review of mathematics school education pedagogical approaches and learning resources. Canberra: Australian Academy of Science.

    Google Scholar 

  • Australian Academy of Science (AAS). (2016). Mathematics by Inquiry. https://www.science.org.au/learning/schools/mathematics-inquiry

  • Australian Council of Learned Academies (ACOLA). (2013). STEM: country comparisons: international comparisons of science, technology, engineering and mathematics (STEM) education. Final report. Melbourne: ACOLA.

    Google Scholar 

  • Australian Government (2015). Restoring the focus on STEM in schools. www.studentsfirst.gov.au/restoring-focus-stem-schools-initiative

  • Barron, B., & Darling-Hammond, L. (2010). Prospects and challenges for inquiry-based approaches to learning. In D. Hanna et al. (Eds.), The nature of learning: using research to inspire practice (pp. 199–225). Paris: OECD.

    Chapter  Google Scholar 

  • Birmingham, S. (2015). Bringing maths into the real world for students (media release). http://www.senatorbirmingham.com.au/Media-Centre/Media-Releases/ID/2860/Bringing-maths-into-the-real-world-for-students

  • Bruder, R., & Prescott, A. (2013). Research evidence on the benefits of IBL. ZDM—The International Journal on Mathematics Education (Zentralblatt für Didaktik der Mathematik), 45(6), 811–822.

    Article  Google Scholar 

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

    Article  Google Scholar 

  • Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while doing mathematical problem solving. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: a new perspective (pp. 117–148). New York: Springer-Verlag.

    Chapter  Google Scholar 

  • Confrey, J. (1991). Learning to listen: a student’s understanding of powers of ten. In E. von Glasersfeld (Ed.), Constructivism in mathematics education (pp. 111–138). Dordrecht: Springer.

    Chapter  Google Scholar 

  • de Corte, E., Verschaffel, L., & Depaepe, F. (2008). Unraveling the relationship between students’ mathematics-related beliefs and the classroom culture. European Psychologist, 13(1), 24–36.

    Article  Google Scholar 

  • Fielding-Wells, J. (2015). Identifying core elements of argument-based inquiry in primary mathematics learning. 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. 229–236). Sunshine Coast: Mathematics Education Research Group of Australasia.

    Google Scholar 

  • Fielding-Wells, J., & Makar, K. (2008). Student (dis)engagement with mathematics. Paper presented at the annual conference of the Australian Association of Research in Education (AARE): Brisbane. http://www.aare.edu.au/08pap/mak08723.pdf

  • Fielding-Wells, J., & Makar, K. (2012). Developing primary students’ argumentation skills in inquiry-based mathematics classrooms. In K. T. Jan van Aalst, M. J. Jacobson, & P. Reimann (Eds.), The future of learning: proceedings of the 10th International Conference of the Learning Sciences [ICLS2012]—Vol 2 (pp. 149–153). International Society of the Learning Sciences: Sydney, NSW.

    Google Scholar 

  • Franke, M. L., & Carey, D. A. (1996). Young children’s perceptions of mathematics in problem-solving environments. Journal for Research in Mathematics Education, 28(1), 8–25.

    Article  Google Scholar 

  • Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225–256). Charlotte: Information Age Publishing.

    Google Scholar 

  • Franke, M. L., Turrou, A. C., Webb, N. M., Ing, M., Wong, J., Shin, N., & Fernandez, C. (2015). Student engagement with others’ mathematical ideas: the role of teacher invitation and support moves. The Elementary School Journal, 116(1), 126–148.

    Article  Google Scholar 

  • Fry, K. (2013). Students ‘holding’ the moment: learning mathematics in an inquiry mathematics classroom. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (pp. 306–313). Melbourne: MERGA.

    Google Scholar 

  • Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35, 258–291.

    Article  Google Scholar 

  • Hattie, J. (2008). Visible learning: a synthesis of over 800 meta-analyses relating to achievement. New York: Routledge.

    Google Scholar 

  • Hunter, R. (2012). Coming to know mathematics through being scaffolded to “talk and do” mathematics. International Journal of Mathematics Teaching and Learning (21 Dec issue), 1–12. Available at http://www.cimt.org.uk/journal/hunter2.pdf.

  • Kazemi, E., & Stipek, D. (2001). Promoting conceptual understanding in four upper-elementary mathematics classrooms. Elementary School Journal, 102, 59–80.

    Article  Google Scholar 

  • Makar, K. (2011). Learning over time: pedagogical change in teaching mathematical inquiry. In J. Clark et al. (Eds.), Proceedings of the Mathematics Education Research Group of Australasia annual conference (Beth Southwell Practical Implications Award). Alice Springs: MERGA.

    Google Scholar 

  • Makar, K. (2012). The pedagogy of mathematical inquiry. In R. Gillies (Ed.), Pedagogy: new developments in the learning sciences (pp. 371–397). Hauppauge: Nova Science.

    Google Scholar 

  • Makar, K. (2016). Developing young children's emergent inferential practices in statistics. Mathematical Thinking and Learning, 18(1), 1–24.

    Article  Google Scholar 

  • Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom. ZDM—The International Journal on Mathematics Education (Zentralblatt für Didaktik der Mathematik), 47(7), 1107–1120. doi:10.1007/s11858-015-0732-1.

    Article  Google Scholar 

  • Makar, K., & Fielding-Wells, J. (2011). Teaching teachers to teach statistical investigations. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education (pp. 347–358). New York: Springer.

    Chapter  Google Scholar 

  • McPhan, G., Morony, W., Pegg, J., Cooksey, R., & Lynch, T. (2008). Maths? Why not? Report for the Department of Education, Employment and Workplace Relations (DEEWR). Canberra: DEEWR.

    Google Scholar 

  • Mills, M., & Goos, M. (2011). Productive pedagogies in the mathematics classroom: case studies of quality and equity. In B. Atweh, M. Graven, W. Secada, and P. Valero (Eds.), Mapping equity and quality in mathematics education (pp. 479–491). Dordrecht, the Netherlands: Springer.

  • National Research Council (NRC). (2002). Adding it up: helping children learn mathematics. Washington, DC: National Academy Press.

    Google Scholar 

  • Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405–435.

    Article  Google Scholar 

  • Queensland School Reform Longitudinal Study (QSRLS). (2001). School reform longitudinal study: classroom observation scoring manual. St. Lucia: The University of Queensland.

    Google Scholar 

  • Resnick, L., Spillane, J., Goldman, P., & Rangel, E. (2010). Implementing innovation: from visionary models to everyday practice. In D. Hanna et al. (Eds.), The nature of learning: using research to inspire practice (pp. 285–315). Paris: OECD.

    Chapter  Google Scholar 

  • Stephan, M. (2015). Sociomathematical norms in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp.563–566). Dordrecht, the Netherlands: Springer.

  • Wells, J. (2014). Developing argumentation in mathematics: the role of evidence and context. Doctoral Dissertation, School of Education, The University of Queensland. doi:10.14264/uql.2015.208.

  • Yackel, E. (1995). Children’s talk in inquiry mathematics classrooms. In P. Cobb & H. Bauersfeld (Eds.), Emergence of mathematical meaning: interaction in classroom cultures (pp. 131–162). Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.

    Article  Google Scholar 

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Acknowledgements

This project is funded by the Australian Research Council (DP170101993).

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Correspondence to Katie Makar.

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Makar, K., Fielding-Wells, J. Shifting more than the goal posts: developing classroom norms of inquiry-based learning in mathematics. Math Ed Res J 30, 53–63 (2018). https://doi.org/10.1007/s13394-017-0215-5

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  • DOI: https://doi.org/10.1007/s13394-017-0215-5

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