Characterising the shape of mathematics teaching decisions made over time: an application of tri-polar analysis

References

• Aguirre, J., & Speer, N. (2000). Examining the relationship between beliefs and goals in teacher practice. Journal of Mathematical Behaviour, 18(3), 327–356.
   Google Scholar
• Andrews, N. (2017). Differences in the forms of content teachers are seen to offer over time: Identifying opportunities for teacher growth. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the tenth congress of the European society for research in mathematics education (pp. 3232–3239). Dublin, Ireland: DCU Institute of Education & ERME.
   Google Scholar
• Andrews, P., & Sayers, J. (2005). How do teachers of mathematics teach? A four-way international comparison. Research in Mathematics Education, 7(1), 139–158.
   Google Scholar
• Brown, L., & Coles, A. (2000). Complex decision making in the classroom: The teacher as an intuitive practitioner. In T. Atkinson, & G. Claxton (Eds.), The intuitive practitioner: On the value of not always knowing what one is doing (pp. 165–181). Buckingham, UK: Open University Press.
   Google Scholar
• Brown, L., & Dobson, A. (1996). Using dissonance – finding the grit in the oyster. In G. Claxton, T. Atkinson, M. Osborn, & M. Wallace (Eds.), Liberating the learner: Lessons for professional development in education (pp. 212–227). London, UK: Routledge.
   Google Scholar
• Chevallard, Y. (1982). Pourquoi la transposition didactique? [Why didactical transposition?] Retrieved from http://yves.chevallard.free.fr/spip/spip/article.php3?id_article=103
   Google Scholar
• Clark, C., & Peterson, P. (1986). Teachers’ thought processes. In M. C. Wittrock (Ed.), Handbook of research on teaching (third edition) (pp. 255–296). New York, NY: Macmillan.
   Google Scholar
• Clarke, D., Emanuelsson, J., Jablonka, E., & Mok, I. (eds.). (2006). Making connections: Comparing mathematics classrooms around the world. Rotterdam, Netherlands: Sense Publishers.
   Google Scholar
• Drake, P., Wake, G., & Noyes, A. (2012). Assessing ‘functionality’ in school mathematics examinations: What does being human have to do with it? Research in Mathematics Education, 14(3), 237–252.
   Google Scholar
• Foster, C. (2013). Mathematical etudes: Embedding opportunities for developing procedural fluency within rich mathematical contexts. International Journal of Mathematics Education in Science and Technology, 44(5), 765–774.
   Google Scholar
• Hoogland, K., Pepin, B., de Koning, J., Bakker, A., & Gravemeijer, K. (2018). Word problems versus image-rich problems: An analysis of effects of task characteristics on students’ performance on contextual mathematics problems. Research in Mathematics Education, 20(1), 37–52.
   Web of Science ®Google Scholar
• Jackson, P. (1968). Life in classrooms. Reissued as Jackson, P. (1990) Life in classrooms. New York, NY: Teachers College Press.
   Google Scholar
• Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. London, UK: The Falmer Press.
   Google Scholar
• Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
   Google Scholar
• Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Mason, J. (1996). Personal enquiry: Moving from concern towards research. Milton Keynes, UK: The Open University.
   Google Scholar
• Mason, J. (2002). Researching your own practice: The discipline of noticing. Abingdon, UK: Routledge.
   Google Scholar
• Mason, J., & Davis, B. (2013). The importance of teachers’ mathematical awareness for in-the-moment pedagogy. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 182–197.
   Google Scholar
• Mason, J., & Johnston-Wilder, S. (2004). Fundamental constructs in mathematics education. Abingdon, UK: RoutledgeFalmer.
   Google Scholar
• McNair, K. (1978). Capturing in-flight decisions: Thoughts while teaching. Educational Research Quarterly, 3(4), 26–42.
   Web of Science ®Google Scholar
• Pirie, S., & Kieren, T. (1989). A recursive theory of mathematical understanding. For the Learning of Mathematics, 9(3), 7–11.
   Google Scholar
• Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26(2), 165–190.
   Google Scholar
• Sandelowski, M., Voils, C. I., & Knafl, G. (2009). On quantitising. Journal of Mixed Methods Research, 3(3), 208–222.
   PubMed Web of Science ®Google Scholar
• Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1–94.
   Google Scholar
• Schoenfeld, A. H. (2011). How we think: A theory of goal-oriented decision making and its educational applications. Abingdon, UK: Routledge.
   Google Scholar
• Schön, D. A. (1983). The reflective practitioner: How professionals think in action. Reprinted as D. A. Schön (2011) The reflective practitioner: How professionals think in action. Farnham, UK: Ashgate.
   Google Scholar
• Seltzer-Kelly, D., Westwood, J., & Pena-Guzman, M. (2012). A methodological self-study of quantitizing: Negotiating meaning and revealing multiplicity. Journal of Mixed Methods Research, 6(4), 258–274.
   Web of Science ®Google Scholar
• Speer, N. M. (2005). Issues of methods and theory in the study of mathematics teachers’ professed and attributed beliefs. Educational Studies in Mathematics, 58(3), 361–391.
   Google Scholar
• Stigler, J., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York: Free Press.
   Google Scholar
• Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Teacher Education, 10(4-6), 217–237.
   Google Scholar
• Teddlie, C., & Tashakkori, A. (2003). Major issues and controversies in the use of mixed methods in the social and behavioral sciences. In A. Tashakkori, & C. Teddlie (Eds.), Handbook of mixed methods in social and behavioral research (pp. 3–50). Thousand Oaks, CA: Sage.
   Google Scholar
• Vappula, H., & Clausen-May, T. (2006). Context in maths test questions: Does it make a difference? Research in Mathematics Education, 8(1), 99–115.
   Google Scholar
• Watson, A. (2007). The nature of participation afforded by tasks, questions and prompts in mathematics classrooms. Research in Mathematics Education, 9(1), 111–126.
   Google Scholar
• Watson, A. (2008). How secondary teachers structure the subject matter of mathematics. Proceedings of the British Society for Research Into Learning Mathematics, 28(3), 126–131.
   Google Scholar
• Wilson, M., & Cooney, T. (2002). Mathematics teacher change and developments: The role of beliefs. In G. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127–148). Dordrecht, Netherlands: Kluwer Academic Publishers.
   Google Scholar