Advertisement

Journal of Mathematics Teacher Education

, Volume 22, Issue 1, pp 95–124 | Cite as

The challenge of changing teaching: investigating the interplay of external and internal influences during professional learning with secondary mathematics teachers

  • Karina J. WilkieEmail author
Article

Abstract

Mathematics teaching at secondary levels has proven surprisingly resistant to change over the past century. This study draws on two theoretical models to investigate how the process of changing secondary teaching in algebra through school-based professional learning might occur, and its relationship to different external and internal influences on teachers and researchers. A cyclic change model is used to discuss three different change pathways that were found amongst six practising secondary teachers participating in an algebra teaching experiment, one phase of a larger design-based research project. Meta-didactical transposition is used to examine the dynamics between teachers and researchers and the institutional dimension of professional learning. Affordances and constraints related to the teachers’ internal domains and social contexts in responding to professional learning opportunities are discussed. The bidirectional nature of brokering processes between teachers and researchers during professional learning is examined.

Keywords

Teacher professional learning Classroom experimentation Meta-didactical transposition Teacher beliefs Algebra Secondary mathematics 

References

  1. Arzarello, F., Robutti, O., Sabena, C., Cusi, A., Garuti, R., Malara, N., et al. (2014). Meta-didactical transposition: A theoretical model for teacher education programmes. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era (pp. 347–372). Dordrecht: Springer.Google Scholar
  2. Bakker, A., & van Eerde, D. (2015). An introduction to design-based research with an example from statistics education. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 429–466). Dordrecht: Springer.Google Scholar
  3. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.Google Scholar
  4. Baumgartner, E., Bell, P., Hoadley, C., Hsi, S., Joseph, D., Orrill, C., et al. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8.Google Scholar
  5. Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H., et al. (2014). The relationship between teachers’ mathematical content and pedagogical knowledge, teachers’ perceptions, and student achievement. Journal for Research in Mathematics Education, 45(4), 419–459.Google Scholar
  6. Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook on research on mathematics teaching and learning (pp. 669–706). Charlotte, NC: Information Age Publishing.Google Scholar
  7. Chapman, O. (2014). Overall commentary: Understanding and changing mathematics teachers. In J. Lo, K. R. Leatham & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 295–310). Basel: Springer International Publishing.Google Scholar
  8. Chevallard, Y. (1985). La transposition didactique. Grenoble: La Pensée Sauvage.Google Scholar
  9. Chick, H. (2009). Teaching the distributive law: Is fruit salad still on the menu? In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides: Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia (Vol. 1, pp. 1–8). Palmerston North: MERGA.Google Scholar
  10. Clarke, D., & Hollingsworth, H. (1994). Reconceptualising teacher change. In G. Bell, B. Wright, N. Leeson, & J. Geake (Eds.), Challenges in mathematics education: Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia (pp. 153–164). Lismore, NSW: Southern Cross University.Google Scholar
  11. Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947–967.Google Scholar
  12. Cobb, P., Wood, T., & Yackel, E. (1990). Chapter 9: Classrooms as learning environments for teachers and researchers. Journal for Research in Mathematics Education. Monograph, 4, 125–210. (Constructivist Views on the Teaching and Learning of Mathematics).Google Scholar
  13. Dweck, C. S. (2010). Mind-sets and equitable education. Principal Leadership, 10(5), 26–29.Google Scholar
  14. Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147–164). New York: Macmillan.Google Scholar
  15. Gravemeijer, K., & van Eerde, D. (2009). Design research as a means for building a knowledge base for teachers and teaching in mathematics education. The Elementary School Journal, 109(5), 510–524.Google Scholar
  16. Gregoire, M. (2003). Is it a challenge or a threat? A dual-process model of teachers’ cognition and appraisal processes during conceptual change. Educational Psychology Review, 15(2), 147–179.Google Scholar
  17. Guskey, T. R. (1986). Staff development and the process of teacher change. Educational Researcher, 15(5), 5–12.Google Scholar
  18. Guskey, T. R. (2002). Professional development and teacher change. Teachers and Teaching, 8(3), 381–391.Google Scholar
  19. Hiebert, J. (2013). The constantly underestimated challenge of improving mathematics instruction. In K. R. Leatham (Ed.), Vital directions for mathematics education research (pp. 45–56). New York: Springer.Google Scholar
  20. Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 371–404). Charlotte, NC: National Council of Teachers of Mathematics, Information Age Publishing.Google Scholar
  21. Hill, H., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualising and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.Google Scholar
  22. Hodgen, J., Küchemann, D., & Brown, M. (2010). Textbooks for the teaching of algebra in lower secondary school: Are they informed by research? PEDAGOGIES, 5(3), 187–201.Google Scholar
  23. Huberman, M. (1992). Teacher development and instructional mastery. In A. Hargreaves & M. G. Fullan (Eds.), Understanding teacher development (pp. 122–142). New York, NY: Teachers College Press.Google Scholar
  24. Huberman, M. (1995). Professional careers and professional development. In T. R. Guskey & M. Huberman (Eds.), Professional development in education: New paradigms and practices (pp. 193–224). New York: Teachers College Press.Google Scholar
  25. Johnson, N. (1996). Reconceptualising schools as learning communities. Reflect, 2(1), 6–13.Google Scholar
  26. Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. L. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). New York: Taylor & Francis Group.Google Scholar
  27. Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7(3), 203–235.Google Scholar
  28. Keazer, L. M. (2014). Teachers’ learning journeys toward reasoning and sense making. In J. Lo, K. R. Leatham & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 155–180). Basel: Springer International Publishing.Google Scholar
  29. Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 707–762). Charlotte, NC: National Council of Teachers of Mathematics, Information Age Publishing.Google Scholar
  30. Lave, J. (1996). Teaching, as learning, in practice. Mind, Culture, and Activity, 3(3), 149–164.Google Scholar
  31. Markworth, K. A. (2010). Growing and growing: Promoting functional thinking with geometric growing patterns. (Unpublished doctoral dissertation), University of North Carolina at Chapel Hill. Available from ERIC (ED519354).Google Scholar
  32. Nathan, M. J., & Koedinger, K. R. (2000). Teachers’ and researchers’ beliefs about the development of algebraic reasoning. Journal for Research in Mathematics Education, 31(2), 168–190.Google Scholar
  33. Petrou, M., & Goulding, M. (2011). Conceptualising teachers’ mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 9–25). London: Springer.Google Scholar
  34. Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4–15.Google Scholar
  35. Rakes, C. R., Valentine, J. C., McGatha, M. B., & Ronau, R. N. (2010). Methods of instructional improvement in algebra: A systematic review and meta-analysis. Review of Educational Research, 80(3), 372–400. doi: 10.3102/0034654310374880.Google Scholar
  36. Robutti, O., Cusi, A., Clark-Wilson, A., Jaworski, B., Chapman, O., Esteley, C., et al. (2016). ICME international survey on teachers working and learning through collaboration: June 2016. ZDM Mathematics Education, 48(5), 651–690.Google Scholar
  37. Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4–13.Google Scholar
  38. Sfard, A. (2005). What could be more practical than good research? On mutual relations between research and practice of mathematics education. Educational Studies in Mathematics, 58(3), 393–413.Google Scholar
  39. Shaw, K. L., & Jakubowski, E. H. (1991). Teachers changing for changing times. Focus on Learning Problems in Mathematics, 13(4), 13–20.Google Scholar
  40. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.Google Scholar
  41. Simon, M. A., & Tzur, R. (1999). Explicating the teacher’s perspective from the researchers’ perspectives: Generating accounts of mathematics teachers’ practice. Journal for Research in Mathematics Education, 30(3), 252–264.Google Scholar
  42. Steele, M. D., Hillen, A. F., & Smith, M. S. (2013). Developing mathematical knowledge for teaching in a methods course: The case of function. Journal of Mathematics Teacher Education, 16(6), 451–482.Google Scholar
  43. Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.Google Scholar
  44. Sutherland, R. (2002). A comparative study of algebra curricula. London: Qualifications and Curriculum Authority (QCA).Google Scholar
  45. 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
  46. Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17(5), 397–428.Google Scholar
  47. Wilkie, K. J. (2016a). Learning to teach upper primary school algebra: Changes to teachers’ mathematical knowledge for teaching functional thinking. Mathematics Education Research Journal, 28(2), 245–275.Google Scholar
  48. Wilkie, K. J. (2016b). Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school. Educational Studies in Mathematics, 93(3), 333–361.Google Scholar
  49. Wilson, P. H., Edgington, C., Sztajn, P., & DeCuir-Gunby, J. (2014). Teachers, attributions, and students’ mathematical work. In J. Lo, K. R. Leatham & L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 115–132). Basel: Springer International Publishing.Google Scholar
  50. Yates, L. (2003). Interpretive claims and methodological warrant in small-number qualitative, longitudinal research. International Journal of Social Research Methodology, 6(3), 223–232.Google Scholar
  51. Zhang, Q., & Stephens, M. (2013). Utilising a construct of teacher capacity to examine national curriculum reform in mathematics. Mathematics Education Research Journal, 25(4), 481–502.Google Scholar
  52. Zwiep, S., & Benken, B. M. (2013). Exploring teachers’ knowledge and perceptions across mathematics and science through content-rich learning experiences in a professional development setting. International Journal of Science and Mathematics Education, 11(2), 299–324.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Faculty of EducationMonash UniversityFrankston, MelbourneAustralia

Personalised recommendations