Changes in mathematics teachers’ self-reported beliefs and practices over the course of a blended continuing professional development programme

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Abstract

The interplay between mathematics teachers’ beliefs and practices has been widely investigated and research has examined how teachers’ beliefs about mathematics, teaching and learning change when participating in continuing professional development (CPD). In this paper, I track teachers’ self-reported beliefs and practice changes as they participate in a 1-year CPD programme intended to support them in learning to teach mathematics through inquiry (LTMI). LTMI is a blended programme that integrates two phases: summer workshops and monthly follow-up meetings held during the scholastic year. Using a case-study design, data focusing on self-reported beliefs and practices were collected, using questionnaires and interviews, from three teachers at different stages: before, during and at the end of the CPD. Results show that, following teachers’ participation in summer workshops, they reported stronger connectionist beliefs. However, by the end of the CPD, while their connectionist beliefs remained strong, teachers reported increased discovery beliefs. Discovery beliefs were consistent with their reported changes in teaching practices. It appears that, in changing from transmission to inquiry teaching, these teachers adopted a non-interventionist and non-interactionist discovery teaching approach. This finding has implications for the design of CPD and, hence, the need to offer a supportive structure that helps teachers to recognise and address the limitations of their practices, along their journey to change towards more inquiry teaching.

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Data availability

The full data set and coding is available online at https://figshare.com/articles/dataset/Teachers_Beliefs_and_practice_change/9891371.

Change history

References

  1. Alfieri, L., Brooks, P., Aldrich, N., & Tenenbaum, H. (2011). Does discovery-based instruction enhance learning? Journal of Educational Psychology, 103(1), 1–18. https://doi.org/10.1037/a0021017.

    Article  Google Scholar 

  2. Artigue, M., & Blomhøj, M. (2013). Conceptualising inquiry-based education in mathematics. ZDM Mathematics Education, 45(6), 797–810. https://doi.org/10.1007/s11858-013-0506-6.

    Article  Google Scholar 

  3. Askew, M., Brown, M., Rhodes, V., Johnson, D., & William, D. (1997). Effective Teachers of Numeracy: Final report to the teacher training agency. London: King's College.

  4. Aulls, M. W., & Shore, B. M. (2008). Inquiry in education: The conceptual foundations for research as a curricular imperative (Vol. 1). New York, NY: Routledge.

    Google Scholar 

  5. Barkatsas, A. T., & Malone, J. (2005). A typology of mathematics teachers’ beliefs about teaching and learning mathematics and instructional practices. Mathematics Education Research Journal, 17(2), 69–90. https://doi.org/10.1007/BF03217416.

    Article  Google Scholar 

  6. Beswick, K. (2005). The beliefs/practice connection in broadly defined contexts. Mathematics Education Research Journal, 17(2), 39–68. https://doi.org/10.1007/BF03217415.

    Article  Google Scholar 

  7. Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational Studies in Mathematics, 79, 127–147. https://doi.org/10.1007/s10649-011-9333-2.

    Article  Google Scholar 

  8. Boaler, J. (2009). The elephant in the classroom: Helping children learn and love maths. London: Souvenir Press.

    Google Scholar 

  9. Boyatzis, R. (1998). Transforming qualitative information: Thematic analysis and code development. Thousand Oaks, CA: Sage.

    Google Scholar 

  10. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa.

    Article  Google Scholar 

  11. British Educational Research Association [BERA] (2018). Ethical guidelines for educational research (4th ed.). London. Retrieved from: https://www.bera.ac.uk.

  12. Buhagiar, M. A., & Murphy, R. (2008). Teachers’ assessments of students learning of mathematics. Assessment in Education: Principles, Policy & Practice, 15(2), 169–182. https://doi.org/10.1080/09695940802164192.

    Article  Google Scholar 

  13. Calleja, J. (2016). Teaching mathematics through inquiry: A continuing professional development programme design. Educational Designer, 3(9). http://www.educationaldesigner.org/ed/.

  14. Calleja, J. (2018). Teacher participation in continuing professional development: Motivating factors and programme effectiveness. Malta Review of Educational Research, 12(1), 5-29. http://www.mreronline.org/issues/issue-1-june-2018/.

  15. Calleja, J. (2019). Learning to teach mathematics through inquiry: A case study of continuing professional development in Malta. PhD Thesis. Nottingham, UK: University of Nottingham. http://eprints.nottingham.ac.uk/55835.

  16. Cross, D. I. (2009). Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education, 12(5), 325–346. https://doi.org/10.1007/s10857-009-9120-5.

    Article  Google Scholar 

  17. Davis, B., Towers, J., Chapman, O., Drefs, M., & Friesen, S. (2020). Exploring the relationship between mathematics teachers’ implicit associations and their enacted practices. Journal of Mathematics Teacher Education, 23, 407–428. https://doi.org/10.1007/s10857-019-09430-7.

    Article  Google Scholar 

  18. Engeln, K., Mikelskis-Seifert, S., & Euler, M. (2014). Inquiry-based mathematics and science education across Europe: A synopsis of various approaches and their potentials. In C. Bruguière, A. Tiberghein, & P. Clément (Eds.), Topics and Trends in Current Science Education. Netherlands: Springer.

  19. Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: The state of the art (pp. 249–253). New York: Falmer.

    Google Scholar 

  20. Felbrich, A., Kaiser, G., & Schmotz, C. (2012). The cultural dimension of beliefs: An investigation of future primary teachers’ epistemological beliefs concerning the nature of mathematics in 15 countries. ZDM Mathematics Education, 44(3), 355–366. https://doi.org/10.1007/s11858-012-0418-x.

    Article  Google Scholar 

  21. Graham, D. J., & Midgley, N. G. (2000). Graphical representation of particle shape using triangular diagrams: An Excel spreadsheet method. Earth Surface Processes and landforms, 25(13), 1473–1477.

    Article  Google Scholar 

  22. Guskey, T. R. (2002). Professional development and teacher change. Teachers and Teaching: Theory and Practice, 8(3/4), 381–391. https://doi.org/10.1080/135406002100000512.

    Article  Google Scholar 

  23. Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.

    Google Scholar 

  24. Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42(2), 99–107. https://doi.org/10.1080/00461520701263368.

    Article  Google Scholar 

  25. Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1.

    Article  Google Scholar 

  26. Kvale, S. (1996). Interviews: An introduction to qualitative research interviewing. Thousand Oaks, CA: Sage.

    Google Scholar 

  27. Lampert, M., & Blunk, M. (1999). Talking mathematics in school: Studies of teaching and learning. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  28. Lazonder, A. W., & Harmsen, R. (2016). Meta-analysis of inquiry-based learning: Effects of guidance. Review of Educational Research, 86(3), 681–718. https://doi.org/10.3102/0034654315627366.

    Article  Google Scholar 

  29. Loucks-Horsley, S., Stiles, K., Mundry, S., Love, N., & Hewson, P. (2010). Designing professional development for teachers of science and mathematics (3rd ed.). Thousand Oaks, CA: Corwin.

    Google Scholar 

  30. Maaß, K., & Artigue, M. (2013). Implementation of inquiry-based learning in day-to-day teaching: A synthesis. ZDM Mathematics Education, 45(6), 779–795. https://doi.org/10.1007/s11858-013-0528-0.

    Article  Google Scholar 

  31. Maaß, K., Swan, M., & Aldorf, A. M. (2017). Mathematics teachers’ beliefs about inquiry-based learning after a professional development course: An international study. Journal of Education and Training Studies, 5(9), 1–17. https://doi.org/10.11114/jets.v5i9.2556.

    Article  Google Scholar 

  32. Mansour, N. (2009). Science teachers' beliefs and practices: Issues, implications and research agenda. International Journal of Environmental and Science Education, 4(1), 25–48. https://eric.ed.gov/?id=EJ884384

  33. Mason, J., & Johnston-Wilder, S. (2006). Designing and Using Mathematical Tasks (2nd ed.). St Albans: Tarquin Publications.

    Google Scholar 

  34. Nathan, M. J., & Knuth, E. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and Instruction, 21(2), 175–207. https://doi.org/10.1207/S1532690XCI2102_03.

    Article  Google Scholar 

  35. OECD. (2009). Creating effective teaching and learning environments: First results from TALIS. Paris: OECD.

    Google Scholar 

  36. OECD. (2019). TALIS 2018 Results (Volume I): Teachers and school leaders as lifelong learners. TALIS, OECD Publishing, Paris. https://doi.org/10.1787/1d0bc92a-en.

    Article  Google Scholar 

  37. Pajares, M. F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(2), 307–332. https://doi.org/10.3102/00346543062003307.

    Article  Google Scholar 

  38. Parveva, T., Noorani, S., Ranguelov, S., Motiejunaite, A. & Kerpanova, V. (2011). Mathematical Education in Europe: Common challenges and national policies. Brussels: EACEA. P9 Eurydice.

  39. Patton, M. Q. (2002). Qualitative research and evaluation (3rd ed.). Thousand Oaks, CA: Sage.

    Google Scholar 

  40. Piaget, J. (1970). Structuralism. New York: Harper & Row.

    Google Scholar 

  41. Piaget, J. (1985). The equilibration of cognitive structure: The central problem of intellectual development. Chicago, IL: University of Chicago Press.

    Google Scholar 

  42. Polly, D., Wang, C., McGee, J. R., Lambert, R. G., Martin, C. S., & Pugalee, D. (2014). Examining the influence of a curriculum-based elementary mathematics professional development program. Journal of Research in Childhood Education, 28(3), 327–343. https://doi.org/10.1080/02568543.2014.913276.

    Article  Google Scholar 

  43. 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. https://doi.org/10.3102/0013189X029001004.

    Article  Google Scholar 

  44. Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

    Google Scholar 

  45. Schoenfeld, A. H. (2013). Classroom observations in theory and practice. ZDM Mathematics Education, 45(4), 607–621. https://doi.org/10.1007/s11858-012-0483-1.

    Article  Google Scholar 

  46. Skemp, R. (1986). The psychology of learning mathematics. New York: Penguin.

    Google Scholar 

  47. Skott, J. (2015). The promises, problems, and prospects of research on teachers’ beliefs. In H. Fives & M. G. Gill (Eds.), International handbook on teachers’ beliefs (pp. 13–30). New York: Routledge.

    Google Scholar 

  48. Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  49. Swain, J., & Swan, M. (2007). Thinking through mathematics. London: NRDC.

    Google Scholar 

  50. Swan, M. (2006). Collaborative Learning in Mathematics: A challenge to our beliefs and practices. London, England: National Institute for Advanced and Continuing Education (NIACE) National Research and Development Centre for Adult Literacy and Numeracy (NRDC).

  51. Swan, M., & Swain, J. (2010). The impact of a professional development programme on the practices and beliefs of numeracy teachers. Journal of Further and Higher Education, 34(2), 165–177. https://doi.org/10.1080/03098771003695445.

    Article  Google Scholar 

  52. Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 127–146). New York: Macmillan.

    Google Scholar 

  53. Tuan, H. L., Yu, C. C., & Chin, C. C. (2017). Investigating the influence of a mixed face-to-face and website professional development course on the inquiry-based conceptions of high school science and mathematics teachers. International Journal of Science and Mathematics Education, 15(8), 1385–1401. https://doi.org/10.1007/s10763-016-9747-5.

    Article  Google Scholar 

  54. Voss, T., Kleickmann, T., Kunter, M., & Hachfeld, A. (2013). Mathematics teachers’ beliefs. In Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 249–271). Springer, Boston, MA.

  55. Vygotsky, L. (1978). Mind in society. Cambridge, MA: Harvard University Press.

    Google Scholar 

  56. Wenger, E. (1998). Communities of practice: Learning, meaning and identity. Cambridge, MA: Cambridge University Press.

    Google Scholar 

  57. Wilson, S., & Cooney, T. (2002). Mathematics teacher change and development. In G. Leder, E. Pehkonen, & G. Torner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 127–147). Dordrecht: Kluwer.

    Google Scholar 

  58. Yin, R. K. (2003). Case study research: Design and methods. Thousand Oaks, CA: SAGE Publications.

    Google Scholar 

  59. Yurekli, B., Stein, M. K., Correnti, R., & Kisa, Z. (2020). Teaching mathematics for conceptual understanding: Teachers’ beliefs and practices and the role of constraints. Journal for Research in Mathematics Education, 51(2), 234–247. https://doi.org/10.5951/jresematheduc-2020-0021.

    Article  Google Scholar 

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Acknowledgements

I would also like to thank the teachers taking part in this research. Due gratitude goes to the late Prof Malcolm Swan and Prof Jeremy Hodgen for their continuous support and insights, and to Dr. Colin Foster for his guidance during this research and valuable comments provided on earlier drafts of this paper.

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Appendices

Appendix 1. Belief statements

You are presented with three statements about mathematics, learning and teaching.

For each statement, give a percentage (%), so that the three percentages in each section add up to a 100.

figurea

Appendix 2. Sample pen portrait

Chris: Pen portrait prior to his participation in CPD

His self-reported practices and beliefs

My explanations are clearly delivered and include questions directed at individual students. I keep introductions short and do not waste much time on ideas that are ‘out’ of the syllabus. I only ask a few questions and then provide extended periods where students work on exercises from the textbook or a worksheet. The exercises I assign start with a few easy questions and then gradually move to harder examples. I set students working and deal with student difficulties individually while I go around the class. When students are working, I prefer to tell students where they have gone wrong and show them where and how to correct mistakes. I stop the class from time to time to clarify questions that I identify as particularly difficult because it is useful to discuss errors and alternative methods.

I have a formal, yet cheerful and positive relationship with students. I make sure to get to know my students and try to establish a relationship with them first. I feel that the students in my class need to be motivated and prompted all the time. I am not too hard on them. My students seem to like to be organised and prefer to be told what to do. Students have the idea that mathematics is about working lots of problems from the textbook and trying to get as many of them correct as possible.

I believe that students learn best when their own ideas are discussed and investigated, but there is little evidence of this in my classroom. Although I believe that it is more important for students to develop conceptual understanding rather than computational skills, I find it very difficult to do because of many constraints. I feel much pressure to ‘cover’ the syllabus and I want to make sure that students do well in their exams. I feel constrained and frustrated by the scheme of work. I also claim that overloaded syllabi, high-stakes examinations and pressure from parents are constraints that I find hard to overcome.

His typical sequence of classroom actions

  1. 1.

    Provide notes

  2. 2.

    Give an explanation

  3. 3.

    Pose oral questions to the students

  4. 4.

    Devote time for student questioning

  5. 5.

    Give an easy question

  6. 6.

    Demonstrate examples

  7. 7.

    Give a challenging question

  8. 8.

    Assign work to be done individually

Mean percentage weighting on his beliefs statements

Transmission—42%

Discovery—33%

Connectionist—25%

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Calleja, J. Changes in mathematics teachers’ self-reported beliefs and practices over the course of a blended continuing professional development programme. Math Ed Res J (2021). https://doi.org/10.1007/s13394-021-00366-x

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Keywords

  • Belief trajectories
  • Continuing professional development
  • Inquiry teaching
  • Mathematics teachers
  • Self-reported beliefs and practices