Abstract
This study documented the process of evolution of the continuous design and revision of the tools of a novice mathematics teacher educator–researcher (MTE-R) as he planned and implemented design-based professional development workshops for in-service mathematics teachers in Taiwan. In order to effectively facilitate teachers designing and implementing their own conjecturing activities during the workshops, the MTE-R fostered their professional learning and growth through reflection upon students’ performance. From the perspective of activity theory, this study examined the evolution of the MTE-R’s mentoring activities and tools whose design gradually changed from being based on the literature content toward being learner-centered activities with teachers as learners. Such evolution not only enhanced teachers’ learning outcomes, but also facilitated the MTE-R’s own professional growth in different areas, including mathematics, mathematics learning, mathematics teaching, teacher education, and, in particular, the extrapolation of generic examples for understanding mathematical concepts.
Similar content being viewed by others
References
Boyd, P., Baker, L., Harris, K., Kynch, C., & McVittie, E. (2006). Working with multiple identities: Supporting new teacher educators in higher education. In S. Bloxham, S. Twisleton, & A. Jackson (Eds.), Challenges and opportunities: Developing learning and teaching in ITE across the UK. Bristol: ESCalate, Higher Education Academy.
Cañadas, M., Deulofeu, J., Figueiras, L., Reid, D., & Yevdokimov, O. (2007). The conjecturing process: Perspectives in theory and implications in practice. Journal of Teaching and Learning, 5(1), 55–72.
Chapman, O. (2009). Educators reflecting on (researching) their own practice. In R. Even & D. L. Ball (Eds.), The professional education and development of teachers of mathematics (pp. 121–126). New York, NY: Springer.
Chen, J.-C., Lin, F.-L., Hsu, H.-Y., & Cheng, Y.-H. (2014). Integration of conjecturing and diagnostic teaching: Using proceduralized refutation model as intermediate framework. Paper presented at the Joint Meeting of PME 38 and PME-NA 36, Vancouver, Canada: PME.
Cheng, Y.-H. (2000). Student teachers’ learning process of pedagogical concept: The case of generic example for learning mathematics concept. Doctoral dissertation, National Taiwan Normal University, Taipei, Taiwan.
Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit.
Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen, & R.-L. Punamaki (Eds.), Perspectives on activity theory (pp. 19–38). Cambridge: Cambridge University Press.
Engeström, Y. (2001). Expansive learning at work: Toward an activity theoretical reconceptualization. Journal of Education and Work, 14(1), 133–156.
Fuller, F. F. (1969). Concerns of teachers: A developmental conceptualization. American Educational Research Journal, 6(2), 207–226. https://doi.org/10.3102/00028312006002207.
Jaworski, B. (2001). Developing mathematics teaching: Teachers, teacher educators, and researchers as co-learners. In F.-L. Lin & T. J. Cooney (Eds.), Making sense of mathematics teacher education (pp. 295–320). Dordrecht: Kluwer Academic Publishers.
Jaworski, B. (2008). Mathematics teacher educator learning and development. In B. Jaworski & T. Wood (Eds.), The international handbook of mathematics teacher education volume 4: The mathematics teacher educator as a developing professional (pp. 335–361). Rotterdam: SensePublishers.
Jaworski, B., & Potari, D. (2009). Bridging the macro–and micro–divide: Using an activity theory model to capture sociocultural complexity in mathematics teaching and its development. Educational studies in mathematics, 72(2), 219–236.
Kemmis, S., & McTaggart, R. (1988). The action research planner: Geelong. Victoria: Deakin University Press.
Leont’ev, A. N. (1979). The problem of activity in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37–71). New York: Sharpe.
Lin, F.-L. (2006, January). Designing mathematics conjecturing activities to foster thinking and constructing actively. Paper presented at the Keynote address in the APEC-TSUKUBA International Conference, Japan.
Lin, F.-L. (2010). Mathematical tasks designing for different learning settings. In M. Pinto & T. Kawasaki (Eds.), 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 83–99). Belo Horizonte, Brazil.
Lin, F.-L., Hsu, H.-Y., Yang, K.-L., Chen, J.-C., & Lee, K.-H. (2011). Adventuring through big problems as means of innovations in mathematics education. Paper presented at the APEC-Ubon Ratchathani International Symposium on Innovation on Problem Solving-Based Mathematics Textbooks and E-Textbooks, Ubon Ratchathani, Thailand.
Lin, F.-L., & Tsao, L.-C. (1999). Exam math re-examined. In C. Hoyles, C. Morgan, & G. Woodhouse (Eds.), Rethinking mathematics curriculum (pp. 228–239). London: Falmer Press.
Lin, F.-L., & Wu Yu, J.-Y. (2005). False proposition as a means for making conjectures in mathematics classrooms. Paper presented at the Invited speech in Asian Mathematical Conference, Singapore.
Lin, F.-L., Yang, K.-L., Lee, K.-H., Tabach, M., & Stylianides, G. (2012). Principles of task designing for conjecturing and proving: developing principles based on practical tasks. In M. D. Villiers & G. Hanna (Eds.), Proof and proving in mathematics education: The 19th ICMI study (pp. 305–325). New York: Springer.
Mason, J., Burton, L., & Stacey, K. (1982). Thinking mathematically. London: Addison-Wesley Pub. Co.
Mason, J., & Pimm, D. (1984). Generic example: Seeing the general in particular. Educational Studies in Mathematics, 15(3), 277–289.
Nipper, K., Ricks, T., Kilpatrick, J., Mayhew, L., Thomas, S., Kwon, N.-Y., et al. (2011). Teacher tensions: Expectations in a professional development institute. Journal of Mathematics Teacher Education, 14(5), 375–392.
Sakonidis, C., & Potari, D. (2014). Mathematics teacher educators’/researchers’ collaboration with teachers as a context for professional learning. ZDM-The International Journal on Mathematics Education, 46, 293–304.
Schön, D. (1983). The reflective practitioner. How professionals think in action. London: Basic Books.
Tall, D. (1986). Building and testing a cognitive approach to the calculus using interactive computer graphics. Doctoral dissertation, University of Warwick, Coventry, UK.
Tzur, R. (2001). Becoming a mathematics teacher-educator: Conceptualizing the terrain through self-reflective analysis. Journal of Mathematics Teacher Education, 4(4), 259–283.
Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press (Published originally in Russian in 1930).
Zaslavsky, O. (2008). Meeting the challenges of mathematics teacher education through design and use of tasks that facilitate teacher learning. In B. Jaworski & T. Wood (Eds.), The mathematics teacher educator as a developing professional (pp. 93–114). Rotterdam: Sense Publishers.
Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of Mathematics Teacher Education, 7, 5–32.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix 1: Diagnostic conjecturing activity case
Appendix 2: Conjecturing activity case designed by teachers: medians and altitude of triangles
Rights and permissions
About this article
Cite this article
Chen, JC., Lin, FL. & Yang, KL. A novice mathematics teacher educator–researcher’s evolution of tools designed for in-service mathematics teachers’ professional development. J Math Teacher Educ 21, 517–539 (2018). https://doi.org/10.1007/s10857-017-9396-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10857-017-9396-9