Exploring the Feasibility of Co-construction Among Mathematics Teachers and Teacher Educators: Analysis of Discourse in a Product-based Teacher Professional Development Program


  • Ting-Ying Wang National Taiwan Normal University
  • Kai-Lin Yang National Taiwan Normal University
  • Fou-Lai Lin National Taiwan Normal University


co-construction, discourse, mathematics learning task design, teacher professional development program, university-based teacher educator, mathematics teacher education research


Using a product-based teacher professional development workshop in the Just Do Math program as a case, this study investigated the discourse between teachers and teacher educators from three perspectives, namely focus, form, and flow, to see how the two cohorts communicated in the co-construction, whether the co-construction is feasible to produce innovative teaching materials, and what the feasible dialogical modes are for this co-construction. The participants included four experienced university-based mathematics teacher educator and 38 mathematics teachers. The discourse from the eight 3-hour sessions of the workshop was collected. The findings included that both teachers and teacher educators focused more on students' development of concepts than on learning motivation, even if learning motivation was one main problem to be solved. Feasible dialogical modes for co-construction in teacher professional development workshops in the context of East Asian educational cultures were revealed, which could be described as teacher educator-centred but teacher-focused.


Arbaugh, F., & Brown, C. A. (2005). Analyzing mathematical tasks: A catalyst for change? Journal of Mathematics Teacher Education, 8(6), 499–536.

Ausubel, D. P. (1961). In defense of verbal learning. Educational Theory, 11(1), 15–25.

Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). Jossey-Bass.

Bardy, T., Holzaepfel, L., & Leuders, T. (2021). Adaptive tasks as a differentiation strategy in the mathematics classroom: Features from research and teachers’ views. Mathematics Teacher Education and Development, 23(3), 26–53.

Beck, C., & Kosnik, C. (2006). Innovations in teacher education: A social constructivist approach. State University of New York Press.

Boston, M. D., & Smith, M. S. (2011). A ‘‘task-centric approach’’ to professional development: Enhancing and sustaining mathematics teachers’ ability to implement cognitively challenging mathematical tasks. ZDM-Mathematics Education, 43(6-7), 965–977. https://doi.org/10.1007/s11858-011-0353-2

Bragg, L. A., & Lang, J. (2018). Collaborative teacher educator reflection as an approach to redesigning a mathematics education assessment task. Mathematics Teacher Education and Development, 20(3), 80–101.

Bruner, J. (1966). Toward a theory of instruction. Belknap Press.

Bryan, C. A., Wang, T., Perry, B., Wong, N.-Y., & Cai, J. (2007). Comparison and contrast: Similarities and differences of teachers’ views of effective mathematics teaching and learning from four regions. ZDM-Mathematics Education, 39(4), 329–340. https://doi.org/10.1007/s11858-007-0035-2

Chan, K.-L., & Chan, C. L. W. (2005). Chinese culture, social work education and research. International Social Work, 48(4), 381–389. https://doi.org/10.1177/0020872805053461

Chen, J.-C., Lin, F.-L., & Yang, K.-L. (2018). A novice mathematics teacher educator–researcher’s evolution of tools designed for in-service mathematics teachers’ professional development. Journal of Mathematics Teacher Education, 21, 517-539. https://doi.org/10.1007/s10857-017-9396-9

Coburn, C. E., Penuel, W. R., & Geil, K. E. (2013). Research-practice partnerships: A strategy for leveraging research for educational improvement in school districts. William T. Grant Foundation.

Darling-Hammond, L., Hyler, M. E., Gardner, M., & Espinoza, D. (2017). Effective teacher professional development. Learning Policy Institute.

Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Orienta-Konsultit.

Fleming, A., Roble, A., Yao, X., & Brosnan, P. (2015, Nov). Building pedagogical capacity through task design and implementation. Paper presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, MI.

Hargreaves, A. (1991). Contrived collegiality: The micropolitics of teacher collaboration. In J. Blasé (Ed.), The politics of life in schools (pp. 46–72). SAGE Publications.

Hargreaves, A. (1994). Changing teachers, changing times: Teachers’ work and culture in the postmodern age. Cassell.

Horn, I. S. (2010). Teaching replays, teaching rehearsals, and re-visions of practice: Learning from colleagues in a mathematics teacher community. Teachers College Record, 112(1), 225–259. https://doi.org/10.1177/016146811011200109

Hsieh, F.-J. (2006). The foundations of theories. In Department of Mathematics and Information Education, National Taipei University of Education (Ed.), The collection of the results in the classroom observation workshops of teacher professional development for advisory groups of lower secondary mathematics teachers (pp. 5). Department of Mathematics and Information Education, National Taipei University of Education.

Hsieh, F.-J., Lu, S.-S., Hsieh, C.-J., Tang, S.-Z. & Wang, T.-Y. (2018). The conception of mathematics teachers’ literacy for teaching from a historical perspective. In Y. Li & R. Huang (Eds.), How Chinese Acquire and Improve Mathematics Knowledge for Teaching (pp.37-56). Brill: Sense.

Huizinga, T., Handelzalts, A., Nieveen, N., & Voogt, J. (2015). Fostering teachers' design expertise in teacher design teams: conducive design and support activities. Curriculum Journal, 26(1), 137–163. https://doi.org/10.1080/09585176.2014.990395

Jones, K., & Pepin, B. (2016). Research on mathematics teachers as partners in task design. Journal of Mathematics Teacher Education, 19(2–3), 105–121. https://doi.org/10.1007/s10857-016-9345-z

Kaur, B. (2009). Characteristics of good mathematics teaching in Singapore Grade 8 classrooms: A juxtaposition of teachers’ practice and students’ perception. ZDM-Mathematics Education, 41(3), 333–347. https://doi.org/10.1007/s11858-009-0170-z

Kontkanen, J., Kärkkäinen, S., Dillon, P., Hartikainen-Ahia, A., & Åhlberg, M. (2016). Collaborative processes in species identification using an internet-based taxonomic resource. International Journal of Science Education, 38(1), 96–115. https://doi.org/10.1080/09500693.2015.1129469

Kumar, R. S., & Subramaniam, K. (2015). From “following” to going beyond the textbook: Inservice Indian mathematics teachers’ professional development for teaching integers. Australian Journal of Teacher Education, 40(12), 86–103. https://doi.org/10.14221/ajte.2015v40n12.7

Lee, H.-J., & Özgün-Koca, S. A. (2016). Professional development for mathematics teachers: Using task design and analysis. Current Issues in Education,19(2), 1–17.

Leung, F. K. S. (2001). In search of an East Asian identity in mathematics education. Educational Studies in Mathematics, 47(1), 35–51. https://doi.org/10.1023/A:1017936429620

Leung, F. K. S. (2006). Mathematics education in East Asia and the West: Does culture matter? In F. K. S. Leung, K.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural tradition: A comparative study of East Asia and the West (pp. 21–50). Springer.

Leung, F. K. S., Graf, K.-D., & Lopez-Real, F. J. (Eds.) (2006). Mathematics education in different cultural traditions: A comparative study of East Asia and the West. Springer.

Lin, F.-L., Wang, T.-Y., & Yang, K.-L. (2018). Description and evaluation of a large-scale project to facilitate student engagement in learning mathematics. Studies in Educational Evaluation, 58, 178-186. https://doi.org/10.1016/j.stueduc.2018.03.001

Lin, P.-J., & Li, Y. (2009). Searching for good mathematics instruction at primary school level valued in Taiwan. ZDM-Mathematics Education, 41(3), 363–378. https://doi.org/10.1007/s11858-009-0175-7

Little, J. W. (1990). The persistence of privacy: Autonomy and initiative in teachers’ professional relations. Teachers College Record, 91(4), 509–536. https://doi.org/10.1177/016146819009100403

Little, J. W. (2003). Inside teacher community: Representations of classroom practice. Teachers College Record, 105(6), 913-945. https://doi.org/10.1111/1467-9620.00273

Locke, E. A., Latham, G. P., & Erez, M. (1988). The determinants of goal commitment. Academy of Management Review, 13(1), 23–39. https://doi.org/10.2307/258352

Lotman, Y. M. (1988). Text within a text. Soviet Psychology, 24 (3), 32-51. https://doi.org/10.2753/RPO1061-0405260332

Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 International results in mathematics. TIMSS & PIRLS International Study Center, Boston College.

Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 International results in mathematics. TIMSS & PIRLS International Study Center, Boston College.

Ngcoza, K., & Southwood, S. (2015). Professional development networks: from transmission to co-construction. Perspectives in Education, 33(1), 1–12.

Organisation for Economic Co-operation and Development. (2013). PISA 2012 Results in focus: What 15-year-olds know and what they can do with what they know. https://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf

Organisation for Economic Co-operation and Development. (2016). PISA 2015 results (Volume I): Excellence and equity in education. http://dx.doi.org/10.1787/9789264266490-en

Orland‐Barak, L. (2006) Convergent, divergent and parallel dialogues: knowledge construction in professional conversations. Teachers and Teaching: Theory and Practice, 12(1), 13–31. https://doi.org/10.1080/13450600500364547

Pang, J. (2009). Good mathematics instruction in South Korea. ZDM-Mathematics Education, 41(3), 349–362. https://doi.org/10.1007/s11858-009-0169-5

Patrick, S. K. (2022). Collaborating for improvement? Goal specificity and commitment in targeted teacher partnerships. Teacher College Record, 124(1), 164–190. https://doi.org/10.1177/01614681221086104

Penuel, W. R., Fishman, B. J., Cheng, B. H., & Sabelli, N. (2011). Organizing research and development at the intersection of learning, implementation, and design. Educational Researcher, 40(7), 331–337. https://doi.org/10.3102/0013189X11421826

Pepin, B., Gueudet, G., & Trouche, L. (2017). Refining teacher design capacity: Mathematics teachers’ interactions with digital curriculum resources. ZDM-Mathematics Education, 49(5), 799–812. https://doi.org/10.1007/s11858-017-0870-8

Peressini, D. D., & Knuth, E. J. (1998). Why are you talking when you could be listening? The role of discourse and reflection in the professional development of a secondary mathematics teacher. Teaching and Teacher Education, 14(1), 107–125. http://dx.doi.org/10.1016/S0742-051X(97)00064-4

Piaget, J. (1952). The origins of intelligence in children. International University Press.

Remillard, J. T. (2000). Can curriculum materials support teachers’ learning? Two fourth-grade teachers’ use of a new mathematics text. The Elementary School Journal, 100(4), 331–350. https://doi.org/10.1086/499645

Rigby, J. G., Andrews-Larson, C., & Chen, I.-C. (2020). Learning opportunities about teaching mathematics: A longitudinal case study of school leaders’ influence. Teachers College Record, 122(7), 1–44. http://dx.doi.org/10.1177/016146812012200710

Schön, D. A. (1987). Educating the reflective practitioner. Jossey-Bass.

Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester, Jr., (Ed.), Second handbook of research on mathematics teaching and learning (pp. 199–204). National Council of Teachers of Mathematics.

Supovitz, J. A. (2002). Developing communities of instructional practice. Teachers College Record, 104(8), 1591–1626. https://doi.org/10.1111/1467-9620.00214

Thompson, D. R., & Rubenstein, R. N. (2000). Learning mathematics vocabulary: Potential pitfalls and instructional strategies. Mathematics Teacher, 93(7), 568–574.

Wang, T.-Y., & Hsieh, F.-J. (2016). What teachers should do to promote affective engagement with mathematics—from the perspective of elementary students. Proceeding of the 40th Annual Conference of the International Group for the Psychology of Mathematics Education, Hungary (Vol. 3, pp. 371-378).

Wang, T.-Y., & Hsieh, F.-J. (2017). Taiwanese high school students’ perspectives on effective mathematics teaching behaviors. Studies in Educational Evaluation, 55, 35-45. https://doi.org/10.1016/j.stueduc.2017.06.001

Wang, T.-Y., Lin, F.-L., & Yang, K.-L. (2021). Success factors for a national problem‑driven program aimed at enhancing affective performance in mathematics learning. ZDM - International Journal on Mathematics Education,53, 1121-1136. https://doi.org/10.1007/s11858-021-01285-8

Watson, A., & Sullivan, P. (2008). Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (Eds.), Tools and processes in mathematics teacher education (pp. 109–134). Sense Publishers.

Wilson, P. H., Sztajn, P., Edgington, C., Webb, J., & Myers, M. (2017). Changes in teachers’ discourse about students in a professional development on learning trajectories. American Educational Research Journal, 54(3), 568–604. https://doi.org/10.3102/0002831217693801

Yang, K-L., Lin, F-L., & Tso, T-Y. (2022). An approach to enactivist perspective on learning: mathematics-grounding activities. Asia-Pacific Education Researcher, 31(6), 657-666. https://doi.org/10.1007/s40299-021-00616-3

Zaslavsky, O. (2005). Seizing the opportunity to create uncertainty in learning mathematics. Educational Studies in Mathematics, 60(3), 297–321. https://doi.org/10.1007/s10649-005-0606-5

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). Sense Publishers.

Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of Mathematics Teacher Education, 7(1), 5–32. https://doi.org/10.1023/B:JMTE.0000009971.13834.e1