Using the Co-creation of Approximations of Practice to Build Teachers' Capacity to Facilitate Mathematical Discussions
Keywords:
Mathematics teacher education research, Practice-based teacher education, Approximations of practice, Co-creation curriculum, Mathematical discussionsAbstract
Mathematics teacher educators frequently provide in-service teachers (ISTs) opportunities to practice teaching within the university classroom. While these opportunities are valuable, some question whether they focus too narrowly on learning a particular procedure for teaching instead of learning why and when to use that procedure. To address this concern, we engaged ISTs enrolled in a graduate degree program in the co-creation of practice-based lessons. This study examines what and how ISTs learned during the co-creation process. The results indicate that ISTs improved their understanding of facilitating classroom discussions in three crucial areas: asking conceptual questions, building connections, and using talk moves. Qualitative interview data revealed that ISTs learned through IST collaborations, instructor-IST interactions, and creation versus participation. Lastly, we discuss the teacher's intricate role in the co-creation process.
References
Ball, D. L., & Forzani, F. M. (2009). The work of teaching and the challenge for teacher education. Journal of Teacher Education, 6(5), 497–511. https://doi.org/10.1177/0022487109348479
Bergmark, U., & Westman, S. (2016). Co-creating curriculum in higher education: Promoting democratic values and a multidimensional view on learning. International Journal for Academic Development, 21(1), 28–40. https://doi.org/10.1080/1360144X.2015.1120734
Boerst, T., Sleep, L., Ball, D., & Hyman, B. (2011). Preparing teachers to lead mathematics discussions. Teachers College Record, 113, 2844–2877.
Bovill, C. (2020). Co-creation in learning and teaching: The case for a whole-class approach in higher education. Higher Education, 79, 1023–1037. https://doi.org/10.1007/s10734-019-00453-w
Bovill, C., Cook-Sather, A., Felten, P., Millard, L., & Moore-Cherry, N. (2016). Addressing potential challenges in co-creating learning and teaching: overcoming resistance, navigating institutional norms and ensuring inclusivity in student-staff partnerships. Higher Education, 71, 195–208. https://doi.org/10.1007/s10734-015-9896-4
Bovill, C., Felten, P., & Cook-Sather, A. (2014). Engaging students as partners in learning and teaching (2): Practical guidance for academic staff and academic developers. In Educational Development in a Changing World. Proceedings of the Annual Conference of International Consortium on Educational Development, Stockholm, Sweden.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
Breen, M. P., & Littlejohn, A. (2000). The practicalities of negotiation. In M. P. Breen and A. Littlejohn (Eds.), Classroom decision-making: Negotiation and process syllabuses in practice (pp. 272–295). Cambridge University Press.
Carley, K. (1990). Content analysis. In R. E. Asher (Ed.), The Encyclopedia of Language and Linguistics. Pergamon Press.
Chapin, S. H., O'Connor, C., & Anderson, N. C. (2013). Talk moves: A teacher's guide for using classroom discussions in Math, Grades K-6. Math Solutions.
Church, S. P., Dunn, M., & Prokopy, L. S. (2019). Benefits to qualitative data quality with multiple coders: Two case studies in multi-coder data analysis. Journal of Rural Social Sciences, 34(1), 1–14.
Cook-Sather, A. (2014). Student-faculty partnership in explorations of pedagogical practice: A threshold concept in academic development. International Journal for Academic Development, 19(3), 186–198. https://doi.org/10.1080/1360144X.2013.805694
Cook-Sather, A., Bovill, C., & Felten, P. (2014). Engaging students as partners in learning and teaching: A guide for faculty. Jossey-Bass.
DiCicco‐Bloom, B., & Crabtree, B. F. (2006). The qualitative research interview. Medical Education, 40(4), 314–321. https://doi.org/10.1111/j.1365-2929.2006.02418.x
Franke, M. L., Webb, N. M., Webb, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students' mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(40), 380–392. https://doi.org/10.1177/0022487109339906
Ghousseini, H. (2009). Designing opportunities to learn to lead classroom mathematics discussions in pre-service teacher education: Focusing on enactment. In D. S. Mewborn & H. S. Lee (Eds.), Scholarly practices and inquiry in the preparation of mathematics teachers (pp. 203–218). The AMTE Monograph Series.
Ghousseini, H., & Herbst, P. (2016). Pedagogies of practice and opportunities to learn about classroom mathematics discussions. Journal of Mathematics Teacher Education, 19(1), 79–103. https://doi.org/10.1007/s10857-014-9296-1
Gil, I., Zamudio, L., & King, B. (2019). After presenting multiple strategies, what's next? Examining the mathematical connections made by pre-service teachers. Journal of Mathematics Education at Teachers College, 10(2), 9–20.
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shanan, E., & Williamson, P. W. (2009a). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.
Grossman, P., Hammerness, K., & McDonald, M. (2009b). Redefining teaching, re-imagining teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273–289. https://doi.org/10.1080/13540600902875340
Grossman, P., & McDonald, M. (2008). Back to the future: Directions for research in teaching and teacher education. American Educational Research Journal, 45(1), 184–205. https://doi.org/10.3102/0002831207312906
Heron, J. (1999). The complete facilitator's handbook. Kogan Page.
Janssen, F. J. J. M., Grossman, P., & Westbroek, H. B. (2015). Facilitating decomposition and recomposition in practice-based teacher education: The power of modularity. Teaching and Teacher Education, 51, 137–146. https://doi.org/10.1016/j.tate.2015.06.009
Kavanagh, S. S., Metz, M., Hauser, M., Fogo, Brad., Taylor, M. W., & Carlson, J. (2020). Practicing responsiveness: Using approximations of teaching to develop teachers' responsiveness to students' ideas. Journal of Teacher Education, 7(10), 94–107. https://doi.org/10.1177/0022487119841884
Kazemi, E., Franke, M., & Lampert, M. (2009). Developing pedagogies in teacher education to support novice teachers' ability to enact ambitious instruction. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing Divides. Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia, Palmerston North, NZ (Vol. 1, pp. 12–30).
Kazemi, E., Lampert, M., & Ghousseini, H. (2007). Conceptualizing and using routines of practice in mathematics teaching to advance professional education: Report to the Spencer Foundation. Spencer Foundation.
Kennedy, M. (2016). Parsing the practice of teaching. Journal of Teacher Education, 67(1), 6–17. https://doi.org/10.1177/0022487115614617
Korthagen, F. A. J., & Wubbels, T. (2001). Learning from practice. In F. A. J. Korthagen (Ed.) Linking practice and theory: The pedagogy of realistic teacher education (pp. 32–50). Lawrence Erlbaum.
Krussel. L., Edwards, B., & Springer, G. (2004). The teacher's discourse moves: A framework for analysing discourse in mathematics classrooms. School Science and Mathematics, 104(7), 307–312. http://dx.doi.org/10.1111/j.1949-8594.2004.tb18249.x
Kurasaki, K. S. (2000). Intercoder reliability for validating conclusions drawn from open-ended interview data. Field Methods, 12(3), 179–194. https://doi.org/10.1177/1525822X0001200301
Lampert, M. (2005, April 13). Preparing teachers for ambitious instructional practice: Learning to listen and to construct an appropriate response. Paper presented at Demography and Democracy in the Era of Accountability, the Annual Meeting of the American Educational Research Association, Montreal, Canada.
Land, R., Cousin, G., Meyer, J. H. F., & Davies, P. (2005). Threshold concepts and troublesome knowledge: Implications for course design and evaluation. In C. Rust (Ed.), Improving student learning: Diversity and inclusivity. The Oxford Centre for Staff Development.
Mann, S. J. (2008). Study, power and the university. Open University Press.
Martinez, M. E. (2006). What is metacognition? Phi Delta Kappan, 87(9), 696–699. https://doi.org/10.1177/003172170608700916
McDonald, M., Kazemi, E., & Kavanagh, S. S. (2013). Core practices and pedagogies of teacher education: A call for a common language and collective activity. Journal of Teacher Education, 64(5), 378–386. https://doi.org/10.1177/0022487113493807
Meyer, J. H. F., & Land, R. (2006). Threshold concepts and troublesome knowledge: An introduction. In J. H. F. Meyer & R. Land (Eds.), Overcoming barriers to student learning: Threshold concepts and troublesome knowledge (pp. 3–18). Routledge Falmer.
Michaels, S., & O'Connor, C. (2015). Conceptualizing talk moves as tools: Professional development approaches for academically productive discussion. In L. B. Resnick, C. A. Asterhan, & S. N. Clarke (Eds.), Socializing intelligence through talk and dialogue (pp. 347–362). American Educational Research Association.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Authors.
Philip, T., Souto-Manning, M., Anderson, L., Horn, I., Andrews, D. J. C., Stillman, J., & Varghese, M. (2019). Making justice peripheral by constructing practice as "core": How the increasing prominence of core practices challenges teacher education. Journal of Teacher Education, 70(3), 251–264. https://doi.org/10.1177/0022487118798324
Savin-Baden, M., & Howell-Major, C. (2013). Qualitative research: The essential guide to theory and practice. Routledge.
Schutz, K. M., Danielson, K. A., & Cohen, J. (2019). Approximations in English language arts: Scaffolding a shared teaching practice. Teaching and Teacher Education, 81, (10 –111). https://doi.org/10.1016/j.tate.2019.01.004
Schutz, K. M., Grossman, P., & Shaughnessy, M. (2018). Approximations of practice in teacher education. In P. Grossman (Ed.), Teaching core practices in teacher education (pp. 57–83). Harvard Education Press.
Shaughnessy, M., & Boerst, T. (2017). Uncovering the skills that pre-service teachers bring to teacher education: The practice of eliciting a student's thinking. Journal of Teacher Education, 69(1), 40–55. https://doi.org/10.1177/0022487117702574
Sleep, L. (2012). The work of steering instruction toward the mathematical point: A decomposition of teaching practice. American Educational Research Journal, 49(5), 935–970. https://doi.org/10.3102/0002831212448095
Smith, M. S., & Stein, M. K. (2011). Five practices for orchestrating productive mathematics discussions. National Council of Teachers of Mathematics.
SocioCultural Research Consultants, LLC. (2020). Dedoose (Version 7.0.23). www.dedoose.com
Tyminski, A. M., Zambak, V. S., Drake, C., & Land, T. J. (2014). Using representations, decomposition, and approximations of practices to support prospective elementary mathematics teachers' practice of organizing discussion. Journal of Mathematics Teacher Education, 17(5), 463–487. https://doi.org/10.1007/s10857-013-9261-4
Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge University Press. https://doi.org/10.1017/CBO9780511803932
Zeichner, K. (2012). The turn once again toward practice-based teacher education. Journal of Teacher Education, 63(5), 376–382. https://doi.org/10.1177/0022487112445789
