Rehearsing Instruction in One-on-one Mathematics Coaching
Keywords:mathematics coaching, instructional coaching, teacher professional development, teacher learning, rehearsal
While there is evidence that rehearsing instruction with groups of teachers can support their learning, whether this is the case in one-on-one coaching settings remains largely unexplored. In this exploratory self-study, I examined my coaching work with a cadre of mathematics teachers to determine whether and how rehearsing instruction in one-on-one coaching provides individual teachers with opportunities to learn. I found that rehearsing instruction during one-on-one planning conversations can give rise to teacher learning opportunities. Three features of the rehearsal activity appeared central to the learning opportunities: (a) framing the instructional situation so that the teacher understands the context for the rehearsal, (b) acting out a range of student solution strategies during the rehearsal, and (c) analysing and discussing specific instructional decisions the teacher made while rehearsing instruction. This work contributes to research on coaching by clarifying that rehearsals can be potentially productive one-on-one coaching activities and by highlighting what is involved in incorporating rehearsals into one-on-one coaching with mathematics teachers.
Anthony, G., Hunter, J., & Hunter, R. (2015). Supporting prospective teachers to notice students’ mathematical thinking through rehearsal activities. Mathematics Teacher Education and Development, 17(2), 7–24. https://mted.merga.net.au/index.php/mted/article/view/271
Baldinger, E. E., Campbell, M. P., & Graif, F. (2021). Learning to respond to students in discussions: Examining the use of planted errors in an approximation of practice. Journal of Teacher Education, 72(5), 523–537. https://doi.org/10.1177/0022487120977148
Borko, H., Jacobs, J., Eiteljorg, E., & Pittman, M. E. (2008). Video as a tool for fostering productive discussions in mathematics professional development. Teaching and Teacher Education, 24(2), 417–436. https://doi.org/10.1016/j.tate.2006.11.012
Campbell, M. P., Baldinger, E. E., & Graif, F. (2020). Representing student voice in an approximation of practice: Using planted errors in coached rehearsals to support teacher candidate learning. Mathematics Teacher Educator, 9(1), 23–49. https://doi.org/10.5951/MTE.2020.0005
Campbell, P. F., & Griffin, M. J. (2017). Reflections on the promise and complexity of mathematics coaching. The Journal of Mathematical Behavior, 46, 163–176. https://doi.org/10.1016/j.jmathb.2016.12.007
Corbin, J., & Strauss, A. (2015). Basics of qualitative research: Techniques and procedures for developing grounded theory. SAGE Publications.
Elliot, V. (2018). Thinking about the coding process in qualitative data analysis. The Qualitative Report, 23(11), 2850–2861. https://doi.org/10.46743/2160-3715/2018.3560
Gibbons, L. K., & Cobb, P. (2016). Content-focused coaching: Five key practices. The Elementary School Journal, 117(2), 237–260. https://doi.org/10.1086/688906
Gibbons, L. K., & Cobb, P. (2017). Focusing on teacher learning opportunities to identify potentially productive coaching activities. Journal of Teacher Education, 68(4), 411–425. https://doi.org/ 10.1177/0022487117702579
Gibbons, L. K., Kazemi, E., & Lewis, R. M. (2017). Developing collective capacity to improve mathematics instruction: Coaching as a lever for school-wide improvement. The Journal of Mathematical Behavior, 46, 231–250. https://doi.org/10.1016/j.jmathb.2016.12.002
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). Springer.
Horn, I. S., Garner, B., Kane, B. D., & Brasel, J. (2017). A taxonomy of instructional learning opportunities in teachers’ workgroup conversations. Journal of Teacher Education, 68(1), 41–54. https://doi.org/10.1177/0022487116676315
Horn, I. S., & Kane, B. D. (2015). Opportunities for professional learning in mathematics teacher workgroup conversations: Relationships to instructional expertise. Journal of the Learning Sciences, 24(3), 373–418. https://doi.org/10.1080/10508406.2015.1034865
Horn, I. S., Kane, B. D., & Wilson, J. (2015). Making sense of student performance data: Data use logics and mathematics teachers’ learning opportunities. American Educational Research Journal, 52(2), 208–242. https://doi.org/10.3102/0002831215573773
Jackson, K. J., Shahan, E. C., Gibbons, L. K., & Cobb, P. A. (2012). Launching complex tasks. Mathematics Teaching in the Middle School, 18(1), 24–29. https://doi.org/10.5951/mathteacmiddscho.18.1.0024
Kavanagh, S. S., Metz, M., Hauser, M., Fogo, B., Taylor, M. W., & Carlson, J. (2020). Practicing responsiveness: Using approximations of teaching to develop teachers’ responsiveness to students’ ideas. Journal of Teacher Education, 71(1), 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. K. Hunter; B. A. Bicknell & T. A. Burgess (Eds.), Crossing divides Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia, Wellington (Vol. 1, pp. 12–30).
Kazemi, E., Ghousseini, H., Cunard, A., & Turrou, A. C. (2016). Getting inside rehearsals: Insights from teacher educators to support work on complex practice. Journal of Teacher Education, 67(1), 18–31. https://doi.org/10.1177/0022487115615191
Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematics classrooms. Elementary School Journal, 102(1), 59–80.
Knight, J. (2007). Instructional coaching: A partnership approach to improving instruction. Corwin Press.
Lampert, M., Beasley, H., Ghousseini, H., Kazemi, E., & Franke, M. (2010). Using designed instructional activities to enable novices to manage ambitious mathematics teaching. In M. K. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 129–141). Springer.
Lampert, M., Franke, M. L., Kazemi, E., Ghousseini, H., Turrou, A. C., Beasley, H., Cunard, A. & Crowe, K. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), 226–243. https://doi.org/10.1177/0022487112473837
Lampert, M., & Graziani, F. (2009). Instructional activities as a tool for teachers' and teacher educators’ learning. The Elementary School Journal, 109(5), 491–509. https://doi.org/ 10.1086/596998
Luwel, K. (2012). Microgenetic analysis. In N. M. Seel (Ed.), Encyclopedia of the Sciences of Learning (pp. 2265–2268). Springer. https://doi.org/10.1007/978-1-4419-1428-6_4951
Mudzimiri, R., Burroughs, E. A., Luebeck, J., Sutton, J., & Yopp, D. (2014). A look inside mathematics coaching: Roles, content, and dynamics. Education Policy Analysis Archives, 22(53). https://doi.org/10.14507/epaa.v22n53.2014
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. NCTM.
Russell, J. L., Correnti, R., Stein, M. K., Thomas, A., Bill, V., & Speranzo, L. (2020). Mathematics coaching for conceptual understanding: Promising evidence regarding the Tennessee math coaching model. Educational Evaluation and Policy Analysis, 42(3), 439–466. https://doi.org/10.3102/0162373720940699
Saclarides, E. S. (2022). Studying coach-teacher interactions during co-taught mathematics lessons. Investigations in Mathematics Learning. https://doi.org/10.1080/19477503.2022.2052664
Saclarides, E. S., & Munson, J. (2021). Exploring the foci and depth of coach-teacher interactions during modeled lessons. Teaching and Teacher Education, 105, Article 103418. https://doi.org/10.1016/j.tate.2021.103418
Smith, M., & Sherin, M. G. (2019). The 5 practices in practice: Successfully orchestrating mathematical discussion in your middle school classroom. National Council of Teachers of Mathematics.
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313–340. https://doi.org/10.1080/10986060802229675
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. https://doi.org/10.3102/00028312033002455
Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80. https://doi.org/10.1080/1380361960020103
Strauss, A. L. (1987). Qualitative analysis for social scientists. Cambridge University Press.
Wæge, K., & Fauskanger, J. (2021). Teacher time outs in rehearsals: In-service teachers learning ambitious mathematics teaching practices. Journal of Mathematics Teacher Education, 24, 563–586. https://link.springer.com/article/10.1007/s10857-020-09474-0