Abstract
The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field’s understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches’ practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training.
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Notes
The Institute for Learning is a professional development group within the University of Pittsburgh’s Learning Research and Development Center.
The intervention also included a post-lesson conference, but it was not the focus of this study.
Coaches varied in the number of times they co-planned and observed lessons with their partner teachers between training sessions; we asked them to select one for the videotaping.
The rubric for Advancing Questions was constructed with only three different levels purposefully. There were only two fundamental points of distinction. Rather than try to force another distinction, we decided that it would be better to leave only three levels to promote better reliability between raters.
This is noteworthy because teachers’ instructional ratings are sometimes (artificially) raised when the coach joins them during a lesson; coaches’ actions and questioning can raise the level of cognitive demand and/or help to maintain it.
The coach was not a veteran of our project.
Especially noteworthy in the previous coding of this coach was her improvement in guiding discussions of multiple solution strategies in depth; Brianna started lower than the overall mean (all strategies discussed at a very superficial level) but finished above the mean at the top-most score of “at least 2 solution strategies discussed in depth.”
Big ideas and associated essential understandings for developing thinking in various grade bands and topic areas (published by NCTM, 1989, 2000, 2014). For example, for Algebra Grades 3–5, the big ideas relate to the fundamental properties of number and operations, the use of the equals sign to represent equivalence, variables as efficient tools for representing mathematical ideas, quantitative reasoning as a way to understand mathematical relationships, and functional thinking to generalize relationships between co-varying quantities (Blanton et al., 2011).
Holding conversations about goals and how they should guide decision making before and during the lesson are part of the pre-lesson planning conference in the coaching model.
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Funding
The research reported herein was supported by the James S. McDonnell Foundation - Understanding Teacher Change and Teachers as Learners in K-12 Classrooms - grant https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.37717_220020525&d=DwIGaQ&c=vh6FgFnduejNhPPD0fl_yRaSfZy8CWbWnIf4XJhSqx8&r=tr37p-LMKuZcfSC3Gl2yDqo9ZcrJey8lTPYOKaBGIF6yshihKd8RA64oNKKOSEMe&m=w3lZftmD0AgykIJE_VbRuxvkLM1BD7RKyiDUP0sfRk0&s=bK2LiDIcJf4y5xNLhWVnIvV0_uO5dWU861jOABq_o8k&e= and by the Institute of Education Sciences, U.S. Department of Education, through Grant R305H140112 to University of Pittsburgh. The opinions expressed are those of the authors and do not represent views of the foundation or the Institute or the U.S. Department of Education.
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Stein, M.K., Russell, J.L., Bill, V. et al. Coach learning to help teachers learn to enact conceptually rich, student-focused mathematics lessons. J Math Teacher Educ 25, 321–346 (2022). https://doi.org/10.1007/s10857-021-09492-6
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DOI: https://doi.org/10.1007/s10857-021-09492-6