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Recent international reform movements call for attention on modeling in mathematics classrooms. However, definitions and enactment principles are unclear in policy documents. In this case study, we investigated United States high-school mathematics teachers’ experiences in a professional development program focused on modeling and its enactment in schools. Our findings share teachers’ experiences around their discovery of different conceptualizations, appreciations, and conflicts as they envisioned incorporating modeling into classrooms. These experiences show how professional development can be designed to engage teachers with forms of modeling, and that those experiences can inspire them to consider modeling as an imperative feature of a mathematics program. 

Abstract BackgroundTo increase teachers’ capacity to implement high-quality instructional materials with fidelity in their classrooms through a video-based professional learning cycle, the Analyzing Instruction in Mathematics Using the Teaching for Robust Understanding framework (AIM–TRU) research–practice partnership was formed. Drawing upon the design-based research paradigm, AIM–TRU created the initial design for the professional learning cycle and wanted to engage in continued iterative redesign as the year progressed. This necessitated a method, common among those who adjust their designs when applying them in context, by which to document and justify changes made over time to our model. The research contained in this article used qualitative methods to articulate and test the design underlying our professional learning cycle by advancing conjecture mapping, a device by which the embodiments of the design are made transparent to be analyzed in practice. ResultsThe initial design conjectures and activity structures teachers engaged in through our model of professional learning were refined to address three themes that emerged. Firstly, it was found that the ways participants engaged with the mathematics of the lesson were underwhelming, in large part, because our own definition of what rich talk around mathematics should entail was lacking in details such as the mathematical objects in the lesson, the presence of multiple solution pathways, or the various representations that students could use. Second, talk structures did not always allow for equitable exchanges among all teachers. Finally, activity structures did not encourage teachers to delve deeply into the mathematics so they could perceive the lesson as a coherent piece of their own classroom curriculum. Our design conjectures and activity structures were revised over the course of the year. ConclusionsOur use of conjecture mapping allowed us to address the concern with research–practice partnerships that they should develop and utilize tools that make the systemic inquiry they engage in transparent, allowing for other researchers, practitioners, and stakeholders to see the complete design process and make use of the findings for their local context. Implications for this process as a tool for those who pilot and scale professional development are raised and addressed. 

Professional development that privileges teachers’ voice, equity, and the investigation of high-quality instruction is essential to the mathematics education community. However, more research is needed to understand the process, content, and depth of teachers’ learning in this setting. This paper shares our analytic method designed to capture such learning. We integrate three complementary perspectives: Communities of Practice (theoretical framework), Teaching for Robust Understanding (conceptual framework), and Frame Analysis (analytical framework). We show how this method captures changes in teachers’ participation and reification, indicating the process, content, and depth of their learning across their professional development experience. Such work iterates on Frame Analysis and advances the methodology to highlight additional tools to better understand teacher learning about components of powerful classrooms.