In the light of research suggestions, teachers have been tasked to empower students to experience mathematics as a dynamic process of exploration (Boaler & Greeno, 2000; Langer-Osuna, 2017; Romberg, 1994), rather than recalling a static body of knowledge. This task demand teachers to create a fundamentally different learning environment in which teachers "draw information out of students" (Boaler, 2003, p. 4) rather than transferring the information to students. Given the challenges of "moving away from a language of skills ('students will calculate slopes') to the language of understanding ('students will identify common features of linear growth')" (p. 62), for teachers to transition from one teaching approach to the other is not an easy task (Horn, 2012). Even if many teachers engage in informal reflection on their teaching on a daily basis, it might be challenging for teachers to be critical about their own teaching and know what they need to change about their teaching (Hart et al., 1990). Then, the question becomes how to create opportunities for teachers to be critical about what they do in classrooms and "rethink their teaching, rather than merely extend their existing practice" (Horn et al., 2017, p. 51). Related to this question, there are some promising research findings on the use of technology (Goldenberg, 2000) and supplementary curricular materials (Matewos et al., 2019) in challenging routine instructional practices and the interplay between students, teachers, content, and activity (Zbiek et al., 2007). As a special technological tool, I focus on PhET interactive simulations (sims) (phet.colorado.edu), which are intentionally designed to support conceptual understanding of mathematics and science. Building on the research findings on the potential of supplementary curricular materials and instructional technologies being a catalyst for change, in this dissertation study, I step back and examine what a teacher was readily capable of doing and thinking and shed some light on how to create a need for change by using these materials. In this case study, I examined how a middle school mathematics teacher, Linda, used sims and sim-based materials in her lessons over two years and how her instructional practices were similar or different to her non-sim lessons. To capture details on how sims and sim-based materials might function as a catalyst for change, I conceptualized Linda as both a thinker and doer (Horn et al., 2017). My analysis of what Linda thought showed a shift in Linda's attention to problems of practice related to students to problems of practice related to teaching. She reframed problems of practice, including student engagement, and who considered being good a student with an explicit connection between her instructional decisions and student engagement—productive framing. Additionally, Linda identified aspects of her instruction that needed improvement, including content knowledge, questioning, and how to scaffold student engagement in high-level thinking. These were evidence of Linda's motivation to improve her instruction aligned with reform suggestions. In the second part of my analysis, I focused on Linda's sim lessons where she used sims and sim-based materials and her non-sim lessons where she used her business-as-usual materials. I examined what Linda did when she taught in sim lessons in comparison to her non-sim lessons. My analysis of what Linda did showed that Linda was capable of teaching more aligned with reform suggestions. Based on instructional quality assessment rubric scores (Boston, 2012), there were some significant differences between Linda's instruction in sim and non-sim lessons regarding how she attended to student thinking, her questioning, and the mathematical focus of the lessons. Finally, I documented learning opportunities based on what Linda did and how she reflected on her experiences with sims and sim-based materials. This dissertation study shed some light on what teachers might be capable of doing and thinking as they use well-designed supplementary materials enriched with instructional technologies. This study was also an effort to understand and listen to what teachers experience part of their effort to enrich their instruction by using supplementary materials that are available to them. I present and discuss future research and contributions of this study related to the potential of supplementary curricular materials and instructional technologies in catalyzing a change in mathematics classrooms and creating a learning environment for teachers to experiment with these materials, reflect on their experiences, and learn from their own teaching.
