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Abstract The complexity of mathematics teaching is especially evident in lessons where teachers build on students’ genuine ideas, such as problem-based lessons. To enhance teachers’ capacity for rich discussions in problem-based instruction, we have developed a unique approximation of practice: digital asynchronous simulations where teachers make subject-specific decisions for a virtual teacher avatar. The simulations are based on materials and principles from a practice-based professional development (PD) program, implemented with small groups of teachers. The self-paced simulation model offers flexibility and scalability, allowing more teachers to participate on their own schedules, but it lacks key affordances of collaborative PD. To examine how to leverage the affordances of collaborative, practice-based PD, this paper uses a design-based research approach to explicate the mechanisms in which digital simulations can support mathematics teachers’ learning about problem-based lessons. We focus on two cycles of design, implementation, analysis, and revisions of the simulation model, drawing on data from focus groups with mathematics teacher educators, prospective teachers’ performance, and teachers’ reflective assignments. The analysis illustrates how two design principles –Authenticity to the teacher’s work, andNuanced feedback– were transformed to better reflect aspects of practice-based teacher learning. We argue that self-paced, asynchronous simulations with indirect feedback can effectively emulate aspects of collaborative, practice-based PD in supporting teachers’ growth. The paper also contributes to the literature on mathematics teachers’ noticing and decision-making, examining how the two interact in simulated environments. We suggest implications for designing practice-based asynchronous digital simulations, drawing on emerging technologies. 

We illustrate how concepts from systemic functional linguistics are adapted for the analysis of multimodal representations of practice used in activities where teachers and teacher educators transact meanings about practice. We focus on the transactive register used to project practice meanings to the audience of these representations. We showcase the systems called visibility (how much of the classroom experience happening is made visible to the viewer), temporality (how sequence and duration of events are represented), and theme (how semiotic resources maintain and develop themes). We apply these systems to examine the differences between two storyboards of algebra lessons that were used in a professional development context and the different kinds of reactions teachers offered to the different storyboards. 

A central goal of lesson-centered professional development programs (PD) for mathematics teachers is to learn by constructing an artifact, for example, by designing and improving a lesson plan together. That leads to the questions, what does it mean, for mathematics teachers, to improve a lesson? And how can improvements be accounted for in the analysis of the resulting artifacts, especially when these are multimodal? This paper lays the groundwork for answering such questions by drawing on empirical data from a lesson-centered PD program for secondary geometry teachers. We show how semiotic choices were made to convey that the teacher would need to support students when geometry instruction moves from a construction task to a proof, by (1) addressing students’ confusion; and (2) creating a shared language to discuss diagrams. We relate these findings to teachers’ professional growth and the conference theme. 

A central goal of lesson-centered professional development programs (PD) for mathematics teachers is to learn by constructing an artifact, for example, by designing and improving a lesson plan together. That leads to the questions, what does it mean, for mathematics teachers, to improve a lesson? And how can improvements be accounted for in the analysis of the resulting artifacts, especially when these are multimodal? This paper lays the groundwork for answering such questions by drawing on empirical data from a lesson-centered PD program for secondary geometry teachers. We show how semiotic choices were made to convey that the teacher would need to support students when geometry instruction moves from a construction task to a proof, by (1) addressing students’ confusion; and (2) creating a shared language to discuss diagrams. We relate these findings to teachers’ professional growth and the conference theme.