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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. 

Abstract Technology-mediated simulations of teaching are used increasingly to represent practice in the context of professional development interventions and assessment. Some such simulations represent students as cartoon characters. An important question in this context is whether simplified cartoon representations of students can convey similar meanings as real facial expressions do. Here, we share results from an implementation and replication study designed to observe whether and how (1) cartoon-based representations of emotion using graphical facial expressions can be interpreted at similar levels of accuracy as photo representations of emotions using actors and (2) the inclusion of markers of student emotions in storyboard-based scenarios of secondary mathematics teaching affects teachers’ appropriateness rating of the actions taken by a teacher represented in the storyboard. We show graphical representations of emotions can evoke particular intended emotions and that markers of student emotions in representations of practice could cue mathematics teachers into particular judgments of action. The Impact Sheet to this article can be accessed at10.6084/m9.figshare.24219964 

Addressing the need for practice-based teacher education to attend to context, we describe anticipations of a lesson as a case of approximations of practice that may anchor practice to its disciplinary context. After providing a general framework for how to think about anchoring practice in context we consider the StoryCircles process as an approximation of practice and illustrate the variability in anticipations of a lesson that can be generated by different StoryCircles. We use this variability to propose a conceptualization of lesson which is of particular value to practice-based teacher education. 

This paper examines the learning process of facilitators engaging in a practice-based professional development (PD) called StoryCircles facilitator training. We observed the language used by facilitators when engaging in a demonstration1) of practice in which another facilitator leads a group of secondary mathematics teachers engaged in StoryCircles PD to consensus. Subsequently, facilitators simulate the role of teachers in StoryCircles PD to anticipate challenges they, as facilitators, may face. By analyzing facilitators' collective dialogue across the different practice-based approaches within the StoryCircles facilitator training, we highlight the adoption of others' roles within the PD context and facilitators' understanding of their own roles as a result. Findings indicate that the demonstration of a facilitator's practice was a context in which facilitators developed an understanding of their own responsibilities. Meanwhile, simulating the participants' practices allowed facilitators to better understand the role of the facilitator from the demonstration of practice, as they navigated the potential tensions arising from teachers adopting practices that facilitators deemed less desirable. This paper highlights how such situated practice-based learning experiences may be associated with facilitators' perceptions of their roles within the StoryCircles framework, offering insights into the intricacies of PD facilitator training and practice. 

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. 

This paper explores the potential of online lesson visualization and annotation tools in fostering international lesson-centered teacher collaboration. In an era where teachers face diverse challenges and limited opportunities for peer-to-peer collaboration, leveraging digital tools for asynchronous exchanges emerges as a promising avenue for professional development. This paper will illustrate the potential of emerging technologies for supporting cross-cultural exchanges in which teachers can share insights, perspectives, and innovative practices in durable and archivable forms, thereby enriching the collective knowledge base for teaching. We share data from an ongoing project focused on engaging groups of secondary mathematics teachers in collectively refining a single storyboarded lesson. Through collaborative lesson development and iterative refinement, we illustrate how these tools transcend temporal and spatial constraints by sharing data gathered from three different groups involved in cross-cultural exchange (one situated in the western part of the U.S, one situated in the eastern part of the U.S., and one situated in Bulgaria) centered on storyboard representation of a lesson. In this way, we provide insights on how the lean graphics of the storyboard and the asynchronous nature of annotation can foster a culture of continuous improvement and mutual support among mathematics teachers spread over large geographic distances. Ultimately, we advocate for the widespread adoption of online multimedia authoring tools as integral components of contemporary approaches to cross-cultural collaboration on lessons for facilitating meaningful exchanges and promoting excellence in teaching and learning on a global scale 

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. 

Building on student work (SW) in mathematics classroom discussion requires complex decision-making from mathematics teachers. Previous literature on problem-based lessons recommends selecting and sequencing pieces of SW in a way that creates a mathematical storyline, but there is rarely any empirical evidence on how mathematics teachers can master such practices. We use the case of StoryCircles, a lesson-based professional development program, to show how iterative processes in which teachers were engaging with SW assisted them in developing heuristics for a careful selection and sequencing of SW. The results show that these processes involved 1) the teachers’ emerging awareness of features of SW; and 2) an evolving capacity to relate these features to the lesson goal. We discuss design features that fostered these changes. 

This research article contributes to the growing literature highlighting the potential for innovation in mathematics education through design cycles that involve creative risk-taking and failure-based learning. Specifically, we explore how “failed” cycles of StoryCircles—a practice-based professional development approach that centers on teacher collaboration—have been productive in fostering innovations within the program. Our focus is on the challenges that arose in our efforts to enable feedback mechanisms within the StoryCircles system that support teachers’ interrogation of their own instructional practice, as they collaboratively develop lessons and expand their collective knowledge base for teaching mathematics. Through examples of three challenges, we illustrate how various lesson artifacts, including those constructed by teachers in anticipation of implementation and those extracted from actual implementations, failed to serve as the sole source of feedback for supporting teachers’ growth.