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We report preliminary results of selected questions from a national survey of instructors of geometry courses for secondary teachers about the nature of instructor-student interactions. Survey responses (n= 118) are used to indicate six latent constructs describing aspects of instructor-student interaction that in turn quantify hypothesized characteristics of two didactical contracts, which we call inquiry in geometry and study of geometry. We found that instructors whose highest degree is in mathematics education are less likely to rely on a study of geometry contract than instructors whose highest degree is in mathematics. Also, instructors who have previously taught high school geometry are less likely to lecture. 

We report partial analysis of a survey of instructors of undergraduate geometry courses for teachers, attending to how they described the nature of the mathematical work they engage students in and the opportunities to learn that students had. Analysis of latent construct correlations showed that engagement of students in inquiry into geometry was significantly associated with opportunity to learn about mathematical definitions and conjecturing and engagement of students in the study of geometry was significantly associated with opportunity to learn about axioms and about history of geometry. Latent variable means comparisons showed group differences in claimed opportunity to learn between instructors whose highest degree was in mathematics and those whose highest degree was in mathematics education. 

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 

For centuries, there has been a debate about the role of undergraduate education in society. Some have argued that universities should focus on practical skills and knowledge to prepare students for the workforce, while others have supported the idea that universities should prioritize providing a broad understanding of disciplinary knowledge and practices. In this paper, we leverage data collected from 32 interviews to explore how instructors of the undergraduate geometry course for teachers (GeT) talk about the various tensions they experience in their work. Three distinct ways of talking about tensions emerged from the data: the tension as a dilemma that needs to be managed, the tension as a place to take sides, the tension as an opportunity to reframe aspects of the work. In closing we draw connections between these patterns in the data and the two perspectives about the role of undergraduate mathematics courses in preparing PTs for the work of teaching. 

We report on an effort to vet a list of 10 student learning objectives (SLOs) for geometry courses taken by prospective geometry teachers. Members of a faculty online learning community, including mathematicians and mathematics educators who teach college geometry courses taken by prospective secondary teachers developed this list in an effort to reach a consensus that might satisfy various stakeholders. To provide feedback on the final list of 10 SLOs, we constructed and collected responses to a survey in which 121 college geometry instructors ranked a set of potential SLOs, including the 10 proposed SLOs as well as 11 distractors. The 10 SLOs were, for the most part, among the highest ranked by the sample. 

an assemblage of argumentation analytic methods that can support research about faculty learning communities interacting across substantive differences. Drawing on our research with a cross-institutional faculty online learning community, we use data to show how theories from discourse analysis, systemic functional linguistics, and argumentation modeling can be operationalized to support researchers in brooking methodological tensions, including framing argumentation as the topic of or a resource for investigation and considerations of collaborative discourse as both process and content. Our methodological findings illustrate an example of this operationalization, highlighting analysis of transdisciplinary, collaborative discourse in a community composed of instructors of college geometry courses required for pre-service teachers. We share possible uses for this methodological approach vis-a-vis research about the professional work of undergraduate mathematics education and pre-service teacher preparation. 

This theoretical contribution draws on earlier work by Herbst and Chazan (2012; also Chazan et al., 2016) in which they describe the position of a mathematics teacher in an educational institution as accountable to stakeholders who issue four types of professional obligations. We propose an application and adaptation of that framework intended to address the case of instructors who teach undergraduate mathematics courses to future teachers. Considerations of not only the academic but also the professional ends of these courses are key in our application of the theory of obligations. 

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 

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. 

In this poster presentation, we share what our research team has learned by collecting responses from Geometry for Teachers (GeT) students who have taken a mathematical knowledge for teaching geometry (MKT-G) assessment before and after taking the GeT course.