Given the centrality of angle in mathematics curricula and scarcity of research in this area, we investigated 64 PTs' assimilatory domains of angularity by analyzing the angles they indicated when presented with four segments mutually sharing an endpoint. In both interview and written settings, we found PTs were more likely to recognize convex…

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in and for teaching (MKT). We argue that Rowland's (2013) Knowledge Quartet for MKT, in particular, the…

For years, teacher education programs have focused considerable effort on teacher knowledge and how to develop the types of knowledge that matter in teacher education candidates. Meanwhile, candidate dispositions for teaching have received little attention, particularly in mathematics courses for candidates. As developers and practitioners of a…

Multiplication and division are vital topics in upper level elementary school. A teacher's pedagogical content knowledge (PCK) influences both instruction and students' learning. However, there is currently little research examining teachers' PCK within this domain, particularly regarding professional education of future teachers. To help address…

This paper reports an ongoing effort to address the problem of instructional capacity for high school geometry from a systems improvement perspective. In an effort to understand the system that contains the high school geometry instructional capacity problem, we identified key stakeholders and conducted preliminary interviews to learn about the…

This paper reports on an ongoing project aimed at developing an inter-institutional system of professional support for the improvement of the Geometry for Teachers (GeT) courses that mathematics departments teach to preservice secondary teachers. In alignment with the literature on improvement science (see Bryk et al., 2015; Lewis, 2015), it is…

Although research and policy documents provide recommendations to inform secondary mathematics teacher preparation, no single study has addressed the "big ideas" of courses in multiple programs and how those big ideas may be interpreted through the lens of recent research and policy documents. To answer this need, we focused on big ideas…

Professional noticing of student thinking is considered a useful construct to investigate instructional decisions and activity made by teachers to support learning. This paper highlights the findings from one component of a multi-university (United States & Australia) research project focused on improving pre-service secondary mathematics…

The emerging use of approximations of practice in teacher education calls for ways to document teacher candidates' (TCs') skill from their enactments and to determine how TCs' skill develops through such pedagogies. We highlight two cases of secondary mathematics TC development, connecting analyses of two types of approximations--coached…

This paper reports on a project aimed at developing a system of professional support for the improvement of the Geometry for Teachers course that mathematics departments teach to preservice secondary teachers. We share data from interviews with 20 instructors to report on how they perceive their position of geometry instructors and the work they…

We investigate definitions and approaches that preservice secondary mathematics teachers develop about teaching mathematics for social justice while participating in an equity-based, anti-racist professional development program. We analyzed transcripts from seminar sessions of the program where participants discussed different forms of teaching…

In support of standards for the learning and teaching of mathematics and statistics that advocate for the use of technology to promote reasoning and sense making, and to elicit student thinking, we draw on the use of authentic student work in the form of video case instruction to develop prospective secondary mathematics teachers' [PSMTs]…

We conducted a self-study to learn more about how to support the first author's pre-service teachers (PSTs) during their field experiences in an introductory secondary mathematics methods course. The findings highlight how the PSTs' perceptions of the secondary students' mathematics ability was closely related to how they viewed the students'…

Understanding the formation of the professional identities of prospective teachers is important to better understand the decision-making processes of future teachers. Through an exploration of four prospective teachers' visions of practice and designated identities, we found that their images of future students' affective responses while learning…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…