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In this paper we examine how facilitators' prior experiences as mathematics teachers frame their work when facilitating a practice-based professional development (PD) for the first time. We focus on the experiences of a novice facilitator of StoryCircles, a professional learning process in which teachers collectively script and visualize a problem-based lesson, arguing about their rationales for different decisions connected to discussions of students' work. We situate the challenges the facilitator encountered by identifying the expectations that were not met while she was facilitating and offer possible connections to the PD design. We close by suggesting a perspective to account for facilitation challenges. [ABSTRACT FROM AUTHOR]

A historical review of mathematics textbooks suggests a canonical method to solving equations that teachers often see as “the” way to solve equations. In this paper, we examine data from a nationally-distributed sample of 524 secondary mathematics teachers who responded to scenario-based survey items that represent the instructional situation of solving equations. The items featured scenarios in which students presented non-canonical solution methods and asked participants to share how they would respond. Using a framework that draws on systemic functional linguistics, we describe the linguistic resources teachers used. While closed moves are frequently used to avoid discussion of non-canonical solutions, our results suggest that teachers find ways to make regular use of: (1) closed moves for accommodating non-canonical solutions and (2) open moves when steering the conversation back to the canonical method. [ABSTRACT FROM AUTHOR]

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 problem from their perspective. We use these interview data to describe the system in more detail and to identify six major factors contributing to the high school geometry instructional capacity problem. [ABSTRACT FROM AUTHOR]

Researchers have identified students' difficulties reasoning about inverse functions. Through our review of this literature, three meanings stand out: a formal, 'undoing', and quantitative meaning. Using these meanings as a guide, we analyzed student work collected from a lesson on the topic of inverse functions taught by an experienced high school mathematics teacher, using a novel task. In analyzing the data, we noticed tensions between students' understanding of the context and of inverse function as treated in curricula. In this paper, we illustrate these tensions and describe potential implications for students' productive construction of the meanings of inverse function. [ABSTRACT FROM AUTHOR]

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 essential to develop and deploy practical measurement tools to inform improvement. We describe three key forms of measurement our team has been using to drive this work as well as some preliminary findings. [ABSTRACT FROM AUTHOR]

Using mixed-effects regression, we analyzed teachers' responses to a multimedia survey of instructional practices in posing proof problems in geometry. Teachers described and rated for appropriateness three different ways of involving students in deciding what to prove, including one in which the teacher chooses the givens and the conclusion to prove, and two others that expand the students' role in different degrees. While teachers recognized the former as normative, their ratings identified an alternative as more appropriate, having more positive value, and less negative value than the normative one. This alternative has students propose the givens or the conclusion to prove, and it allows the teacher to control the complexity of instruction by endorsing one proposal before students are to write the proof. [ABSTRACT FROM AUTHOR]

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 do in the course. To inspect this set of interviews, we use the framework of professional obligations to the discipline, to individual students, to the institution, and to the classroom community. We share how references to these professional obligations emerged in the interview data. [ABSTRACT FROM AUTHOR]

Graduate student teaching assistants (GTAs) are responsible for the instruction of undergraduate students in critical introductory courses, but are not yet in the position of professors. Given their unique status, we ask if there are differences in how graduate students and professors express their agency when speaking about their responsibilities and how graduate students position themselves as members of the community of mathematicians. We use tools from systemic functional linguistics (Halliday, 1994) to analyze 16 interviews with graduate students and professors from research I universities. We found important differences in how graduate students and professors perceive their agency, and agency varies according to whether it concerns disciplinary or institutional responsibilities. Future research can investigate how to create more opportunities for developing the agency of GTAs in institutional decisions. [ABSTRACT FROM AUTHOR]

We show validation data of surveys that estimate high school teachers' recognition of four obligations of the mathematics teaching profession. Measures of internal consistency show three instruments reliably measure three of the four obligations, while the fourth has lower internal consistency. Factor analyses support a 3-factor model for the disciplinary obligation and 2-factor models for each of the individual, institutional, and interpersonal obligations. We inspected correlations between recognition of obligations and teachers' beliefs: Low correlations found suggest recognition of obligations and beliefs are different constructs. [ABSTRACT FROM AUTHOR]

We discuss affordances and liabilities of using a storyboard to depict a written case of a teacher's dilemma that involves race, opportunity to learn, and student community. We rely on reflections by the teacher educator who authored the written case and later depicted it as a storyboard to use it with his preservice teachers (PSTs). The analysis involved, first, organizing the signifiers in each of the two representations of practice into what we call concentric spheres of stratification, and secondly, contrasting the various meanings attributed to signifiers by both the author and his PSTs. We suggest that the resources of storyboard allow for more inquiry and alternative narratives than is available from the single modality of text in the written case. [ABSTRACT FROM AUTHOR]

This paper is part of a three-year inquiry that supports and investigates the work of groups of mathematics teacher educators using technological tools to design and implement multimedia practice-based teacher education curriculum materials. This paper describes the kinds of activities, interactions, and tools used by mathematics teacher educators to engage in such work. Using Engeström's Activity Theory as a framework, we organize our observations of the groups' work sessions, noting differences across the groups' objectives and ways of organizing the division of labor and tools for engaging in the work. Our results suggest the activity of collective curriculum development amongst teacher educators can take on at least three distinct types of interactions. We present these types of interactions as "caricatures" (Lambdin & Preston, 1995), using data from all of the groups to represent composite descriptions. [ABSTRACT FROM AUTHOR]

We examine responses from a national sample of high school mathematics teachers to a questionnaire, which had been developed to study teachers' recognition of a system of hypothesized norms that stipulate that geometry proof problems are to be posed using a diagrammatic register. We report on the psychometric properties of the questionnaire, as well as the relationship between these mathematics teachers' mathematical knowledge for teaching geometry (MKT-G) and their stances on breaching those norms. Although Herbst et al. (2013) hypothesized that the system consisted of five distinguishable sub-norms, the factor structure of the questionnaire suggested that two of those norms might not truly be distinguishable. We also found a positive and significant relationship between teachers' MKT-G and their stances on breaching two of the determined components of the system of norms. [ABSTRACT FROM AUTHOR]