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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. 

In this report, we share the design of a year-long professional development program for university math instructors that we developed and refined as the Anti-deficit Learning and Teaching Project (Adelante). The program is a community learning project wherein minoritized students, STEM peer mentors, and math instructors (graduate students and instructional faculty) build relationships as they share their knowledge and experiences with race, gender, and mathematics. Culturally relevant pedagogy (Ladson-Billing, 1995) frames the goals of the community learning in terms of deep mathematical knowledge, cultural knowledge, and sociopolitical consciousness. The program activities are inspired by the Funds of Knowledge for Teaching project (Moll et al., 1992) wherein teachers are offered opportunities to build meaningful relationships with students and their communities. An anti-deficit perspective (Adiredja et al., 2020) guides the learning experience for all participants. Not only are minoritized students assumed to have cultural and intellectual assets for learning, but the project also aims to dismantle deficit master narratives (Solórzano & Yosso, 2002) about these students and their capacity to learn. Instructors worked on explicitly challenging deficit narratives about their students as they engaged in the program’s activities. The project also takes an anti-deficit approach to instructor development, focusing on their individual growth and agency, joy in teaching, and mental health. We also position ourselves as learners to the experience and wisdom of the staff and students at the university cultural centers. The core activities for the PD engage teachers to: (a) participate in five PD meetings on anti- deficit teaching and Inquiry Based Learning (IBL) teaching method; (b) lead a five-day math summer bridge workshop in Pre-Calculus, Calculus I, II, Vector Calculus, or Linear Algebra immediately following the meetings; (c) participate in critical conversations about race and gender in STEM with students at the cultural centers; (d) conduct a semi-structure interview with one of their students from the summer workshop about their STEM experience; and (e) participate in group reflection meetings debriefing their experience in the activities. Preliminary analysis of two of the three cohorts of participants found that most instructors developed a more humanizing approach to their teaching and their students (Gutiérrez, 2018). IBL helped instructors to explicitly challenge deficit narratives about minoritized students in the classroom, wherein most observed their students engaging in deep mathematical reasoning. Interviewing one of their students also shifted deficit narratives that developed in the classroom for some instructors. The workshop served as a space to try out previously learned teaching ideas (student centered teaching) without constraints from curriculum and assessments. Doing so reinvigorated many instructors’ passion for teaching, especially those who are more experienced. 

Teaching professional development (TPD) in collegiate mathematics has expanded over the last few decades. Providers of TPD, people who organize and facilitate professional learning about teaching, are at the center of this growth. Yet, little is known about who Providers are and what they do. To better understand the national landscape of Providers of TPD within university mathematics departments, this report shares data from a national survey where respondents were Providers. The focus here is on findings from survey questions asking about characteristics of Providers and the “providees” with whom they work, along with formats, topics, and activities used in TPD. Results suggest that Providers value active, learner-centered instructional methods promoted by research and policy. However, in the TPD itself, formats, topics, and activities commonly used by Providers may preach but not regularly practice activity-based methods. 

In this poster we illustrate how stewardship, a particular kind of leadership, in the complex system of mathematics instructional development requires decentering and interconnecting. This theory development for professional growth of faculty agents for change expands on earlier work describing how instructional practices used by providers of teaching-focused professional development in seminars about teaching (for graduate students) could be beneficial both for learning high-powered approaches to teaching of undergraduate mathematics and for building a foundation for future change-agent work. Here we move one level up and present an analogous argument about practices for stewards who are teaching about teaching about teaching. The poster illustrates the multilevel system with an expanded model that incorporates learning objectives for provider professional learning and the instructional practices of such professional learning in ways that showcase (and teach about) decentering and interconnecting. 

Even though algebraic conceptual understanding is recognized as a critical skill, existing larger scale validated algebra assessments consist mostly of computational tasks, or only assess a very narrow range of conceptions in a smaller focused domain. Further, few instruments have been validated for use with college students. In this paper, we describe the creation and validation of an algebra concept inventory for college students. We describe how items were administered, revised, and tested for validity and reliability. Results suggest that algebraic conceptual understanding is a measurable construct, and that the instrument has reasonable validity and reliability. Revision and validation is ongoing; however, lessons learned thus far provide information about what conceptual understanding in algebra might look like and how it might be assessed. 

Here we explore how college students across a wide range of courses may conceptualize symbolic algebraic properties. We draw on the theory of Grundvorstellungen (GVs) to analyze how learner conceptions may or may not align with instructional goals. In analyzing interviews, several categories of conceptions (descriptive GVs) emerged that may help us to better understand how students conceptualize symbolic properties during instruction. 

Studies show that Research-Based Instructional Strategies (RBIS) help students learn, however their adoption has been slow. The Teacher Centered Systematic Reform Model (TCRM) is a general model for organizing enablers and barriers to adoption of new teaching methods that includes departmental, personal and teacher thinking factors. We used the TCRM model as a framework to assess the amount of formal lecture reported by 634 mathematics instructors in their undergraduate courses. Regression analyses found that instructors who participated in Project NExT (a professional development workshop) during their early careers were less likely to use lecture than non-participants. Other significant predictors of lecture less included evaluation expectations emphasizing active teaching methods, involvement in equity and diversity efforts, and prior experience with RBIS. Factors with a positive correlational association with lecture included evaluation efforts by departments where lecture was expected. Results confirmed some prior models in different disciplines. 

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. 

Authors of this proposal are members of an inter-institutional working group focused on the teaching and learning of transformations in college geometry courses taken by prospective secondary teachers. After exploring axioms and definitions for transformational geometry in our courses, we decided to shift to identifying not just what, but how students were learning about transformations in our courses. To explore this, we began a lesson study (Boyce et al., 2021). In this report, we discuss our engagement in the lesson study, its outcomes, and new directions.