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As coursework extends beyond arithmetic, students encounter forms of equivalence beyond numerical equality. This study examines how college students characterize equivalence in mathematics generally, and specifically for equations and expressions. Responses from 198 students were analyzed and coded as numerical or non-numerical. Across questions, most responses appealed to numerical criteria, treating equivalence as equality to a single number, with higher prevalence of non-numerical criteria correlating with higher-level courses. We observed multiple variants of both numerical and non-numerical criteria, including converting algebraic expressions to numbers to justify equivalence. Findings highlight the need for educators to support students in distinguishing types of equivalence and their associated criteria. 

The Carnegie Classification sorts institutions by their different styles of education. Two prominent types of institutions are high research activity universities (R1) and liberal arts focused colleges (LA). Institutional characteristics may positively (e.g. Eide et al., 1998) or negatively (e.g. Astin, 1997) affect graduate school aspirations. We analyzed responses from a national undergraduate mathematics major sample using chi-squared and Mann-Whitney U tests to identify differences between students’ knowledge about graduate school and its application process by these two types of institutions. Using this same sample, we used chi-squared tests to explore the differences between departmental (professors, advisors, and mentors) support by institution type. We interpret these results with the theories of social and cultural capital and offer suggestions for future research investigations. 

Applying to graduate school in mathematics requires both a desire to attend graduate school, but also an understanding of the application process. The more students know about the process, the more successful they are in their pursuit of admission to a graduate program. We examined mathematics majors’ knowledge of both graduate school and the graduate school application process as part of a larger study examining barriers to students applying to graduate school in mathematics. We also examined the impact of mentors on student interest in graduate school and whether having a mentor has an impact on student knowledge of graduate school. We frame and explain our results using the theory of social capital. 

In this paper, we discuss our experience collaborating with mathematicians to increase their use of active learning pedagogy in a proof-based linear algebra course. We use this experience to attend to three primary research objectives. First, we identifi ed three primary categories of instructor considerations that would determine whether or not they would incorporate a proposed strategy. Second, we observed and made sense of which of these were most prominent for these mathematicians. Third, we determined what combination of considerations needed to be satisfi ed to warrant the implementation of a strategy by these mathematicians. 

In this paper, we discuss our experience collaborating with mathematicians to increase their use of active learning pedagogy in a proof-based linear algebra course. We use this experience to attend to three primary research objectives. First, we identifi ed three primary categories of instructor considerations that would determine whether or not they would incorporate a proposed strategy. Second, we observed and made sense of which of these were most prominent for these mathematicians. Third, we determined what combination of considerations needed to be satisfi ed to warrant the implementation of a strategy by these mathematicians. 

This study explores the evolving approaches of eight foundational math course coordinators, uncovering key insights into their coordination strategies and mechanisms to enhance their efforts. These coordinators oversee critical courses, including College Algebra, Quantitative Reasoning, Introductory Statistics, Math for Architecture and Construction Management, Precalculus, Calculus, and mathematics courses for prospective elementary teachers. Through a dataset derived from surveys, self-reflections, and professional development workshops, we investigated their perspectives and experiences as coordinators. We analyzed data from both the coordinators and the graduate student instructors they oversee. Specifically, we highlight the integration of instructional routines that promote mathematical reasoning and the development of course-specific dynamic calendar systems, both of which have the potential to improve the instructional effectiveness and coordination of foundational math courses. Our findings offer fresh perspectives on how to better support course coordinators in their crucial role, ultimately benefiting both instructors and students. 

Graduate student instructors (GSIs) in mathematics play a pivotal role in shaping undergraduate education and are the future of collegiate mathematics faculty. As part of their development, GSIs are expected to engage in teaching-focused professional development (TPD), particularly in evidence-based strategies like Active Learning (AL) methods. However, higher education is only beginning to explore how to effectively measure GSIs' growth in teaching skills through such TPD. This study examines the learning process of 47 novice GSIs from three universities, specifically focusing on their evolving understanding of AL before and after participating in TPD. By analyzing the GSIs' own definitions of AL, the research highlights changes in their knowledge and alignment with the intended TPD outcomes. The findings provide insight into the effectiveness of TPD on AL, while also offering recommendations for structuring future evaluations of TPD impact on GSI teaching knowledge and skills. 

This preliminary report shares an outcome from a summer professional development (PD) activity with university instructors. Instructors participated in four PD meetings, then immediately taught a five-day summer workshop using inquiry, working primarily with first-generation minoritized students. While instructor participants’ exit interviews of the project identified their experience in the summer PD as pivotal to their development, we know little of how students experienced the instructors’ teaching during the workshop. Our analysis focuses on two items from student post-workshop survey wherein students shared their feedback of their instructor and their experiences more broadly. This analysis allowed us to get a good sense of the instructors’ individual practices and revealed convergence in their practices. Pedagogically, instructors utilized group work and deemphasized direct instructions, while prioritizing students’ engagement in discussions and struggling through conceptual ideas. Relationally, instructors were responsive to students’ mathematical needs and created a respectful, safe, and welcoming classroom environment.