Prior studies have identified the impact beliefs have on mathematics instructors' instructional practice, such as their choice to (or not to) lecture. However, the role of instructional context role in influencing beliefs and instruction has not been thoroughly researched. This paper explores how course context and beliefs could impact mathematics…

The ability to distinguish between exact and inexact differentials is an important part of solving first-order differential equations of the form Adx + Bdy = 0, where A(x,y) [not equal to] 0 and B(x,y) [not equal to] 0 are functions of x and y However, although most undergraduate textbooks motivate the necessary condition for exactness, i.e. the…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…

AB 1705 requires colleges to validate their math placement policies and associated enrollment practices to ensure that students begin in coursework that gives them the best chance of completing the initial transfer-level math requirements for their academic goal. If students are required to enroll in prerequisite coursework prior to the…

This article presents an instructional technology-based cycle model intended to support and facilitate the teaching and learning of mathematics, particularly calculus. The study used quantitative methods with quasi-experimental research that uses non-randomised assignments of the study group that are categorised into experimental and control…

This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students' horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the…

The promotion of belonging, purpose, and growth mindset through subtle social psychological interventions has been shown to positively impact student outcomes (Lazowski & Hulleman, 2016; Walton & Cohen, 2007; Yeager & Walton, 2011; Yeager et al., 2016). This study explores how instructor messaging and intentional course design can…

This article reports on a study of Kuwaiti college students' knowledge about the concept of functions. It also shows the connections these students make between different representations of functions. The results indicated that most students (96%) were unable to provide a definition of a function and only a third could provide examples of a…

We present our analysis of 254 Calculus I final exams from U.S. colleges and universities to identify features of assessment items that necessitate qualitatively distinct ways of understanding and reasoning. We explore salient features of exemplary tasks from our data set to reveal distinctions between exam items made apparent by our analytical…

Students are entering postsecondary institutions without the mathematical skills needed to be successful in science, technology, engineering, and mathematics majors (STEM), leading to a shortage of qualified graduates. Consequently, institutions must identify ways to increase satisfaction and performance in mathematics. Mindset theory, with…

In this reflection of teaching, we describe a series of activities that introduce the Taylor series through dynamic visual representations with explicit connections to students' prior learning. Over the past several decades, educators have noted that curricular materials tend to present the Taylor series in a way that students often interpret as…

This study explored the lived experiences of eleven transfer students as they described their experiences in Calculus 2 at very high research land grant institutions (R1). This qualitative investigation focused on the psychological phenomenon of transition as the transfer students perceived, reflected, made sense, and understood their transition…

This article describes the content validation of the Transitioning Learners to Calculus in Community Colleges Institutional Self-Assessment Tool. The instrument comprises five content areas, each with an associated set of items representing practices to promote the success of underrepresented racially minoritized (URM) students as they transition…

We describe how one department moved from skepticism to wide-spread embrace of coordinated Calculus I. Data played a crucial role in this process. Details of this journey, including successful strategies and missteps, may provide insight and perspective to other departments starting on, or immersed in, similar transformational adventures.

This study investigates the embodied, symbolic, and formal reasoning of two fourth-year university students while exploring geometric reasoning about the Cauchy-Riemann equations with the aid of "Geometer's Sketchpad (GSP)." These students participated in a teaching activity designed to encourage shifts between embodied, symbolic, and…