Passing the introductory calculus sequence is critical to undergraduate students' retention in STEM programs. This study examines the relations between three interrelated processes found to influence mathematics learning and achievement: spatial skills, spatial anxiety, and math anxiety. Additionally, it examines the role of gender on these…

The rise of virtual learning established e-learning as an emerging education delivery method (Jones et al., 2022). One of the barriers to virtual education was the lack of insight into the quality of students' online learning experience. For instance, without an active instructor to clarify the course content, virtual learners viewed instructional…

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…

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 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…

Research suggests learning assistant (LA) programs can be a change lever to support the institutionalization of active learning in postsecondary education. Some research suggests LAs offer unique benefits for STEM courses, independent from other change levers, but more research needs to be done to understand how LAs support active learning…

Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…

In this dissertation I explore instructors' work with instructional tasks as they plan to introduce various representations of derivatives. Drawing on the notion of "framing" from sociology, I adopt a situative lens to study calculus instructors' planning of instructional tasks. I rely on Herbst and Chazan's (2012) notion of…

The recent push toward active learning -- engaging students in the learning process -- is meant to benefit students. Yet there is still much to learn about students' perceptions of this phenomenon. We share results from an interview study of students' perceptions of features of two active learning models institutionalized at a large…

Calculus continues to be an important topic of discussion among mathematics education researchers given how it often acts as a gatekeeper for students in STEM. In their extensive 2017 review of calculus literature, Larsen and colleagues identified two main areas of applied research that had largely been neglected: research related (1) to efforts…

Background/purpose: This study aims to improve students' mathematical critical-numeracy thinking skills by applying the Problem-Based Learning-Autograph model. Materials/methods: This study used a mixed method with a sequential explanatory strategy, and the research design is a one-group pretest-posttest design. The population included students…

This article presents reflections on a research that investigated processes operationalized by mathematical thoughts and practices which sought explanations for the ways of being of mathematical objects in their correlations in the socio-cultural context throughout our human history and how these ways of being they were captured, and still are, by…

This study investigates how three widely used calculus textbooks realise integrals as a potential to prompt mathematical competencies, adapting the rating scheme used in Boesen et al. ("The Journal of Mathematical Behavior," 33:72-87, 2014), Pettersen and Braeken ("International Journal of Science and Mathematics Education,"…

The learning of calculus concepts is considered challenging for students. This claim is actual for calculus in general and for specific concepts in particular. In this paper, we focus on the concept of the inflection point. We argue that one of the roots of this problem is the lack of a useful and productive meaning of the concept--the…