The enduring debate surrounding college algebra, traditionally a gateway for STEM pathways, underscores the necessity for curricular evolution in response to the rising popularity of non-STEM majors. This dissertation explores the success of an applied college algebra course designed for non-STEM students. The study aimed to determine whether this…

Calculus has long been known as a "gateway course" to STEM fields in postsecondary education. To moderate this gatekeeping effect, Montclair State University researchers developed a peer-led, inquiry-based instructional support (IBIS) to run parallel to Calculus classes. The design of the IBIS model was informed by an instructional…

Undergraduate students' understanding of function continuity has not been explored broadly in previous research. The relevant findings in the literature are predominantly concerned with calculus students' understanding and misconceptions of continuity. Many of these misunderstandings are tied to the relationships which continuity has with limits…

In this paper we develop a case for introducing a new teaching tool to undergraduate mathematics. Lean is an interactive theorem prover that instantly checks the correctness of every step and provides immediate feedback. Teaching with Lean might present a challenge, in that students must write their proofs in a formal way using a specific syntax.…

Student success is an integral part of systemic change research. However, students' lived experiences and voices are often subdued in this programme, leaving the change that occurs to be evaluated upon measures that do not capture a holistic view of the experiences students and their shifting identities during the roll-out of those changes. These…

Active learning practices, like groupwork, are becoming more widely used in post-secondary mathematics classrooms. These practices are often talk-intensive and require interpersonal interactions. As such, it remains an open question the extent to which practices like groupwork equitably support students with different social identities, including…

Promoting equitable classrooms is a goal of postsecondary mathematics education, but there is still limited research on how faculty learn to teach more equitably. Despite the variety of techniques developed in primary and secondary education, there has been less use in higher education. This manuscript focuses on the 'assigning competence'…

Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area,…

The number of undergraduates placing into developmental or "remedial" coursework continues to increase. This rise is concerning because developmental or "remedial" coursework creates barriers for many students. This mixed method study examines a holistic approach to placement. After one-on-one interviews with mathematics…

Play has been discussed by mathematicians and mathematics educators as essential to mathematical progress and has been widely acknowledged to have a role in learning. Yet, play is rarely acknowledged, leveraged, or studied for mathematics learners beyond early childhood. Moreover, there are theoretical and empirical challenges with designing for…

This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the…

Contributing to research on undergraduate students' thinking about problem solving tasks, the present study reports on students' reasoning about two initial-value problems i.e. first-order linear ordinary differential equations with initial conditions. A qualitative analysis of task-based interviews and work written by 34 students revealed that…

Undergraduate concepts are often first introduced in a single-dimensional setting and then extended to multiple dimensions. For instance, many undergraduate real analysis students will first learn of the metric topology on [set of real numbers] before being exposed to more general metric spaces. I conducted a paired teaching experiment (Steffe…

In our study we exploit digital tools in order to foster a relational approach to mathematics undergraduate students. Specifically, we designed formative assessment workshops based on peer feedback, with the aim to promote self-assessment and reflection on one's own mathematical activity. In the paper we describe the design of an educational…

Counting is an intellectual activity that is usually identified with the assignment of positive whole numbers ("1, 2, 3, 4, ...") in one-to-one correspondence with a collection of items in one's attentional field. Taking into account a broader, "combinatorial" meaning of the term, counting extends far beyond this description.…