Through galleries of graphs and short filmstrips, this paper aims to sharpen students' eyes for visually recognizing continuous functions. It seeks to develop intuition for what visual features of a graph continuity does and does not allow for. We have found that even students who can work correctly with rigorous definitions may not be able to…

Fostering students' mathematical creativity is important for their understanding and success in mathematics courses as well as their persistence in STEM, but it necessitates intentional instructional actions, such as designing and implementing tasks that have the potential to foster creativity. As teaching innovation requires support for…

In the precalculus curriculum, logistic growth generally appears in either a discrete or continuous setting. These actually feature distinct versions of logistic growth, and textbooks rarely provide exposure to both. In this paper, we show how each approach can be improved by incorporating an aspect of the other, based on a little known synthesis…

In our modern world, we are inundated and grapple with data daily. As mathematicians, we are often more comfortable discussing the behavior of functions presented analytically, in contrast with the data-driven or tabular presentations of functions ubiquitous in our culture. This paper introduces an entry-level course, Mathematical Modeling and…

Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

Homework is prevalent in mathematics courses, as are cumulative final exams. This study incorporated the memory science concepts of the "testing effect" and "spacing effect" in the homework and final exam of college mathematics courses. By replacing some new homework problems with review problems, students had additional…

The complexity in understanding the [epsilon-delta] definition has motivated research into the teaching and learning of the topic. In this paper I share my design of an instructional analogy called the Pancake Story and four different questions to explore the logical relationship between [epsilon] and [delta] that structures the definition. I…

In the continual pursuit of classroom learning effectiveness, researchers and educators aim to develop strategies that improve student performance and learning. One such strategy is to create academically homogeneous environments where students are grouped into classes based on their preconceived academic ability. The research team tests this…

In the calculus classroom, integrating applications with the theoretical and procedural conveys the relevance of the material. Since Newton and Leibniz developed calculus in the context of physics and astronomy, applications in these fields tend to predominate. To engage and excite our students, pedagogical considerations must include broader…

Income inequality is a central social justice concern, and hence excellent motivation for real-world applications in mathematics classrooms at every level. We describe the "Mathematics for Social Justice" course at Saint Michael's College, giving a specific example of one of the typical social justice projects for the course, and showing…

In the context of national collaborative efforts to increase the prevalence of active learning strategies in undergraduate precalculus and calculus classrooms, we discuss the context, strategy, and processes used at one university to create change within a mathematics department. We highlight the use of a unified active learning approach and the…

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students…

In this paper, we will describe the experience of the authors in using process-oriented guided inquiry learning (POGIL) in calculus at four institutions across the USA. We will briefly examine how POGIL compares to and fits in with other kinds of inquiry-based learning approaches. In particular, we will first discuss the unique structure of a…

We offer many specific detailed examples, several of which are new, that instructors can use (in lecture or as student projects) to revitalize the role of complex variables throughout the curriculum. We conclude with three primary recommendations: revise the syllabus of Calculus II to allow early introductions of complex numbers and linear…

Addressed toward course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across…