Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative…

College Algebra has been the main credit bearing mathematics course for many college students, but only one in five students at the community college level were passing this course. Students that did not have a mathematics dependent major seen College Algebra as a gatekeeper for completing college. With several students struggling to complete…

A study was conducted considering a mathematics learning center as a figured world, that is, as a social space that is treated as if individuals within the space share certain meanings about the space and interactions within it (Holland et al., 1998) from the perspective of the undergraduate peer tutors employed in it (for the larger study, see…

Taking the challenges presented by shifting to online instruction mid-semester due to the COVID-19 global pandemic, I tried to utilize prompts on discussion boards as test questions. The prompts for these questions were to create a triple integral satisfying certain conditions, and when a person posted their integral, no one else could use the…

The development of modeling skills in mathematics is essential for individuals to understand, describe, control, and predict phenomena around them. This article describes the results of an investigation to find out how an activity -- based on a Models and Modeling Perspective -- stimulates the mathematics modeling skills of undergraduate students…

The pedagogical discussion between the merits of traditional learning versus online learning provides much discussion from both camps. Following the Coronavirus of 2019 pandemic in the spring of 2020, undergraduate students enrolled in the freshman Single Variable Calculus course at the United States Military Academy at West Point were forced to…

A case study of calculus instructional material (comprising of lecture notes and tutorial practice worksheets) designed by teachers from a Singapore pre-university is presented in this paper. As textbooks have not been available for mathematics at the pre-university levels, the instructional material was a product of the teachers' collaborative…

The goal of this research is to make a theoretical reflection about connections that contributes to the development of the model for mathematical connections originally proposed by Businskas, and extended with the contributions of other researchers. This model is used in the most relevant investigations in this field. As a consequence of the…

Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

We present results of a research developed with first semester students from a Colombian Public University based on classroom intervention in a precalculus laboratory course mediated by an interactive mathematical software. We characterize and exemplify the cognitive skills of explanation, justification, argumentation and validation, using a…

In higher education, Learning Assistants (LAs)--a relatively recent evolution grounded in peer mentorship models--are gaining popularity in classrooms as universities strive to meet the needs of undergraduate learners. Unlike Teaching Assistants, LAs are undergraduate students who receive continuous training from "faculty mentors" in…

In this research we investigate how mathematics teachers, as graduate students, estimate the value of [pi] by exploring the problem of "squaring the circle" using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to…

Existing literature reviews of calculus learning made an important contribution to our understanding of the development of mathematics education research in this area, particularly their documentation of how research transitioned from studying students' misconceptions to investigating students' understanding and ways of thinking per se. This paper…

The Mathematics Department at Cornell University has recently secured a grant from the University to implement systemic change in how we teach courses that reach students at critical transition points in their mathematical development. In this article, we report on the changes made to our large multi-section first-semester calculus course in order…

Despite shifting to emergency remote teaching, a teacher's role and responsibility was to keep teaching their course to the same high academic standards as before COVID-19 upended our community. Meeting this challenge, without being able to use many well-established teaching practices, was also an unwanted opportunity to learn and experiment with…