The Mathematical Association of America's "Precalculus to Calculus: Insights and Innovations Conference" brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we…

Students' procedural knowledge and conceptual understanding of matrices can improve when they use technology, in particular spreadsheets, as a tool. Complex real-world applications of matrix calculations are time-consuming and prone to errors if done by hand, yet calculations can be performed easily with spreadsheets. In this article, the author…

Background: The Learning Assistant (LA) model with its subsequent support and training has evidenced significant gains for undergraduate STEM learning and persistence, especially in high-stakes courses like Calculus. Yet, when a swift and unexpected transition occurs from face-to-face to online, remote learning of the LA environment, it is unknown…

The goal of the present study is to investigate the impact of procedural and conceptual teaching on students' mathematical performance over time. For this purpose, implicit differentiation and integration by parts were taught in two different ways to first-year university students of two different calculus courses: one course with Conceptual…

Background: Graduation rates in engineering programs continue to be a concern in higher education. Prior research has documented an association between students' experiences in first-year mathematics courses and graduation rates, but the influences of the mathematics courses completed and the grades earned are not fully understood. Purpose: The…

Office hours are an essential component of the faculty-student relationship. At present, however, few rigorous studies are available to guide faculty toward best practices in their implementation. In this study, the authors analyze survey results (n = 169) from a calculus course that included required office hours attendance. Results are presented…

Analyzing the test scores of more than 10,000,000 students who participated in the Advanced Placement (AP) math exams from 1997 to 2019, this study examined the direction and magnitude of the trend in gender disparity by race in participation in and top achievement on AP Calculus AB, Calculus BC, and Statistics exams. The results of this study…

Students' perceptions of cost are important predictors of academic and motivational outcomes. Though cost has been described as the anticipated effort one must put forth on an activity and what an individual sacrifices to complete a task, no known work has examined the extent to which anticipated cost beliefs predict experienced cost or whether…

Gateway courses are high-enrollment, low completion introductory courses foundational to a major. Because these courses have a disproportionately negative impact on the retention and persistence of Latinx students to their desired STEM major, we refer to these understudied, high-stakes courses as gatekeeping courses. Framing our exploratory study…

Massive pretrained language models have garnered attention and controversy due to their ability to generate humanlike responses: Attention due to their frequent indistinguishability from human-generated phraseology and narratives and controversy due to the fact that their convincingly presented arguments and facts are frequently simply false. Just…

Discovery learning has long been a part of mathematics teaching in the elementary and middle grades. Since the 1960s and 1970s, based on the work of Jean Piaget, Jerome Bruner, and others, helping students 'discover' or 'construct' their own understandings of mathematical concepts through well-designed activities facilitated by a competent teacher…

At the introductory level, projectile motion is usually considered under the assumption of the absence of air resistance. Even the simplest case of linear drag might be beyond the students, as it requires some familiarity with differential equations. This leaves many students wondering about the effect of air resistance on the motion and the way…

For many years, multiple representations have played a major role in the teaching and learning of mathematics (NCTM, 2014). The present study defined and investigated a particular phenomenon called representational conflict, which can arise when students simultaneously use multiple representations on the same mathematical task. Representational…

The purpose of this study is to examine the characteristics of students' thinking about graphs while evaluating statements from Calculus. We conducted clinical interviews in which undergraduate students evaluated mathematical statements using graphs to explain their reasoning. We report our classification of students' thinking about aspects of…

This study focuses on students' understanding of multiple representations of functions. It examines student responses to a task in which calculus students are asked to evaluate the derivative at a point of the cubing function when represented piecewise. Results suggest that attending to the graph of the piecewise function does not improve…