Recent studies of the transition from school to university mathematics have identified a number of epistemological gaps, including the need to change from an emphasis on equality to that of inequality. Another crucial epistemological change during this transition involves the movement from the pointwise and global perspectives of functions usually…

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…

This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…

Derivatives and integrals are two important concepts of calculus which are precondition topics for most of mathematics courses and other courses in different fields of studies. A majority of students at the undergraduate level have to master derivatives and integrals if they want to be successful in their studies However, students encounter…

We investigate the nature of Calculus I homework at five PhD-granting universities identified as having a relatively successful Calculus I program and compare features of homework at these universities to comparable universities that were not selected as having a successful program. Mixed method analyses point to three aspects of homework that…

Introductory college calculus students in the United States engaged in an activity called Peer-Assisted Reflection (PAR). The core PAR activities required students to: attempt a problem, reflect on their work, conference with a peer, and revise and submit a final solution. Research was conducted within the design research paradigm, with PAR…

Action-Process-Object-Schema (APOS) Theory is applied to study student understanding of directional derivatives of functions of two variables. A conjecture of the main mental constructions that students may do in order to come to understand directional derivatives is proposed and is tested by conducting semi-structured interviews with 26 students…

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

Our research focuses on the learning of series as a consequence of institutional choices for their teaching. Our analyses of textbooks and teaching practices led us to conjecture the existence of some implicit contract rules in the teaching of series: in particular, the teaching of series is made almost exclusively in the algebraic setting, with…

Background: Calculus is a foundational course for STEM-intending students yet has been shown to dissuade students from pursuing STEM degrees. In this report, we examine factors related to students and instructors reporting a lack of time in class for students to understand difficult ideas and relate this to students' and instructors' perceptions…

The ability to retain educationally relevant content in a readily accessible state in memory is critical for students at all stages in schooling. We hypothesized that a high degree of stress in mathematics courses can threaten students' mathematics self-concept and lead to a motivation to forget course content. We tested the aforementioned…

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about…

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an…

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of…

This case study details the integration of an online grading platform in a Calculus program. Initially implemented to increase the efficiency and quality of grading written assessments in a large undergraduate program, the effects were many and surprising. Two main concerns surfaced that we needed to address, namely: (1) consistency in grading;…