Several studies have explored students' understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students' understanding of the Fundamental Theorem of Calculus (FTC). In addition, students' metacognitive experiences and skills whilst solving FTC questions have not…

In an effort to improve upon Calculus I instruction at our institution, we designed a pilot study that incorporated a variety of evidence-based classroom practices. The goal was not to formally test known successful teaching interventions. Rather, the purpose was to develop and identify course materials and instructional methods that would not…

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

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…

Calculus at the college level has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. It is a foundation course for all STEM majors and, if mastered well, should provide students with a positive and successful first-year experience and gateway into more advanced courses. Studies have shown that a…

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

The experimental design was conducted to investigate the use of Microsoft Mathematics, free software made by Microsoft Corporation, in teaching and learning Calculus. This paper reports results from experimental study details on implementation of Microsoft Mathematics in Calculus, students' achievement and the effects of the use of Microsoft…

This paper reports a study on retention of core concepts in differential and integral calculus by examining the knowledge of two pre-service mathematics students. The study is conducted using a mixed method approach and the obtained data were analyzed using theory of three worlds of mathematics. The results showed that having good understanding of…

Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

The body of literature on a Writing-to-Learn (WTL) approach in math courses offers up a variety of assignment types from which to choose. However, few of these articles provide empirical evidence on the ways these writing assignments contribute to students' learning. This mixed-methods study, conducted at the University of New Mexico, a…

This paper reports a study on retention of differential and integral calculus concepts of a second-year student of physical chemistry at a Danish university. The focus was on what knowledge the student retained 14 months after the course and on what effect beliefs about mathematics had on the retention. We argue that if a student can quickly…

The goals of this dissertation were to examine how novice calculus teachers used questions in their classrooms, how those questions and their use might change after video case-based course coordination, and what evidence of influence on student learning might be seen in undergraduate student achievement. This research focused on one way to elicit…

The purpose of this exploratory, mixed-methods study was to compare student performance in flipped and non-flipped sections of Calculus I. The study also examined students' perceptions of the flipping pedagogy. Students in the flipped courses reported spending, on average, an additional 1-2 hours per week outside of class on course content.…

There has been a national call to transition away from the traditional, passive, lecture-based model of STEM education towards one that facilitates learning through active engagement and problem solving. This mixed-methods research study examines the impact of a supplemental Peer-Led Team Learning (PLTL) program on knowledge and skill acquisition…

This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…