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…

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…

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…

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…

In a national context of high failure rates in freshman calculus courses, the purpose of this study was to understand who is struggling, and why. High failure rates are especially alarming given a local environment where students have access to a variety of academic, and personal, assistance. The sample consists of students at Colorado State…

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

On a national level, data indicate that about 40 percent of students in calculus courses finish with a grade of D or F, drop the course, or withdraw (Reinholz, 2009). This high failure rate has led to research studies investigating the teaching of calculus at the national level (House, 1995). Calculus courses have a history of high failure rates,…

The purpose of this action research was to investigate how the use of technology promotes interaction to foster high school students' mathematical understanding. This mixed method study is guided by social-constructivist theory (Vygotsky, 1978) and framed within Moore's (1989) model of learner-content, learner-instructor, and learner-learner…