This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

This study examines the relationships among students' perceptions of autonomy, competence, and relatedness, self-determined motivation, and achievement across two different undergraduate Calculus learning environments at the same institution. Furthermore, it also exposits how learning environments are not culturally or socially neutral by…

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…

In an effort to maintain the global competitiveness of the United States, ensuring a strong Science, Technology, Engineering and Mathematics (STEM) workforce is essential. The purpose of this study was to identify high school courses that serve as predictors of success in college level gatekeeper courses, which in turn led to the successful…

This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior…

As part of a study on the effects of teaching with a Modified Moore Method (MMM), a survey containing 20 items from Schoenfeld's (1989) investigation of attitudes and beliefs about mathematics was administered to students in undergraduate precalculus classes. The study included one section of precalculus taught with an MMM, a student-centered and…

Issues related to college access and the need for a pipeline of STEM teachers, provided the impetus for the Ohio Board of Regents (OBR) to issue a call for Ohio universities to design pre-college experiences for high school students with three major goals in mind: (a) improvement in mathematics, science, or foreign language learning; (b) increased…

This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional his understanding of periodic functions was unconventional David engaged…

This article explores the use of problem posing in the calculus classroom using investigative projects. Specially, four examples of student work are examined, each one differing in originality of problem posed. By allowing students to explore actual questions that they have about calculus, coming from their own work or class discussion, or…

Over one-third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results…

Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core-Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate, however, much less is known about how prepared these students are for post-secondary education. Therefore this study involving students within one tracked…

Graphing techniques are used to demonstrate the inverse function theorem and that the graph of the inverse function can be obtained by flipping the graph about the line y=x. (MP)