In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas,…

Students who actively engage in metacognitive thinking and self-regulation and are self-motivating appear to be more successful than those who take a more passive role in learning. This causal comparative research study explored whether increasing metacognitive awareness through participating in metacognitive surveys outside of class improved…

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the…

The present study sought to design calculus tasks to determine students' preference for visual or analytic processing as well as examine the role of preferred mode of processing in calculus performance and its relationship to spatial ability and verbal-logical reasoning ability. Data were collected from 150 high school students who were enrolled…

In this study we aimed to understand who was struggling in freshman calculus courses, and why. Concentrating on the Fall sections of the class, the best predictors for success (R[superscript 2] = 0.4) were placement test results, the student's own appraisal of the quality of mathematics teaching they received in high school, and the Motivated…

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…

Technology can help develop understanding of abstract mathematical concepts through visualisation and graphic representation. The teaching and learning of calculus can be challenging as it involves abstract and complex ideas. The purpose of this study was to investigate how students and teachers attempt to use TI-Nspire, the latest graphing…

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of…

Presented at the Advanced Placement Annual Conference (APAC) in Las Vegas, July 2007. This presentation explores the demographic and course-taking patterns that have been identified behind what students take AP exams and how to best reach the population of students that are not currently taking AP exams.

This project described the characteristics and teaching behaviors of those successfully teaching AP® Calculus AB and AP English Literature and Composition to underrepresented minority students. Its purpose was to assist educators in improving the participation and performance of underrepresented minority students in AP classes. Study results…