Several examples of solid figures that calculus students can use to exercise their skills at estimating volume are presented. Although these figures are bounded by surfaces that are portions of regular cylinders, it is interesting to note that their volumes can be expressed as rational numbers. (JJK)

Elementary error estimation in the approximation of functions by polynomials as a computational assignment, error-bounding functions and error bounds, and the choice of interpolation points are discussed. Precalculus and computer instruction are used on some of the calculations. (KR)

Analyzes the influence of calculus performance on choosing a mathematics, science, or engineering (MSE) major, noting the role of diverse students' participation in the Emerging Scholars Program (ESP), which helps strengthen calculus performance and encourage persistence in MSE. Findings suggest that ESP students earn higher calculus grades than…

Develops and validates an instrument for determining student preferences for multiple representations of functions and establishes baseline data for future research. Students showed preferences for representations of functions which varied between contextualized and noncontextualized settings. Students' preferences for the two settings were more…

The Wisconsin Emerging Scholars Program (WESP) is a nonremedial, multicultural workshop approach to learning calculus that emphasizes community and collaboration. This approach is designed to foster substantial participation of underrepresented ethnic minority students and alleviate the problems of isolation and lack of support in a large,…

An individualized project is introduced to accompany a differential equations course with different modules ranging from standard to advanced levels with "Matlab" scripts. (Contains 1 figure.)

The purpose of this study was to explore the use of a cognitive computer tool by undergraduate calculus students as they worked cooperatively on mathematical tasks. Specific attention was given to levels of cognitive demand in which the students were engaged as they completed in-class labs with the assistance of MathCAD. Participants were assigned…

This correlation study examined the relationship between gender and the students' attitude and prior knowledge of using one of the mathematical software programs (MATLAB). Participants were selected from one community college, one state university and one private college. Students were volunteers from three Calculus I classrooms (one class from…

Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students' thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of "pedagogical…

This longitudinal study examined the effects of providing an accelerated mathematics curriculum in heterogeneously grouped middle school classes in a diverse suburban school district. A quasi-experimental cohort design was used to evaluate subsequent completion of advanced high school math courses as well as academic achievement. Results showed…

This paper focuses on the cognitive processes that occur while students are exploring motion graphs. In a classroom experiment, we examine how high-school students (aged 17), with backgrounds in calculus and physics, interpret the graphs they create through drawing the path of the movement of their hand with a computer mouse. Based on recent, and…

The purpose of this report is to outline the state of the art in calculus assessment and to indicate directions for explorations in assessment that will enable educators to gain a deeper understanding of student learning in order to improve student learning through calculus instruction. The purpose is accomplished in the context of two major…

This document promotes a better awareness of available technological tools, their implementation, and their advantages and applications in teaching and learning mathematics. Principles for successful implementation are: (1) computation should be an integral part of instruction; (2) software and curriculum development should go hand-in-hand; (3)…

This booklet is the second in a series of nine from the Teacher Training Institute at Hofstra University (New York), and describes the capstone course on calculus in secondary school mathematics, which was planned in response to numerous requests from the participants of the previous cycles. Included in this booklet are: (1) an introduction; (2)…

Results of a study that compared the performance of students in high technology programs in engineering and computer science are presented, with emphasis on students' mathematical preparation. The study population involved 175 transfer students who completed their mathematical prerequisites at three community colleges and 188 students who…