Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

These analyses form part of a three-year project looking at mathematical thinking as a socially organized activity. We revisit data from a University Calculus class using tools from two theoretical perspectives, used increasingly in mathematics education research: (1) semiotic mediation; and (2) discursive practices. We highlight how different…

This report explores first year undergraduate mechanical engineering and mathematics students' conceptions of the derivative and the contribution that membership of different departments may have on these conceptions. Quantitative results suggest that mechanical engineering students develop a proclivity for rate of change aspects of the derivative…

This paper presents preliminary hypotheses about the relationship between faculty goals for the introductory calculus-based physics course and their beliefs about student learning of problem solving. All faculties have problem solving as a major goal for their courses. There appears to be however, an instructional paradox. When discussing how…

This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…

MathView is a computer algebra system designed to foster interactive exploration of mathematics. MathView is designed so that mathematics, both symbolic and graphic, is highly interactive. Change to a proposition in a MathView notebook produces a cascade of changes to the conclusions that are tied to the proposition. This structure helps to create…

This paper reviews an approach for finding optimal solutions to the traveling salesman problem, a well-known problem in combinational optimization, and describes implementing the approach using the MAPLE computer algebra system. The method employed in this approach to the problem is similar to the way ant colonies manage to establish shortest…

The University of South Carolina at Hilton Head offers a major in Hotel, Restaurant, and Tourism Administration (HRTA). Many students in the HRTA major take both the HRTA Tourism course and a business calculus course. An interdisciplinary research project was designed in an effort to interest these students in the power of calculus as a…

This paper describes a pilot program at the City University of New York Brooklyn College which pairs an English as a Second Language (ESL) reading and writing class with a Calculus I class. The class focuses on students' language development but makes use of themes, readings, and vocabulary from calculus. This model requires coordination before…

The view promoted is calculus can be reduced to totally algebraic manipulation through use of elementary notions and facts of ring theory, which enable one to do calculus in the hyperreal number system. This approach holds promise of producing increased student conceptual sophistication and manipulative ability. (MP)

Part 2 considers the limit of a sequence and extends this to include ideas such as continuity, derivative, and integral. The discussion concludes with an example of a finite or "counted completely" set, the Fermat primes. (MK)

Reports on a pilot program studying the use of computer software to enhance spatial skills presumed to be related to success in calculus. Addresses the effects of such a program on female and minority students. Results indicated that the combined effects of the computer, drawing and drafting, and gender variables explained 31% of the variance in…

Describes the preparation for the implementation of a Mathematica-based calculus curriculum and the curriculum selection process at Indiana University of Pennsylvania. Contains a summary of the problems encountered and the resulting modifications. Evaluation of the curriculum implementation, some reasons for its demise, and suggested future…

Describes a rugby problem designed to help students understand the maximum-minimum situation. Presents a series of explorations that locate an optimal place for kicking the ball to maximize the angle at the goalposts. Uses interactive geometry software to construct a model of the situation. Includes a sample student activity. (KHR)

Describes an approach to the design of learning environments around a computer algebra kernel. Presents two environments to help students learn precalculus. Provides students with symbolic, graphic, and numeric tools as well as functionalities to help them build proofs. (Author/KHR)