Reflects on the history of the calculus reform movement and the development of course implementation projects, including use of technology in instruction. Highlights several themes permeating reform courses: reform calculus is more hands-on, students are expected to understand complex mathematical concepts in more connected ways, and new…

Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

Concludes that writing about the executive processes of problem solving, difficulties encountered, alternative strategies that might have been used, and the problem solving process in general helped students in the treatment group learn to use executive processes more quickly and more effectively than students in the control group. (Author/NB)

What initially appears to be a standard maximum-minimum problem presents, with a particular independent variable, a wealth of calculus and algebraic subplots. Uses graphing calculator technology to reinforce the "pencil and paper" solution and open the problem to lower level mathematics courses. (Author/NB)

Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)

Investigated (n=61) undergraduates' ability to unpack informally written mathematical statements into the language of predicate calculus in an introduction to proofs and mathematical reasoning. Found that students were unable to construct proofs or validate them. Appendices are "A Sample Validation" and "Building a Statement Image." (MKR)

Presents a situation in which differential calculus is used with inverse trigonometric tangent functions to maximize an angle measure. A negative distance measure ultimately results, requiring a reconsideration of assumptions inherent in the initial figure. (Author/MKR)

Clarified is the assertion that the so-called complementary function is indeed the general solution of the homogeneous equation associated with a linear nth-order differential equation. Methods to obtain the particular integral, once the complementary function is determined, are illustrated for both cases of constant and of variable coefficients.…

This article provides three examples from elementary calculus concerning the use of the long ago popular method of parametric differentiation as an alternative form of solution. Included are a partial fraction decomposition, an indefinite integral solution, and an integration by parts. (JJK)

A principle is presented to show that, if the time of passage of light is expressible as a function of discrete variables, one may dispense with the more general method of the calculus of variations. The calculus of variations and the alternative are described. The phenomenon of mirage is discussed. (Author/KR)

Uses real data as a catalyst to explore mathematics. Presents two mathematics activities based on real data, one on earthquakes and the other on demographic data. Discusses the implications of these activities in calculus classes. (ASK)

Studies the later course grades of students enrolled in freshman calculus taught using traditional texts through 1994-95 and the Harvard method which was fully adopted starting in 1995-96. Reports that, in some cases, the results were indistinguishable but some statistically significant patterns were found. (Author/ASK)

Considers some changes that the use of graphics calculators impose on the assessment of calculus and mathematical modeling at the undergraduate level. Suggests some of the ways in which the assessment of mathematical tasks can be modified as the mechanics of calculation become routine and questions of analysis and interpretation assume greater…

Highlights a debate concerning reform calculus between Professor Thomas W. Tucker on the reform side and Professor Howard Swann on the traditional side. (ASK)

Examines advanced students' course taking procedures and their senior year mathematics participation. Concludes that students who took early algebra demonstrated a substantially higher participation rate in advanced mathematics in the later grades of high school than students who did not. (Contains 25 references.) (ASK)