Investigates the effects of instructional environment on students' conceptual understanding and procedural knowledge of calculus. Uses multiple achievement measures to determine the degree to which students from different instructional environments had mastered the concepts and procedures inherent to first semester calculus. Indicates no…

This article traces some of the events leading up to the call for reform, differing aspects of the suggested reform, steps taken, and possible future directions for the reform of calculus instruction. (CW)

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Reviews the underpinnings of synthetic division. Shows how to quickly obtain the coefficients of the Taylor expansion of a polynomial about a point, and a partial fraction decomposition of a polynomial. (MVL)

Investigates the extent to which visual considerations in calculus can be taught and be a natural part of college students' mathematical thinking. Recommends that the legitimacy of the visual approach in proofs and problem solving should be emphasized and that the visual interpretations of algebraic notions should be taught. (YP)

Reports results of a survey of demographics and work and study habits of college freshmen mathematics students. No statistically significant correlation was found between work hours and grade outcome. (Author/MKR)

An interactive, multimedia text for calculus instruction that contains the entire contents of a corresponding textbook is evaluated and found to have features that enhance concepts with dynamic examples of graphs and problems that make good use of animation, audio, and video. Its design accommodates diverse student abilities and educational…

Calls for the use of the zoom feature of graphing calculators to help students better understand the concept of derivatives. (MKR)

Described are various ways that a computer algebra system (MAPLE) was used to facilitate the resequencing of skills and applications within an elementary college-level business calculus course. Experimental results confirmed earlier findings that skills acquisition is not a prerequisite to conceptual understanding or problem-solving ability. (JJK)

Describes the problem-solving behaviors of six novice subjects attempting to solve an electrostatics problem in calculus-based college physics. The level of qualitative thinking exhibited by these novices was determined. Sound procedural knowledge and problem representation were suggested as an integral part of skilled problem solving in physics.…

Following a short history of calculus reform efforts, this article discusses curriculum development and research on student learning with respect to the concepts of function, limits and continuity, the derivative, and the integral; the availability and influence of new technologies on curriculum development; the consideration of the role of the…

Describes an activity, bungee jumping, that is fun and effective in illustrating energy transformation. The activity incorporates biology, physics, and calculus into one unit. (ZWH)

Under the assumption that the current perplexing state of calculus instruction is a result of the presuppositions inherent within conventional teaching practices, the author examines why calculus is taught the way it is, indicates unprofitable practices that result from the way calculus is taught, and recommends possible ameliorative actions. (JJK)

Reports the results of students' performance as measured by grades after the completion of the first three-quarters of calculus using the materials of the Calculus Consortium based at Harvard University. The results are presented in graphical form. The improvement is dramatic for the weaker students and moderate or none for the better students.…

Using a physical picture, an expression for the maximum possible transverse velocity and orientation required for that by a linear emitter in special theory of relativity has been derived. A differential calculus method is also used to derive the expression. (Author/KR)