Criticizes the method of using calculators for the purpose of selecting candidates for L, for the limit value of a function. Suggests an alternative: a working formula for calculating the limit value L of a real function in terms of infinitesimals. (Author/ASK)

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base "e." A similar link is established for families of functions obtained by composing…

As a precursor to lessons on prime decomposition and reducing fractions, rules are generally presented for divisibility by 2, 3, 5, 9, and 10 and sometimes for those popular composites such as 4 and 25. In our experience students often ask: "What about the one for 7?" and we are loathe to simply state that there isn't one. We have yet to see a…

We introduce a cooperative learning, group lab for a Calculus III course to facilitate comprehension of the gradient vector and directional derivative concepts. The lab is a hands-on experience allowing students to manipulate a tangent plane and empirically measure the effect of partial derivatives on the direction of optimal ascent. (Contains 7…

This paper describes a modification of a popular TV game show, "American Idol[R]," conducted in an undergraduate calculus course. The focal point of this game show is to get students to interact in competitive self-assessment. Student competition is an effective device to engage students in the learning process. Placing students in the role of…

How the notion of limit can be developed through a meaningful approach is discussed. Selected portions of the high school calculus course are described, and errors on a test are analyzed. (MNS)

This paper describes the design and initial data analysis of an ongoing study to determine the important elements, as perceived by faculty, of the learning and teaching of problem solving in the context of an introductory calculus-based physics course. To elicit instructors' beliefs that inform their instructional choices, an interview around…

This study compared the test scores of AP Calculus students. Two methods were used to work the calculus problems: the traditional pencil and paper method and the graphing calculator method. Four researcher-constructed assessments on various calculus topics were administered over a six-week period to two sections of high school AP Calculus…

Most presentations of mathematical ideas are suggested as being backwards from the way they evolved. Two alternatives are discussed, both emphasizing mathematical processes. (MP)

A course of mathematical methods for students of different degree programs is outlined. An approach to the teaching of the course is described which allows continuity between sections of apparently different material. (MP)

Examines the performance of two groups of students in traditionally-taught second semester calculus: students who took reform first semester calculus and students who took traditionally-taught first semester calculus. Identifies and explores the issues that reform students faced as they transitioned into traditionally-taught second semester…

Presents a semiotic analysis of the potential of computer algebra systems (CAS) for enabling mathematical activity on a conceptual level higher than usual. Illustrates examples of theoretical points from a development project in the context of a first year university course in calculus. Discusses how CAS may be used in a didactical analysis and in…

A historical approach to the teaching of calculus provides the students with a better understanding of the material than the standard approach and helps as well to introduce them to the relationship between mathematics and other aspects of our culture. Describes in some detail a course in calculus which is based on such an approach. (Author/PR)

The interrelationship between the various forms of the Planck radiation equation is discussed. A differential equation that gives intensity or energy density of radiation per unit wavelength or per unit frequency is emphasized. The Stefan-Boltzmann Law and the change in the glow of a hot body with temperature are also discussed. (KR)

Lists several problems that have proven to be successful in getting students to think about topics and notions they thought they knew. Indicates that students have not only solved the conundrums (often with help), but also developed them further into research projects. (Author/ASK)