This article presents two classroom episodes in which students were exposed to the value of asking questions and to the different roles played by proof in mathematics. The conversation in the two episodes is outlined in the article. The setting was a classroom of fifteen good high-school students, who were studying calculus. These episodes…

The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her "paradigmatic physical" context and begins to address…

The idea of a graphing portfolio and its implementation in two levels of traditional university calculus courses is described. The activity of graphing helps students to gain a broader and deeper understanding of the connection between a function and its graph.

States the principal-agent theory is difficult to teach because of its technical complexity and intractability. Indicates the equilibrium in the contract space is defined by the incentive parameter and insurance component of pay under a linear contract. Describes a graphical approach that students with basic knowledge of algebra and…

In this article, the author describes an individualized term project that is designed to increase student understanding of some of the major concepts and methods in multivariate calculus. The project involves having each student conduct a complete max-min analysis of a third degree polynomial in x and y that is based on his or her social security…

Developing students' abilities to communicate technical information is increasingly becoming a higher priority. A calculus course is an appropriate setting for the beginning of this development. In particular, this article relates the details behind a letter-writing assignment that the author has created to address this development.

This note provides a simple method to extend the usual Leibniz rule for higher derivatives of the product of two functions to several functions, which is within the reach of freshman calculus students.

This paper discusses a result of Li and Shen which proves the existence of a unique periodic solution for the differential equation x[dots above] + kx[dot above] + g(x,t) = [epsilon](t) where k is a constant; g is continuous, continuously differentiable with respect to x , and is periodic of period P in the variable t; [epsilon](t) is continuous…

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

Free, open, online homework help sites appear to be extremely popular and exist for many school subjects. Students can anonymously post problems at their convenience and receive responses from forum members. This mode of tutoring may be especially critical for school subjects such as calculus that are intrinsically challenging and have high…

Calculators used widely by students, teachers, scientists, engineers and many others provide an interesting case study of a compelling technology that has helped change the way many professionals work. They not only help in enhancing problem solving skills of most individuals, but also help visualise solutions to problems in a better way. Research…

The history of Fermat's Last Theorem, recounted in the theatrical piece "Fermat's Last Tango," is a useful vehicle for introducing students to the variety of personalities, processes, and products involved in advanced mathematical investigation. The musical's accessible, informative, and positive portrayal of mathematicians and their work is…

We provide an overview of the Calculus Pilot Project that was undertaken by the Rochester Institute of Technology in the 2001 and 2002 academic years. A brief discussion of demographics is followed by a description of three specific steps that, in concert, increased student success rates by over 16%. (Contains 3 tables and 5 figures.)

A primary gateway to a career in engineering is the attainment of the bachelor of science degree in engineering. In contrast, a common barrier to becoming an engineer is failure to attain the degree. Those variables that are related to college graduation are often in place prior to college admission. The purpose of this study was to examine the…

Despite its frequent use, there is little understanding of the concept of differential among upper high school and undergraduate students of physics. As a first step to identify the origin of this situation and to revert it, we have done a historic and epistemological study aimed at clarifying the role and the meaning of the differential in…