As hypothesized, less advanced students benefited most from a high instructional support treatment (personalized system of instruction) used in an introductory calculus course. Furthermore, as level of prior mathematics preparation increased, the achievement differences between the high and low instructional support (lecture) decreased. (Author/CP)

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…

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)

Investigates how animation is used to improve students' comprehension of the limit concept in an experimental course in which the main topics are approximation and interpolation by Taylor polynomials. Uses Mathematica software to generate the dynamic graphics, visualize the process of convergence, and give meaning to the definitions. Analyzes…

Describes and compares the Archimedes and the Zu Xuan approaches in computing the volume of sphere in the East and West. Discusses how to motivate a group of teacher trainees to relate these two approaches to the evolution of calculus ideas. (Author/KHR)

Presented is a method of interchanging the x-axis and y-axis for viewing the graph of the inverse function. Discussed are the inverse function and the usual proofs that are used for the function. (KR)

Discussed are the vital properties that an operator must have to be called a derivative and how derivatives work. Presented is an extension of the derivative that uses least squares to find the line of best fit. (KR)

Reports on the use of technology to enhance the teaching of ordinary differential equations, gives examples of laboratory activities using cooperative learning, and discusses assessment of student learning. MacMath, TI-81 graphing calculators, and Maple were used in the course. (Author/MKR)

Six specific instances in which supplemental instruction (SI) leaders guide student inquiry in college algebra and calculus are described. The active learning strategies used in the situations are analyzed, focusing on the role of the leader and the support provided by SI leader training and supervision. (MSE)

Described is an activity that uses the techniques of integral calculus to determine the volume of a bundt cake. The cake is used as an example of a solid of revolution. Included are the procedures and assumptions used by students to solve this problem. (KR)

Describes a classroom experience in which the teacher experiments with integrating mathematics history into a calculus class by presenting a historical problem taken from L'Hopital to be solved by the students. Extracts the role that history can play in teaching mathematics from the experience. (MDH)

The crisis confronting calculus and mathematics education generally results from a number of failed assumptions implicit in the dominant lecture-homework-exam methodology used in teaching mathematics. Positive resolution of this crisis can be found in adopting a noncompetitive, collaborative approach to mathematics education. (Author)