Presents a college calculus program based on the discovery method and the educational psychology literature used to develop it. Lists departmental, educational, and calculus reform goals, and describes characteristics of the program, including relaxed atmosphere, use of visualization, and supplemental teaching techniques. (13 references) (MKR)

Proposes a calculus curriculum combining formative knowledge, mathematical foundations, and instrumental knowledge in mathematics. Discusses each of these components, the organization of a core calculus course, and the use of problem solving in calculus instruction. (10 references) (MKR)

Compares experiences in two calculus courses for non-science majors: a traditional business calculus course and a course using materials from the Calculus Consortium based at Harvard. The latter program is recommended. (MKR)

Hypermedia provides an easy-to-use option for adding visualization, via the computer, to the classroom. Some examples of this medium are presented, including applications in basic linear algebra and calculus, and a tutorial in electromagnetism. (Author)

Offers calculus students and teachers the opportunity to motivate and discover the first Fundamental Theorem of Calculus (FTC) in an experimental, experiential, inductive, intuitive, vernacular-based manner. Starting from the observation that a distance traveled at a constant speed corresponds to the area inside a rectangle, the FTC is discovered,…

Presents one model for a liberal arts mathematics course that combines probability and calculus. Describes activities utilized in the course to heighten students' interest and encourage student involvement. Activities include use of visualization, take-home tests, group problem solving, research papers, and computer usage with DERIVE computer…

Describes numerical differentiation and the central difference formula in numerical analysis. Presents three computer programs that approximate the first derivative of a function utilizing the central difference formula. Analyzes conditions under which the approximation formula is exact. (MDH)

Describes an attempt to increase business calculus students' desire to learn by overcoming typical low levels of mathematical preparation and motivation utilizing a corporate structure managed by the students. Includes 10 sample problems from fictitious corporations. (JJK)

Discusses and provides sample lessons of learning by discovery and weekly problem sets, which are presented as alternative methods for teaching college calculus. Both approaches stress conceptual understanding and guide the students to explore the ideas of calculus in small groups in a computer laboratory setting. (JJK)

Describes the mechanics of group work in the college mathematics classroom specifically group formation, preliminary class work, class and group discourse, individual and group assignments, and impact on test taking. Includes examples from a first-semester calculus course. (JJK)

To build understanding of, and the ability to use, first-year science and engineering calculus, students were introduced to differential equations and asked to carry out research on differential equation modeling projects. Describes a model for the research paper; appendices provide a copy of the student handout and five examples of student…

Describes a course designed by Moravian College, Pennsylvania, to integrate precalculus topics as needed into a first calculus course. The textbook developed for the course covers the concepts of functions, Cartesian coordinates, limits, continuity, infinity, and the derivative. Examples are discussed. (MDH)

Short essay questions are introduced into the calculus course as a technique to involve students with their own learning. Provides (1) instructions to the student for writing the report; (2) results of using the technique; and (3) reasons for using writing in mathematics classes. (MDH)

This paper describes the use of cooperative groups in teaching calculus. It discusses benefits and drawbacks of group techniques and presents reactions from both students and the author. (Author)

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)