Considers some changes that the use of graphics calculators impose on the assessment of calculus and mathematical modeling at the undergraduate level. Suggests some of the ways in which the assessment of mathematical tasks can be modified as the mechanics of calculation become routine and questions of analysis and interpretation assume greater…

Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

Discusses a precalculus project in which students create a model United Nations to present and discuss the long-term prognosis for individual countries given data on population growth and food production. Students compare exponential and linear functions to determine whether starvation will occur and prepare oral and written presentations of their…

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Some concrete examples of the use of historical materials in developing certain topics from precalculus and calculus are presented. Ideas which can be introduced with a reformulated curriculum are discussed in five areas: algorithms, combinatorics, logarithms, trigonometry, and mathematical models. (MNS)

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)

Examples of subroutines that generate both symbolic and graphic solutions to differential equations are presented for the two computer algebra systems, MAPLE and Mathematica. Included are the listings for the Mathematica procedures developed for use in this article. (JJK)

Discusses an activity which models the building of a tunnel by ants using the definitions of derivative and indefinite integral from calculus. Includes a discussion of reasonableness and interpretation of the problem. (MKR)

Discusses a pedagogical approach to calculus based on the question: What kinds of problems should students be able to solve? Includes a discussion of types of problems and curriculum threads for such a course. Describes a projects-based calculus with examples of projects and classroom activities. (Author/MDH)

This article describes a calculus lesson that illustrates the nature of cycles in simple systems of nonlinear differential equations through the use of the Lotka-Volterra predator-prey model as incorporated in the computer software package, Phaser (version 1.0). (JJK)

Discusses the problem of finding the amount of fence it would require for the outfield fence of a baseball field of given dimensions. Presents different solution methods for each of the levels from grades 9-12. The different methods incorporate geometry, trigonometry, analytic geometry, and calculus. (MDH)

Presented are student activities that involve two standard problems from geometry and calculus--the volume of a box and the bank shot on a pool table. Problem solving is emphasized as a method of inquiry and application with descriptions of the results using graphical, numerical, and physical models. (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…