Presents three sample problems related to arithmetic and algebra, geometry, and calculus, indicating, in each case, similar problems that could be posed. Includes a discussion of positive benefits which result by asking students "Can you derive the result differently?" (JN)

Shows that Simpson's rule can be obtained as the average of three simple rectangular approximations and can therefore be introduced to students before they meet any calculus. In addition, the accuracy of the rule (which is for exact cubes) can be exploited to introduce the topic of integration. (JN)

Ralston proposes that the decrease in the importance of calculus in the world of mathematics is accelerating and the world of applied mathematics is changing rapidly. He briefly presents arguments for discrete mathematics. Then follow reactions from McLane, Wagner, Hilton, Woodriff, Kleitman, and Lax, and a response by Ralston. (MNS)

The author argues that the existence and uniqueness theorems of elementary differential equations must be taught prior to some simple initial value problems. (SD)

Presented is a method utilizing partial derivatives for determining the energy saved per dollar by substituting bicycling for driving a car while not reducing jobs dependent upon the auto industry. (SL)

This paper focuses on high school preparation for calculus and discusses trends involving student performance, curricula, teachers, and tests. Implications for the transition to calculus in college and the mathematics major are also discussed. (KHR)

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…

In this paper are described some features of the intensive use of math software, primarily DERIVE, in the context of modeling in an introductory university course in differential equations. Different aspects are detailed: changes in the curriculum that included not only course contents, but also the sequence of introduction to various topics and…

This study investigates the relationship between enrollment in economics in seventeen institutions-scattered nationwide-and the initiation of more extensive mathematics requirements. (Author)

This article (the 1971 Presidential Address to the Mathematical Association of U. K.) makes a plea that college teachers of mathematics should be better aware of the applications of mathematics in other subjects. As an example, the author describes the use of differential equations to solve certain vibrational problems in mechanical engineering.…

A discussion of the relation between traffic density, speed and flow, used as an illustration of the ideas of functions and mathematical models. (MM)