It is surprising to students to learn that a natural combination of simple functions, the function sin(1/x), exhibits behaviour that is a great challenge to visualize. When x is large the function is relatively easy to draw; as x gets smaller the function begins to behave in an increasingly wild manner. The sin(1/x) function can serve as one of…

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

These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics K-6. In view of the experiences of other curriculum groups and of the general discussions since 1963, the present report initiates the next step in evolving the "Goals".…

Solves the problem of defining a smooth piecewise linear approximation to a given function. Discusses some alternative approaches to the problem. (YP)

Discusses a classroom presentation using a Tonka toy truck's forward and backward motion that (1) develops a graphical representation of the truck's one-dimensional motion; (2) creates graphs representing constant velocity; (3) leads students to a definition of average velocity; and (4) introduces the concept of instantaneous velocity. (MDH)

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…

Described is a way that elemental mathematics can be applied to explain an astronomical phenomenon. The fact that the extreme of sunrise and sunset do not occur on the shortest or longest days of the year is analyzed using graphs and elementary calculus. (KR)

Discussed are several activities suitable for students from middle school through high school designed to furnish concrete experiences with the concepts of rate of change and slope and approximating areas, the central themes of differential and integral calculus. The implementation of national curriculum standards is stressed. (CW)

Discusses the use of computers in calculus classes. Describes activities in four laboratories providing with the problems of the laboratories. (YP)

Explains graphing functions when using LOTUS 1-2-3. Provides examples and explains keystroke entries needed to make the graphs. Notes up to six functions can be displayed on the same set of axes. (MVL)