Numerical tables of mathematical functions are in continual demand by scientists and engineers for preliminary surveys of problems before programming for computing machines. This handbook was designed to provide scientific investigators with a comprehensive and self-contained summary of the mathematical functions that arise in physical and…

Explores the effects of varying the coefficients in the general quadratic function using graphing calculators. (MKR)

Discusses a method of graphing polar equations using information from the Cartesian graphs of trigonometric functions. (MKR)

Investigates the relationship between a fourth-degree polynomial function's parameters and its graph. (MKR)

Presents an activity which focuses on the graph of sine and cosine functions and other properties that can easily be inferred from the graph. (ASK)

Explores an unexpected connection between a function, its inverse, and the arithmetic mean, algebraically and graphically. (MM)

Discusses the notion that knowledge grows exponentially and describes its growth mathematically by an exponential function. Growth patterns in subfields of knowledge or research areas are described citing related research. Interpretation of growth rate statistics and forecasts are included. Thirty-three references and statistics used for graphs…

Discussion of the nature of the algebraic and graphical representations of functions focuses on a study integrating cognitive research and the development of an intelligent tutoring system (ITS), the Function Characteristics Tutor, to evaluate the effects of pairing representations of mathematical functions on high school students. (Author/LRW)

Introduces the concept of function using graphs or pictorial representations of functions. Presents four activities for grade levels 8-14 that use the natural progression from qualitative graphs to quantitative graphs to tables to equations for introducing the theme of distance from an object as a function of time. (Author/NB)

Reports on a study of students' responses to two types of questions on final examinations in calculus. Concludes that the two kinds of understanding--pointwise and across time--are clearly distinguishable. Discusses the differences between these two types of understanding. (ASK)

The typical path of instruction in high school algebra courses for the study of polynomial functions has been from linear functions, to quadratic functions, to polynomial functions of degree greater than two. This paper reports results of clinical interviews with an Algebra II student. The interviews were used to probe into the student's…

Presents a programing subroutine which will create a graphical plot that occupies any number of columns specified by user and will run with versions of BASIC programming language. Illustrations of the subroutine's ability to operate successfully for three possibilities (negative values, positive values, and both positive and negative values) are…

Presents responses to a problem that appeared in the May 2000 issue. The problem was to determine different ways to divide 8 cookies between 3 people. Includes student work from grades 1, 3, and 5. (KHR)

Uses parametric equations and a graphing calculator to investigate the connections among the algebraic, numerical, and graphical representations of functions. (MKR)

Presents results from a study that examined students' understanding of connections between algebraic and graphical representations of functions. Discusses a possible reason for the inadequate and often absent connections that students made between them. (ASK)