One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

It is shown that the well-known Lorentz formula for time dilation can be derived from a distance-time graph plotted for a spaceship communicating with Earth.

Inscriptions are central to the practice of science. Previous studies showed, however, that preservice teachers even those with undergraduate degrees in science, generally do not spontaneously produce inscriptions that economically summarize large amounts of data. This study was designed to investigate the production of inscription while a group…

Research findings show the difficulties younger students have in working with graphs. Higher mental operations are necessary for a skilled interpretation of abstract representations. We suggest connecting a concrete representation of the modeled problem with the related graph. The idea is to illustrate essential mental operations externally. This…

We describe a computer tutorial that introduces the concept of the steady state in enzyme kinetics. The tutorial allows students to produce graphs of the concentrations of free enzyme, enzyme-substrate complex, and product versus time in order to learn about the approach to steady state. By using a range of substrate concentrations and rate…

This paper discusses a research study that focused on middle grades students' abilities to read and to move between different graphical representations before and after instruction. The data analyzed were collected from a group of 76 sixth grade students who were in 3 different mathematics classes in a middle school located in central North…

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…

This book contains 40 lessons in problem solving divided into five chapters. Chapter 1 contains several lessons in which solutions are derived through investigation of numerical patterns. Chapter 2 contains lessons in which problem-solving situations are presented in a graphical context. It also includes two lessons in which students construct…

Information graphics or diagrams are two-dimensional maps of relationships that present information. Creators and interpreters of diagrams need to know what makes some diagrams more effective in communicating information. This paper suggests a theoretical framework for diagram classification to make this possible. This framework consists of two…

The statistical analysis of data from a single-subject design is somewhat controversial. The procedure most often chosen to examine data from a single-subject design involves the visual inspection of the graphed outcome variable over time. Problems associated with this procedure are discussed, and questions about the use of traditional statistical…

Outlines a teaching method using graphs for explaining phase changes and the effect of pressure and the relationships between temperature, entropy, enthalpy, energy, Gibbs function, Helmholtz function and volume. (GS)

Library directors at 164 universities, colleges, and community colleges in California were surveyed in fall 1986 on their hiring of temporary librarians over 5 fiscal years, 1982-83 through 1986-87. The response rate was 90%. Results indicated that: (1) all types of academic libraries employ temporary librarians; (2) the number of temporary…

The use of computer graphic techniques with basic student enrollment statistics is examined to promote understanding of changes in student flow as a function of spatial distribution. Basic initial student enrollment data that serve as input into predictive flow models were modeled at Eastern Kentucky University. The following commercially…

A graphical method is proposed which allows one to visualize a real matrix and its inverse. In this scheme, various special properties of the matrix are easily recognized. Up to 5x5 matrices can be graphed on an average page if the range of values does not exceed two orders of magnitude. (Author/LS)

Two new types of graph paper are described; focus-focus conic paper and focus-directrix paper. Both types make it easier to draw families of conics. Suggestions for further work are given as is a method for establishing a connection with other ways of looking at the conic sections. (LS)