Graphs from media sources and questions developed from them can be used in the middle school mathematics classroom. Graphs depict storage temperature on a milk carton; air pressure measurements on a package of shock absorbers; sleep-wake patterns of an infant; a dog's breathing patterns; and the angle, velocity, and radius of a leaning bicyclist…

Presented are two exercises on the differential geometry of curves. A generalization dealing with smoothness conditions is given that relates the two exercises. Included are the definitions, theorems, propositions, and proofs. (KR)

Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

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

Suggests ways in which mathematical models can be presented and developed in the classroom to promote discussion, analysis, and understanding of issues related to energy consumption. Five problems deal with past trends and future projections of availability of a nonrenewable resource, natural gas. (Contains 13 references.) (MDH)

Presented is a concrete, realistic way of representing concepts of coordinate geometry. Students represent the coordinates in a living version of a five-by-five square geoboard. Procedures and examples for using this activity are included. (KR)

Examines research on computers as cognitive enhancers, focusing on applications software that includes spreadsheets, graphing, and databases. Appropriate computer-based problem-solving environments for young children are reviewed, and implications for teachers are suggested. (Contains eight references.) (LRW)

An approach to teaching electrochemical driving force that helps students comprehend the forces that govern ion flux across biological membranes and sets the stage for more elaborate analysis of biochemical signals is presented. Background information and two sample problems and answers are included. (KR)

Entering a value into a calculator and repeatedly performing a function f(x) on the calculator can lead to the solution of the equation f(x)=x. Explores the outcomes of performing this iterative process on the calculator. Discusses how patterns of the resulting sequences converge, diverge, become cyclic, or display chaotic behavior. (MDH)

This document is a collection of activity-based mathematics lessons for grades 5-8 from the "Ideas" department in "Arithmetic Teacher: Mathematics Education through the Middle Grades." Each lesson includes background information, objectives, directions, extensions, and student worksheets. A matrix is included which correlates…

This research focuses on the graphics calculator in calculus and its impact on students' abilities to work with graphical, numerical, and symbolic representations. Three courses are compared, two of which are taught with less emphasis on the use of graphing calculators. The format of the course emphasizing calculator use is more traditional than…

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…

A method of graphing multivariate data, called the star plot, is very useful in educational contexts because it provides teachers and guidance counselors with information not present in unsupplemented student achievement data. The utility of the method can be seen in analysis of data from a study of factors related to the problem-solving ability…

This document consists of 51 articles (originally published in the "Arithmetic Teacher") which provide teachers with ideas for manipulative aids and activities. Guidelines used to select articles for this collection called for them to have a clear purpose and be related to a contemporary topic in the elementary school mathematics curriculum, to…

Models of the motion of an object through space are discussed. The material begins with the simplest view possible in which gravity is the only force examined. Discussion progresses to an examination of the drag force, which is the resistive air force of the wind. Suggestions for further improvements are made at the conclusion of the presentation.…