Included in this section are brief articles on making up a story to explain a graph, the inverse of a function of a single variable, and exotic horse-race wagering and combinatorics. (MNS)

This paper describes student difficulties in first-year calculus classes and suggests some instructional strategies to address these difficulties. Participants in this study were 200 low socio-economic background freshmen majoring in business in Brazil. Results show that the main difficulties are related to lack of understanding of algebraic…

The lesson details an approach to teaching positive and negative numbers which uses number pairs and generates inverses that initially avoid any mention or use of negative signs. The material moves pupils from development of key concepts to the use of more standardized notation for number operations. (MP)

The approach discussed intuitively illustrates how a problem can be analyzed by breaking it down into parts. The method makes extensive use of graphs of absolute value functions and is broken down into three stages. Each stage is covered in some detail. (MP)

The usual methods for solving quadratic equations are noted to require either the use of numerical formula or curve plotting on graph paper. The method described here enables pupils to solve equations using only a 45 degree setsquare, graph paper, and a pencil for those which have both real roots and real coefficients. (Author/MP)

A technique for teaching the graphing of polar coordinate equations is presented. This approach involves the use of an auxiliary graph in rectangular coordinates and is thought to aid students in understanding of problem-solving situations such as in dealing with points of intersection and determination of limits of integration. (MP)

An unusual shape is considered, and properties and steps in drawing it are detailed. The focus is on development and presentation of a computer program that will draw the curve. The program is written in BASIC with special plotting commands for a Techtronix computer, but is adaptable to other systems. (MP)

Activities designed for pupils to read and draw distance-time graphs and use the slopes to draw conclusions about car speeds are presented. Worksheets designed for duplication for classroom use are included, and suggestions for supplementary activities involving speed-time graphs are provided. (MP)

A program designed to plot three-dimensional graphs is described and presented. The program allows the user to select maximum and minimum ranges for X, Y, and Z, and can enlarge a graph on the screen or look at a portion away from the origin. It is in Applesoft BASIC. (MP)

A discussion on the general equation of a line shows how students can be lead to discover mathematical properties, find how one discovery leads to another, see how different branches of mathematics can lead to a solution, and be provided with a starting point for studying special mathematical topics. (MP)

Presents a method for graphically illustrating Le Chatelier's principle, suitable for the general chemistry undergraduate. (CS)

This reprint of a Project Solo curriculum module discusses graphing by computer, gives an example of a BASIC program used to graph a second degree polynomial, and provides suggested exercises in programing. (MK)

Graphs and charts are discussed in terms of levels of applications and skills necessary for effective use. Five activities, most appropriate for upper-elementary or junior high students, are suggested. (MK)

This article discusses procedures that have been developed to empower students with disabilities to take responsibility for graphing data reflecting their own academic performance. It discusses training methods for teaching students self-graphing and the benefits of self-monitoring. Examples are provided of different types of computer graphs.…

Graphing activities shouldn't end with data collection; they can be vehicles for communicating information, tools for stimulating discussion and debate, and techniques for engaging students in real mathematical thinking. Graphing activities for primary and intermediate students are suggested. (IAH)