Adapts a metaphor to draw attention to four aspects of the relationship between originator and user, and the communication medium: the problem of encoding information in graphic form, diagrams as tools for enquiry and thought, illustrations as aids to learning, and illustrations as aids to problem solving. (Author)

Presents an interesting problem intended to introduce students to an application of algebra and to help them make the transition from arithmetic to algebra. Uses different problem representations including making successive approximations, interpreting graphs, and solving equations. Discusses pedagogical issues involved. Contains 11 references.…

Investigates the extent to which visual considerations in calculus can be taught and be a natural part of college students' mathematical thinking. Recommends that the legitimacy of the visual approach in proofs and problem solving should be emphasized and that the visual interpretations of algebraic notions should be taught. (YP)

Described is a situation where students are allowed to enlist the aid of a computer graphing program to produce graphs for their lab reports. (KR)

In this paper, two classes of graphs of arbitrary order are described which contain unique Hamiltonian cycles. All the graphs have mean vertex degree greater than one quarter the order of the graph. The Hamiltonian cycles are detailed, their uniqueness proved and simple rules for the construction of the adjacency matrix of the graphs are given.…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

This study examined problem solving as a function of display type (table/graph) and numeric function (linear/nonlinear) in four problem solving domains. Twenty-two stimulus problems were developed, and line graph and table displays were constructed for each problem. Half of the displays contained linear numeric functions and the other half…

Graphical solutions are illustrated for several algebra problems including finding roots of a quadratic equation, solving mixture and motion word problems, factoring the difference of two squares, and constructing the square root of a positive number. (MN)

A restaurant menu is used to apply mathematics to real situations. A variety of mathematical problems, as well as applications to other content areas, is suggested. (JT)

Curiosities offer an interesting alternative to traditional methods of attacking problems. An illustrative situation is given, with graphical, computer, and analytical methods used to solve the problem. (MNS)

Presents ideas related to: (1) graphs (considering patterns, periodic functions, and problem-solving); (2) curing common errors (such as an incorrect way of canceling); (3) the median of a trapezoid; and (4) using a telephone directory to teach probability, graphing, random-number tables, reading tables, calculating percentages, and other topics.…

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)

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)

The use of a computer to help honors second-year algebra students graph quadratic and higher-order polynomials is discussed. Sample computer programs are included. (MP)