Presents examples which help students think visually about algebraic operations on vectors and the associated mappings of the plane. The pictures help students actively participate in defining new functions by enabling them to compose simpler known functions. Conversely, functions can be factored into the composition of simple functions. (JN)

Examines the study of transformations which result from cross-sections of a prism. The study involves some model-making, which in turn introduces some new problems of drawing and construction. The material is presented with the practicalities of classroom teaching in mind. (Author/JN)

Deriving all Pythagorean triples from simple patterns within an addition table is presented, with formulas included. (MNS)

Using sweeps to find areas, applications of reflections to miniature golf, and zeroing in on zeroes are each considered in the brief articles in this department. (MNS)

Eleven experiments are presented, extending ideas for graphing functions presented in two previous articles. Computer program listings are included. (MNS)

Cognitive psychology, artificial intelligence, and computer technology have advanced so much that it is feasible to build computer systems that are as effective as intelligent human tutors. Computer tutors have been developed for teaching students to do proofs in geometry and to write computer programs in the LISP language. (JN)

Presents a problem to produce a chart in which a driver can look up the time in seconds it took to travel one mile and find out how fast the car was traveling in miles per hour. Several programs to solve the problem are listed and discussed. (JN)

A narcissistic number is a positive integer equal to the sum of its digits raised to an integral power. For example, 15 is equal to 1-cubed plus 5-cubed plus 3-cubed (a narcissistic number of order three). A computer program to find narcissistic numbers up to 10,000 is given and discussed. (JN)

Having students try to generate their own random numbers can lead to much discovery learning as one tries to create 'patternlessness' from formulas. Developing an equidistribution test and runs test, plus other ideas for generating random numbers, is discussed, with computer programs given. (MNS)

The properties of the cube are explored. A set of activities is given that forms the basis of a class project on discovery. (MNS)

Imaginative ways of using calculators to explore decimal fractions with secondary school and some middle school students are given. Four explorations on terminating and repeating decimals, the length of periods, and relationships are described. An appendix presents mathematical proofs. (MNS)

Issues about computer use are addressed by a discussion activity designed to help students think about situations and understand various points of view. Four situations are given, each presented from the viewpoints of four persons. (MNS)

Parallel surveys showed that mathematics is a subject that loses its appeal with further study. New college students beginning mathematics courses were compared with students entering postgraduate teacher training courses by contrasting their experiences in secondary school mathematics and their anticipation of experiences in college mathematics.…

Two versions of a page of exercises using set ideas are presented, one in plain language and one in technical language. Some questions and answers about the appropriateness of set terminology and symbols are then given. (MNS)

The use of trial-and-error strategies to solve problems is endorsed. Types of problems with which trial and error is effective are discussed, with examples of how it is used, and teaching considerations are briefly considered. A computer program for one problem is included. (MNS)