Problems involving multicolored cubes are discussed with examples of Instant Insanity and Rubik's Cube cited. Sections cover defining chameleonic cubes, producing such a cube, and extending understanding to multidimensional cubes. One theorem proved is that for each positive integer, every cube of that size is chameleonic. (MP)

It is viewed understandable that many teachers consider fractions one of the most difficult mathematical topics to teach. School experiences need careful planning to include sequential activities which develop accurate concepts, and concepts are thought best developed by activities which move along the concrete-to-abstract continuum. (MP)

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

Describes techniques intended to provide the teacher (or student) with insights to the solution of the problems of constructibility of squares of area c and determination of the numbers of squares, and a method for the construction of constructible integers of area c. (DS)

An excursion in applied mathematics is detailed in a lesson deemed well-suited for the high school student or undergraduate. The problem focuses on an experimental missile guidance system simulated in the laboratory. (MP)

The use of the Computer to Help In Problem Solving (CHIPS) is described, along with Small Computers Aiding Mathematical Problem-solving and Investigations (SCAMPI). Sample activities involving combinations and "shuffles" of elements are used to highlight the use of computers, with the BASIC programing language featured. (MP)

It is noted that students sometimes have the misconception that square roots of integers are evenly spaced. The difficulty seems suited to approaches with calculators and computers, and is viewed arithmetically, graphically, and algebraically. It is suggested that differences between roots of successive pairs of consecutive integers be examined…

The need for incorporating algorithmics into mathematics instruction is presented. The proliferation of computers is seen to have made the designing of algorithms an essential skill. Examples are given, and the view that mathematics will lose much prestige and importance if algorithmics is not integrated into it is presented. (MP)

Gardening is the theme for a series of worksheets that present a variety of problem-solving activities that emphasize the construction, use, and interpretation of diagrams, graphs, and tables. The material is designed for duplication for classroom use, and suggestions for ways of going further are provided with each activity. (MP)

The mathematics of an educational game commonly known as "Frogs" is analyzed to see different mathematical concepts imbedded in it. (MP)

Ways are identified in which typical textbook word problems can be used to better fulfill their role in the development of mathematical concepts and a sound instructional program of mathematical problem solving. (MP)

An extensive investigation of pupil understanding of fractions at the secondary education level showed the majority tended to avoid using fractions, could not generalize about them, and probably did not see them as an extension of the set of whole numbers. (MP)

Some methods of proof of traditional algebra problems using geometric methods are explored. The techniques used come from the original Greek approaches to these mathematical questions. (MP)

The concept and use of proof in mathematics are examined. Uses and purposes of proofs are listed and described. (MP)

Number walks are suggested as reinforcement activities for newly learned concepts. Children walk along a display of mathematical tasks, responding to each as they walk along. (MP)