The development and use of a taxonomy for describing the way distance students plan work and use course materials to complete mathematics exercises is detailed. The taxonomy was developed from an exploratory study but the initial results are viewed as having implications for educational use in many situations. (Author/MP)

The development of symbolic computer algebra designed to manipulate abstract mathematical expressions is discussed. The ability of this software to mimic the standard patterns of human problem solving represents a major advance toward "true" artificial intelligence. (MP)

A sample mathematical application problem that can be solved with computer programing is discussed. (MP)

An attempt is made to link the domain of mathematics and the natures and abilities of mathematicians to that which is perceptual, presentational, and implicit. (MP)

In this bibliographic essay, the author suggests commercial educational products (manipulative materials, activity cards, patterning materials, games, films and filmstrips) which can be used to promote divergent thinking in elementary and secondary mathematics instruction. Price, source, and grade level are listed for each item. (SJL)

A history of perfect numbers is presented, which briefly covers the 27 values known at this time. (MP)

A 20-question quiz on the uses of numbers in the real world is presented. (MK)

This clinical, exploratory study describes processes used by 8 ninth-graders learning to solve non-routine geometry problems and changes in those processes as instruction in heuristic methods was given. Directions for future research are indicated, and several hypotheses to be investigated are suggested. (DT)

Presents a variety of mathematical games from all over the world using pen and paper, or single-board setups. (ASK)

Presents an activity to involve students in mathematical communication and creative thinking. The activity is similar to the "pass it along" gossip game in which each person in a chain adds a piece of information. The class analyzes the resulting mathematics problem using George Polya's problem-solving techniques. (MKR)

Presents responses to a problem that appeared in the April, 1999 issue of this journal. The problem involves finding kite heights compared to each other. (KHR)

Presents a word problem designed to encourage students to create systematic methods for counting and develop probability concepts. Involves sharing eight cookies between three people. (KHR)

Features responses to a problem that appeared in the January, 2001 issue of this journal. The problem concerned finding all of the shape combinations of two colors of blocks in four-block combinations. (KHR)

Examines the balance model and identifies the issues that divide scientists. Describes learning situations that were the subject of the empirical study which involved 40 students in two 8th-grade classes. Shows the presence of negative numbers gave rise to many errors. Discusses the relevance of the balance model and analyzes the arguments put…

Presents activities designed to engage students in an experiential and theoretical application of problems in precalculus and to study geometry, coordinate systems, rates, linear applications, and the concept of function. Illustrates problem situations and includes student worksheets and a teacher's guide. (KHR)