When problems defy solution, mathematicians can settle for "almost." This branch of mathematics (called computational complexity) encompasses both the number of parts involved in a problem and the intricacy of their interrelatedness. Current research in this area is discussed, considering various computer applications involved. (JN)

Several brief articles are included in this section. "Purple Puzzlers" are challenging problems for algebra students. "Linear Invaders" is a game to reinforce concepts of graphing lines. "The Diagonal Method" is used to prove that the real and natural numbers cannot be put into one-to-one correspondence. (MNS)

Index cards, masking tape, pizza shells, golf tees, and empty soda bottles can be used to make manipulative objects to be used in children's mathematics games. Twenty-two games that provide practice in number drills and problem solving are described, along with instructions for making objects needed for the games. (PP)

Discusses two computer programs ("Billiard Ball" and "Taxman") that foster the development of higher-level thinking skills in children. Indicates that children develop such skills as planning ahead, analyzing, and using models/diagrams in the first program. Includes list of 26 programs with price, source, hardware needed, and…

Two successful procedures for evaluating problem-solving performance in the classroom are shared. Five goals for teaching problem-solving are noted, followed by a discussion of evaluating a child's performance through joint use of: (1) analyzing written work; and (2) observing and questioning students. (MP)

University graduates in China are viewed as the new mandarin class in China. University entrance examinations are seen as the modern counterpart of the long tradition of civil service examinations. It is noted that China's 630 universities and colleges only accommodate four to five percent of those seeking admission. (Author/MP)

Seven applications problems are presented for gifted students to solve by writing microcomputer programs. (MNS)

This game uses attribute blocks to encourage the formation of problem-solving strategies, provide drill in the addition of randomly generated numbers, and aid in pupil recognition of pictorial representations of geometric shapes. The material is based on the psychological principles common to other attribute games. (MP)

The game of Yahtzee is analyzed to some extent through methods of elementary probability. Several different problems are posed, and these serve to illustrate both mathematical concerns and game play strategy. Solutions are provided to all questions at the conclusion and suggestions for further questions are presented. (MP)

Results are presented of an impromptu exploration of polar formulas for volumes of revolution for certain plane regions. The material is thought to be unique, and to offer room for student exploration. It is felt pupil investigation can lead to increased pupil interest in both polar coordinates and calculus. (MP)

The topics of computer-assisted instruction, computer-augmented problem solving, and computer-managed instruction are discussed. In the field of computer-assisted instruction, uses of the computer for drill and practice, tutorial purposes, and simulation are examined. (Author/JN)

Performance was contrasted on mathematical story problems in two formats, a drawn version and the usual verbal one, with 262 fifth graders. The drawn format resulted in superior problem-solving performance. There was a significant ATI between field independence-dependence and format treatments, although the overall treatment effects were not…

A problem is detailed which has a solution that embodies geometry, trigonometry, ballistics, projectile mechanics, vector analysis, and elementary computer graphics. It is felt that the information and sample computer programs can be a useful starting point for a user written code that involves missiles and other projectiles. (MP)

A sample problem shows some pitfalls in approximating square roots when working with calculators or computers. (MP)

Teaching ideas related to the instruction of decimal division as the opposite of multiplication, an approach to approximating logarithms that help reveal their properties, and the simple creation of algebraic equations with radical expressions for use as exercises and test questions are presented. (MP)