An approach to how to expand explorations of determinants is detailed that allows evaluation of the fourth order. The method is built from a close examination of the product terms found in the expansions of second- and third-order determinants. Students are provided with an experience in basic mathematical investigation. (MP)

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)

Variations on a card trick are noted, with a formula for generalizing them. Another trick which can be proved with algebraic principles is then presented. (MNS)

Work with recurring decimals provides pupils with an opportunity for exploration and examination of a wide variety of mathematical ideas and strategies. Examples of work done by one group of pupils who were presented with an opportunity to explore such decimals is featured. (MP)

Three alternative methods of finding averages of two numbers are presented. (MP)

Two mental algorithms, one for addition and one for subtraction, are described. It is felt such algorithms should be taught explicitly. The usual process taught for paper and pencil is seen to inhibit mental arithmetic, and a need to include mental algorithms in the regular mathematics curriculum is promoted. (MP)

An approach to teaching pupils the long division algorithm that relies heavily on a consistent and logical approach to estimation is reviewed. Once learned, the division estimator can be used to support the standard repeated subtraction algorithm. (MP)

Examples of student-developed methods for dividing fractions and dividing and multiplying whole numbers are presented. Both are selected to show mathematical creativity in general mathematics students which would often be overlooked. (MP)

A procedure for constructing a magic cube is presented, with related teaching activities appropriate for students familiar or unfamiliar with the algorithm covered. (MP)

A study to investigate one of the mechanisms teachers may use to convince themselves incorrectly that students have learned science concepts requiring formal operational ability is presented. The investigation indicates instructors may actually teach and test for memorization of algorithms rather than understanding. (MP)

Interesting mathematical questions that require computations involving fractions, percentages, and decimals are presented. The material is designed for students in the middle school grades, but many of the ideas could be used with higher or lower level pupils. (MP)

Contrary to Anderson (EJ 187 936), his rule for equation identification is a necessary but not sufficient condition; furthermore, the choice of two-stage or ordinary least squares depends on results and not on methodological properties of estimators. Modification of Anderson's rule and a means for choosing between estimates is offered. (Author/CP)

Presented three algorithms to university students in an introductory laboratory chemistry course and found that differences in the effects of representation modes--flow charts, lists, and standard prose--were complex and changed over 10 lab sessions. There was no evidence that representation mode affected critical thinking ability or final grade.…

Explains that Year 5 students in ten British schools took a mathematics division test twice in the school year. The test involved context and bare problems to identify changes in approach as the standard algorithm was introduced. Reports that 52 percent of students gained a higher score on the second test. (CMK)

Discusses ranking techniques for document retrieval and proposes an evaluation, or filtering, technique that reduces costs and memory usage by early recognition of which documents are likely to be highly ranked. Highlights include index design, ranked query evaluation, reducing the number of accumulators, inverted file structures, and experimental…