Provided is an activity designed to give grades 7-12 students opportunities to discover numerical patterns and to derive general conclusions from observing data. The activity focuses attention on patterns in products such as 33x34, 333x334, and 3333x3334. Three worksheets and answers are included. (JN)

An investigation concerning the sum of square digits is described to show college mathematics students how mathematicians really work. A computer program is included. (MNS)

Six seven-year-old children were interviewed to investigate the quality of their solutions to whole-number tasks. Detailed analyses are provided of interviews with a girl who displayed an operative counting scheme (numerical extension) and a boy with a figurative counting scheme (intuitive extension). (MNS)

Recent research indicated that properly structured, meaningful counting activities can lead to improved performance in both number skills and logical operations. Suggested counting activities are then presented. (MNS)

A nine-year-old's conception of fractions was compared with his knowledge of units. He had effective schemes for solving some partition problems but did not consistently use units of different sizes in interpreting fractions. His solutions to equivalence problems showed no coherent method of verification. (MNS)

The problem of finding cube roots when limited to a calculator with only square root capability is discussed. An algorithm is demonstrated and explained which should always produce a good approximation within a few iterations. (MP)

Several subtraction algorithms are analyzed to see if they involve borrowing. The main focus is on an analysis of a procedure called the residue method. The operational arithmetic which underlies the symbolic manipulations is examined and conditions where the method does and does not use borrowing are highlighted. (MP)

A program designed to calculate pi using a Monte Carlo simulation based on "throwing darts" at a quarter circle of unit radius inscribed in a unit square is presented. (MP)

A finger method for subtraction that has proved successful with many young subtraction-troubled mathematics students is presented. (MP)

Calculator use by kindergarten and first-grade pupils was examined to see whether they could perceive and use the "counter button." Results indicated pupils at this age could use calculators as a tool, and further research is encouraged. (MP)

Some techniques for developing the ability to multiply and divide by powers of ten with ease and understanding are presented. (Author/MK)

Describes the accomplishments and life of the gifted Chinese mathematician Hua Lo-Keng. Hua is noted for his efforts in popularizing mathematics and for his work in number theory, in particular his contributions to Waring's problem. Hua has published 150 papers in respected journals and is the author of nine books. (Author/DS)

This is a review of the current research in mathematics involving breadth of ideas. Research includes topics in number theory, classification of all finite simple groups, the representation of group aids in their application to the study of symmetry. (Author/SA)

Five intuitive explanations of division by zero that arise from the common models used in the elementary school to introduce whole number division are presented. (MK)