An algebra in which the basic operations correspond to lowest common multiple and greatest common factor is developed through questions which can be explored by the able high school mathematics student. (FL)

The author discusses how quantitative aspects enrich and clarify our knowledge of history. Statistical concepts of population and economic value are described for the Pilgrims, the American Revolution, and the Civil War. (RS)

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)