A modern approach to the study of mathematical structure in the fifth class (grade eight) of French schools is described. Students make a number of experiments with various mathematical concepts in an attempt to discover interesting properties. (FL)

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)