This student discussion guide is intended to accompany "Discovery in Mathematics," a text for teachers. This guide is a part of the developing curriculum program that helps students to organize their mathematical experiences in the early school years. The materials in this booklet deal mainly with fundamental arithmetic and algebraic…

Discussed are generalizations and problem solving, unsound uses of generalizations, generalization as data, and student discovery of generalizations. (CT)

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 study was designed to investigate the effects on immediate acquisition, retention and transfer of two methods of presenting selected geometry concepts to sixth grade students. The effects of immediate acquisition and of transfer were measured immediately after presenting the lessons. The effects of retention were measured 1, 11, and 21 days…

This booklet was written for elementary school teachers who want suggestions of the type of activities suited to a mathematics laboratory. The emphasis is not that of a thorough survey of the available activities. Instead, the author uses selected examples to describe the spirit of a laboratory environment. The suggestions include arrangements of…

The first idea discusses the use of Pascal's triangle to discover the total number of gifts presented during the 12 days of Christmas. The second idea looks at an approach to viewing L'Hospital's rule that is geared toward helping beginning calculus students develop a feeling as to why it works. (MP)

Reported are the results of an experimental course taught at the ninth grade level. The course included both modern and traditional topics in algebra. Presented are a rationale for the course, a list of the topics included in the course, a description of instructional techniques and methods used in presenting and developing some of the main ideas…

An exploration approach with calculators that promotes student investigation and development of mathematical processes and concepts is highlighted. The presentation helps to highlight the enormous potential of calculators to facilitate new and imaginative approaches to certain areas of number work, and shows how student interest is promoted. (MP)

It is viewed understandable that many teachers consider fractions one of the most difficult mathematical topics to teach. School experiences need careful planning to include sequential activities which develop accurate concepts, and concepts are thought best developed by activities which move along the concrete-to-abstract continuum. (MP)