Reported are the results of a study which investigated the influence of certain variables within the method of individually guided discovery in mathematics. The independent variables considered were the concepts of ordered partitions and permutations, the level of consolidation or practice after discovery, and the teachers. Also considered were…

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

Two studies investigated the effects of verbalization of discovered generalizations on the retention of those principles. (SD)

This study is one of several conducted by the authors in their investigation of the use of "higher order rules" in the solution of problems. The focus of the current experiment was determination of the compatibility of identified rules with the knowledge of average teenagers, and of the extent to which instruction in higher order rules…

The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)