9: Activity Learning

This review of activity learning in mathematics covers publications from January 1964 through December 1968. In the context of this article activity learning is taken to mean school learning settings in which the learner develops mathematical con-cepts through active participation. This process may involve the manipu-lation of physical materials, the use of games, or partaking in experiments with physical objects. Theory and research on the effects of this type of activity will be discussed in this article under manipulative learning. The second form of activity learning discussed here is presented under the rubric of discovery learning. In this form of learning, the student actively engages in the process of forming mathematical ideas for himself, but does not necessarily use any physical devices in learning mathematics. This review is generally restricted to those studies concerned with classroom instruction in mathematics; it does not include research conducted basically for psychological considerations. There were quite a number of empirical studies, particularly in dis-covery learning, in which comparatively standard research methodology was used. However, much of the research in manipulative learning in mathematics would fit into Johnson's (1966) categories of action-natural-istic or philosophical research. The discovery research reviewed was centered on the North American continent. However, development and research work in manipulative ma-terial and games-oriented learning in mathematics seem to be worldwide in scope (Weaver, 1967). Work has been completed in England (E.