An Initiation into Algebraic Culture through Generalization Activities

Abstract

Consdering algebra as a culture, this chapter looks at the introduction of algebra as a initiation process where generalization activities can be extremely effective. After a reflection on my own immersion into algebra and the evolution of attitudes toward the teaching of algebra, a teaching experiment using gerneralization activities is presented. Two generalizing activities are described in some detail, looking at the behavior of adults in the experimental group in the light of research results of high school students on tests and interviews involving the same activities. the paper concludes with a "cultural" reflection on the teaching experiment and a more general consideration of the role of generalization in the introduction of algebra.