Abstract
It is the purpose of this study to investigate the philosophical and psychological foundations of the problem of using algebra as a means of teaching high school students to do critical and reflective thinking when dealing with problems of everyday living as well as when resolving problems involving quantity or space. The method of attack will be a review of the literature available. This review must yield the philosophical and psychological possibility, the cultural value, and the implications for education of such teaching. Further, it is not simply the intent to criticize; therefore, the study must also lay at least a minimum foundation for any proposed revisions in the course of algebra.