The investigation reported is primarily a description of how college students solve or fail to solve algebra equations. Protocols were collected from two groups of college students; one group was expected to be good solvers, the other group contained many poor solvers. The investigators sought to identify and classify the difficulties students had, and they tried to guess the mechanism which produced those difficulties. They compared the work of successful and unsuccessful solvers, looking for ideas that might help make more solvers be successful, and they tried to identify what must be learned by the student of equation solving. The discussion of findings includes: identification of three types of errors, and sections devoted to kinds of knowledge in algebra, meaning in algebra, errors and the psychology of skill, and characteristics of good solvers. (MK)