Errors and Misconceptions in College Level Theorem Proving

ALGEBRA Abstract algebra, the course from which our examples are selected, is a three hour per week year sequence usually taken in the third year of college. At this stage in a student's education the rapid development of reasoning skills is important and we have taken it as a major objective of the course.algebra, the course from which our examples are selected, is a three hour per week year sequence usually taken in the third year of college. At this stage in a student's education the rapid development of reasoning skills is important and we have taken it as a major objective of the course. Abstract algebra is a particularly good vehicle for teaching reasoning because the proofs are less complicated than, say, advanced calculus, and the notation is not particularly complex. It is also useful that students have not seen this topic before and it is difficult for them to lift proofs from textbooks, so they must rely on their own reasoning and ideas.algebra is a particularly good vehicle for teaching reasoning because the proofs are less complicated than, say, advanced calculus, and the notation is not particularly complex. It is also useful that students have not seen this topic before and it is difficult for them to lift proofs from textbooks, so they must rely on their own reasoning and ideas. THE SOCRATIC-MOORE METHOD We provide the students with a short set of notes containing definitions, theorems, problems, and occasional examples, but no proofs or solutions. We do not give formal lectures although we answer questions. Students present their work in class and we provide evaluations, detailed criticisms and suggestions.