STEP BY STEP PROOFS AND SMALL GROUPS IN FIRST COURSES IN ALGEBRA AND ANALYSIS

Mathematics majors often have problems with the proofs that occur in first courses in algebra or analysis. This article presents a two-part approach to proofs, involving the selective use of both step by step proofs and small group work, that has been successful in several different settings. Both the approach and how it can be implemented are discussed in some detail. Examples illustrating how this two-part approach can be used in first courses in abstract algebra, linear algebra, and real analysis are given, as is a rationale for its use.