RUME 14 (Volume 2)
2011
Portland, Oregon
WHERE IS THE LOGIC IN STUDENT-CONSTRUCTED PROOFS?
Page: 445
Often university mathematics departments teach some formal logic early in a transition-to- proof course in preparation for teaching undergraduate students to construct proofs. Logic, in some form, does seem to play a crucial role in constructing proofs. Yet, this study of forty-two student-constructed proofs of theorems about sets, functions, real analysis, abstract algebra, and topology, found that only a very small part of those proofs involved logic beyond common sense reasoning. Where is the logic? How much of it is just common sense? Does proving involve forms of deductive reasoning that are logic-like, but are not immediately derivable from predicate or propositional calculus? Also, can the needed logic be taught in context while teaching proof-construction instead of first teaching it in an abstract, disembodied way? Through a theoretical framework emerging from a chunk-by-chunk analysis of student- constructed proofs and from task-based interviews with students, I try to shed light on these questions.