RUME 14 (Volume 2)
2011
Portland, Oregon
HOW MATHEMATICIANS USE DIAGRAMS TO CONSTRUCT PROOFS
Page: 430
Although some researchers argue that diagrams can aid undergraduates’ proof constructions, most undergraduates have difficulty translating a visual argument to a formal one. The processes by which undergraduates construct proofs based on visual arguments are poorly understood. We investigate this issue by presenting eight mathematicians with a mathematical task that invites the construction of a diagram and examine how they used this diagram to produce a formal proof. The main findings from the paper were that it was not trivial for mathematicians to translate an intuitive argument into a formal proof and mathematicians used diagrams for multiple purposes, including noticing mathematical properties, verifying logical deductions, representing ideas or assertions, and suggesting proof approaches.