Event Type:

Department Colloquium

Date/Time:

Monday, February 20, 2012 - 08:00 to 09:00

Location:

Kidd 350

Guest Speaker:

Milos Savic

Institution:

New Mexico State University

Abstract:

Proof is central to mathematics education, but many students have difficulty with constructing proofs, especially at the middle undergraduate, and even at the beginning graduate transitions. This talk will describe two different, but related studies that considered important aspects of proving: logic and impasses. I first examined the question, “Where is the logic in proofs?” by coding a variety of undergraduate and graduate student-constructed proofs, looking for the occurrences of “formal logic”, that is logic beyond common sense reasoning. If formal logic occurs frequently, then a unit on logic might beneficially be taught before teaching proving. However, if formal logic occurred infrequently, then teaching logic in context while teaching proving might be more effective. Next I investigated impasses that occur during the proving process, often referred to colloquially as “getting stuck.” With the help of a new data collection technique that I will describe, I have been able to observe mathematicians “getting stuck” while working alone. I categorized the mathematical and non-mathematical ways they used to overcome impasses, many of which involved a period of incubation. This is apparently the first study that examines incubation during the proving process.