PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Undergraduate students reading and using mathematical definitions: Generating examples, constructing proofs, and responding to true/false statements
Page: 364
University students often encounter difficulties making correct use of definitions. This is partly because they are not familiar with the difference between dictionary definitions and mathematical definitions (Edwards & Ward, 2004). However, in order to succeed in upper-level mathematics courses, they must often construct original (to them) mathematical proofs, which intrinsically require the correct use of definitions. Only a little research has been conducted to discover how university students handle definitions new to them (e.g., Dahlberg & Housman, 1997). Our research question is: How do university students use definitions, to evaluate and justify examples and non-examples, to prove results, and to evaluate and justify true/false statements? Data were collected through individual task-based interviews with 23 volunteer students from a transition-to- proof course. There were five definitions but each student considered only one of the five. Content analysis and grounded theory are being used for analysis. Preliminary results are presented.