PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Seeking solid ground: A study of novices’ indirect proof preference
Page: 391
The aims of this study are two-fold: (1) to investigate novices’ proof preferences as indicated by novices’ selection of the “most convincing” argument when engaging in proof comparison tasks involving an indirect and a direct proof; and, (2) to explore the criteria students’ bring to bear on proofs as they engage in proof comparisons. Informed by the cK¢ model of conceptions proposed by Balacheff (2010), analyses indicate that directness was not a primary criterion used for the select of a proof during proof comparisons, even though this criterion was suggested by prior research. Instead, the primary criteria identified in students’ rationales were familiarity and the degree of certainty in one’s understanding of the given proofs, which in turn suggests that it is the subjective sense of being on solid conceptual grounds that determine students’ preferences. These findings are considered in light of the cK¢ model of conceptions.