PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
When nothing leads to everything: Novices and experts working at the level of a logical theory
Page: 579
Building on Antonini and Mariotti’s (2008) theorization of mathematical theorem and research on students’ meta-theoretical difficulties with indirect proof, this study examines mathematics majors’ and mathematicians’: (1) responses and approaches to the validation tasks related to the assertion S*→S, when given a primary statement, S, of the form ∀n, P(n) ⇒ Q(n)) and a secondary statement, S*, of the form used in proofs by contradiction; namely, ∄n, P(n) ∧ ~Q(n)); and, (2) selection of a statement to prove given the choices S* and S. Findings indicate that novice proof writers’ responses differ from advanced students’ and mathematicians’ both in their approaches and selections, with novices tending to become entangled in natural language antonyms and engage in the chunking of, rather than parsing of, quantified statements.