PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Naive Brouwerian Visions: A Study Of Students’ Interpretations Of Non-Constructive Existence Proofs
Page: 413
This paper shares findings from a three-phase study exploring students’ conceptions of non- constructive existence proofs. Data are used to illustrate students’ tendency to apply a naïve Brouwerian lens to non-constructive proofs; that is, a perspective in which learner’s proof conceptions are governed by a potentially subconscious anticipation of construction, which enables the learner to construe proofs of existence (be they constructive or non-constructive) as providing actual instances of (or algorithms for producing) mathematical phenomena. Questions concerning researchers proof scheme inferences are raised.