PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Empirical re-conceptualization: Bridging from empirical patterns to insight and understanding
Page: 159
Identifying patterns is an important part of mathematical investigation, but many students struggle to explain or justify their pattern-based generalizations or conjectures. These findings have led some researchers to argue for a de-emphasis on pattern-based activities, but others argue that empirical investigation can support the discovery of insight into a problem’s structure. We introduce a phenomenon we call empirical re-conceptualization, in which learners identify a conjecture based on an empirical pattern, and then re-interpret that conjecture from a structural perspective. We elaborate this construct by drawing on interview data from undergraduate calculus students and research mathematicians, providing a representative example of empirical re-conceptualization from each participant group. Our findings indicate that developing empirical results can foster subsequent insights, which can in turn lead to justification and proof.