PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Generalization in undergraduate mathematics education
Page: 461
Generalization is a critical component of mathematical thought and thus a goal of instruction. However, most generalization research has focused on pattern generalization and generalization in algebra, not undergraduate mathematics. It is not known whether the generalization frameworks derived from such work adequately describe generalization in undergraduate mathematics, where the sorts of generalizations students must make are not regarding patterns, but rather the meanings of concepts and ideas. In this paper, we propose elaborations on existing generalization frameworks in order to take into account issues in learning advanced mathematics. We use how students generalize their notion of integration from single to multiple integrals as an illustrative case study.