Generalization Across Multiple Mathematical Domains: Relating, Forming, and Extending

Abstract

Abstract Generalization is a critical component of mathematical reasoning, with researchers recommending that it be central to education at all grade levels. However, research on students’ generalizing reveals pervasive difficulties in creating and expressing general statements, which underscores the need to better understand the processes that can support more productive generalizations. In response, we report on results from 146 interviews with 93 participants in middle school through college in the domains of algebra, advanced algebra, trigonometry/pre-calculus, and combinatorics while solving complex problems. Our findings yielded the Relating-Forming-Extending (RFE) Framework, which distinguishes multiple related forms and types of generalizing. We also present two aspects of mental activity that promote generative generalizations: operative activity, and building and refining activity.