RUME 26
2024
Omaha, Nebraska
Towards Systematically Examining Students’ Epistemic Grounds of Developing Mathematical Generalization: A Preliminary Framework
Page: 90
The practice of generalization is a fundamental aspect of mathematics that requires further investigation, particularly in advanced contexts. This paper has sought to address the research gap by presenting a preliminary framework that captures how and on what basis undergraduate students develop and evaluate mathematical generalization. I illustrate each aspect of the framework using examples from two focal students’ generalization of the concept of a group in Abstract Algebra, uncovering important mechanisms and thinking behind their emergent generalizing ideas. The framework has potential to be used more broadly in other mathematical contexts and to inform instructional designs aimed at promoting students’ generalization skills. Key takeaways and potential directions for future research are discussed.