Capacity for mathematical generalization is a hallmark of mathematically gifted students

Abstract

Among students who need differentiated educational attention are those who demonstrate above-average learning abilities. This group includes, in particular, students with high mathematical ability. Among the distinguishing characteristics identified in the literature on mathematics education for students with high mathematical ability is the ability to generalize. First, I will characterize mathematical generalization by showing the different ways it appears in the context of school mathematics: generalization of objects, relationships, operations, and problem-solving methods. Next, I will present students' responses to various problems that require generalization, in order to show how the analysis of these responses reveals different styles of reasoning and ways of generalizing, reflecting the diversity of generalization abilities among students. Furthermore, these types of problems are suitable for use in regular mathematics classes at different grade levels in schools, making them a tool available to teachers to help them identify students with high mathematical potential.