A Gifted High School Student’s Abstraction Process of Divisibility Rules

Abstract

Purpose: Gifted students are often motivated by complex mathematical tasks. Mathematical abstraction allows access to gifted students’ cognitive processes in knowledge construction. The question “How and why do the divisibility rules work?” evokes in them an intellectual need for constructing the working principle of a divisibility rule. Hence, this research focused on a gifted high school student’s abstraction process of divisibility rules. By examining mathematical abstraction through observable actions, this study presents a deeper insight into the gifted student’s thoughts, difficulties, and strategies regarding the working principle of divisibility rules. Design/Methodology/Approach: The data was obtained from a 9th-grade gifted high school student through clinical interviews in a case study research design. The data were analyzed using the RBC+C abstraction theoretical framework's epistemic actions: Recognizing, Building-with, Constructing, and Consolidating. Findings: The gifted student could recognize and use the necessary prior knowledge about divisibility to abstract the divisibility rules. In the construction process, the student explored the complex divisibility rules based on the place values of numbers with different digits. Highlights: The student needed guidance in the process of creating more complex divisibility rules. With the researcher's help, the student could understand even more complicated divisibility rules and consolidate the cognitive way.