A Gifted High School Student's Generalization Strategies of Linear and Nonlinear Patterns via Gauss's Approach. (March 2021)

• Record Type: Journal Article
• Authors: Girit Yildiz, Dilek; Durmaz, Burcu
• Is Part Of: Journal for the education of the gifted. Volume 44:Number 1(2021)
• Page Start: 56
• Page End: 80
• Publication Date: 2021-03
• Subjects: gifted education -- Gauss's approach -- linear and nonlinear pattern generalization; Gifted children -- Education -- United States -- Periodicals; 371.9505
• DOI: 10.1177/0162353220978295
• Languages: English
• ISSNs: 0162-3532

Abstract

Mathematically gifted students have a high potential for understanding and thinking through mathematical relations and connections between mathematical concepts. Currently, it is thought that generalizing patterns algebraically can serve to provide challenges and opportunities that match their potential. This article focuses on a mathematically gifted student's use of generalization strategies to identify linear and nonlinear patterns in the context of a matchstick problem. Data were collected from a 10th-grade gifted student's problem-solving process in a qualitative research design. It was observed that the gifted student's ways of generalizing the linear and nonlinear patterns were different. In a generalization process, the student used figural reasoning in the linear pattern and numerical reasoning in the nonlinear patterns. It was noted that the student explored using Gauss's approach in structuring the general rules of nonlinear patterns. Accordingly, aside from assisting their more gifted students, mathematics teachers may want to consider ways to introduce Gaussian thinking to the benefit of all their students.