Formation Process of Common Divisor Concept: A Study of Realistic Mathematics Education

Abstract

Abstract: Common divisor is one of the concepts that started to be learned in secondary school and forms the basis of many concepts. But students generally have difficulty in making sense of it. The purpose of this study is to investigate concept formation processes of common divisor through a case study on seven sixth grade students. To do this, we designed a learning environment based on Realistic Mathematics Education and tried to determine how students construct the concept. The data collected through group and individual study papers and semi-structured clinical interviews were analyzed with content analysis within the APOS theoretical framework. The findings showed that one student was unable to internalize the action and her thoughts depended on the contextual problem. Other students internalized all common divisors and coordinated them with prime factorization. At the end, students were able to encapsulate all the processes into object by finding the product of common prime numbers. Moreover, students were able to identify greatest common divisor among all common divisors and clarified its meaning.