Investigating teaching methods for the greatest common divisor and least common multiple based on student-oriented teaching and learning from the perspective of a pre-service teacher for middle school

In this paper, we propose a teaching and learning approach designed to guide middle school students in independently constructing a method to re-invent the greatest common divisor (GCD) and least common multiple (LCM) using prime factorization, based on the concepts of GCD and LCM introduced in the 5th grade of elementary school, from the perspective of a pre-service teacher. Additionally, by exploring the connection between this method, which encourages students to construct knowledge on their own, and the new contents they will learn, we examine whether the method proposed in this study plays an appropriate role in an element of a spiral curriculum within the broader framework of the structure of knowledge presented in the process of education(Bruner, 1960).