Hypothetical Learning Trajectory to the Development of Sixth Grade Students' Knowledge about Fractions and Addition-Subtraction in Fractions

Abstract

Fractions are one of the most difficult and complex topics in elementary school mathematics, both in terms of teaching and learning. Indicated research results on students' failure in fractions and teachers' inadequate approaches to teaching fractions reveal the necessity of research for teaching fractions. From this point of view, the purpose of this study is to develop a hypothetical learning trajectory that supports understanding of sixth grade elementary students' addition and subtraction in fractions and to suggest a teaching design on these topics. 16 sixth grade students attended the study in a public school located on the Central Anatolia Region. This research is designed as a teaching experiment which is often used in mathematics education research. Data collection proceeded throughout mathematics classes, two class hours per week for five weeks. At the end of the teaching experiment, a hypothetical learning trajectory and a teaching design for fraction addition and subtraction was proposed. Furthermore, it was revealed that students have learned fraction operations conceptually through the teaching sequence and the multiple representations used in the proposed instructional design for teaching fraction addition and subtraction.