Abstract:

Cuts are one of the most problematic and complex subjects of primary mathematics, especially in terms of both teaching and learning. In addition to the failures of students in the subject of cuts, the research in which the teachers’ unconscious approaches to cuts teaching are in the forefront, requires research to cuts teaching. Based on this requirement, this study aims to develop a predictive learning path map that supports high school sixth grade students to understand the processes of gathering and extracting in cuts and also suggest a teaching design for these topics. The study was attended by a 16th-class volunteer who was studying in a state school located in the province of Anatolia. Research is designed using teaching experiments that are commonly used in mathematical education. In the teaching experiment, the data was collected for five weeks and for two hours of course each week. The research resulted in the development of a TÖYH for the collection and extraction processes with the concept of cutting and cutting, and a teaching design for this subject was proposed. It has also been shown that the multiple representations used with the teaching order specified for the subject of collection and extraction in the cuts used in the recommended teaching design have students learn the subjects conceptually.

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.

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