A primary school student's abstraction processes related to geometric concepts: A teaching experiment based on the hypothetical learning trajectory framework

Increasing students' geometric thinking levels starting from young ages is one of the main goals of mathematics teaching since it is very important in many scientific, technical and professional fields as well as in mathematics. In this study, the mathematical thinking and learning of an elementary school student in the context of geometric concepts will be examined. The aim of this study is to monitor the mathematical abstraction processes of a third grade student regarding geometric objects, shapes, symmetry and basic geometric concepts in a one-to-one teaching experiment designed within the framework of the Hypothetical learning trajectory and to reveal the abstraction mechanisms at the end of this process. In this teaching experiment, a twelve-week classroom teaching experiment was conducted with a thirdgrade primary school student. Piaget's theory of abstraction was used as the theoretical framework to reveal the abstraction mechanisms in the context of the student's abstraction mechanisms in the context of the levels of shape formation and shape decomposition, along with the paths followed by the student in developing understanding and skills related to geometric concepts. Video recordings of the clinical interviews and teaching lessons with the focus students and worksheets were used as data collection tools. The findings of the study revealed that, at the end of the teaching experiment designed within the framework of the Hypothetical learning trajectory, the student was able to abstract the concepts of recognition, naming, properties and relations between geometric objects and shapes; the concepts of symmetry, congruence and line of symmetry; and the concepts of point, line, line segment, ray and angle. It was also observed that the concrete and technological materials used in the process played a supportive role in the deep abstractions of the focus student in addition to their individual actions. Keywords: Mathematics Education, Hypothetical learning trajectory, Geometric concepts, Mathematical abstraction, One-to-one teaching experiment