Students' reflective abstraction of middle school in reconstructing quadratic equation concept based on high mathematical ability

Abstract

A quadratic equation is one of the mathematics concepts that must be learned in secondary school. Students have many difficulties in solving quadratic equations. One of them is experiencing a process skill error. Students need new abstractions and processes to shape experiences to distinguish whether experience falls into student abstraction or beyond student abstraction. Reflective abstraction is students' understanding of mathematics through problems that reflect and reconstruct mental structures, then the scheme is used to solve problems. The reflective abstraction mechanism that can be applied to metal structures is the APOS theory, namely: Actions, Processes, Objects, and Schemes to construct new mental structures. The process of mental reconstruction of each student is different, so for the formation of mathematical concepts, it needs mathematical abilities. In other words, if someone has good mental reconstruction abilities, hopefully, his concept formation is also good. This research conducted using a qualitative approach. The subject of this research was selected from grade 9 junior high school students in Surabaya. Students must answer two tests, namely tests of mathematical abilities and reflective abstraction tests. Analysis and categorization of scores were carried out on both tests. Then two students who has high mathematical ability was selected as subject. Semi-structured interviews is conducted individually for each subject. The purpose of this study is to find out the reflective abstraction of students that have reconstructing concept of quadratic equations in terms of high mathematical ability. The results of the study indicate that the subject can solve the problem according to the stages of the APOS.