The purpose of this study is to determine a person's ability to perform mental activities mechanically in associating new information received with previously owned information (reconstruction) which is a reflective abstraction. The process of reconstructing the concepts of quadrilaterals and triangles by students uses the mental mechanism approach of APOS theory (interiorization, encapsulation, de-encapsulation, coordination). The process can be known by observing students and analyzing the results of student work, starting with determining 1 class to be given a mathematical ability test. 29 students were present when the math ability test was given. The results of the mathematical ability test were analyzed and then found 2 students of different sexes with moderate ability. The first student is male and the second student is female, hereinafter referred to as the research subject, then the research subject is given the task of quadrilateral and triangle. The results showed that female students had done all stages of reflective abstraction in APOS theory. So, that these students were at the level of relational understanding. Meanwhile, male students only did several stages in the reflective abstraction stage on the APOS theory so that these students were included in the level of instrumental understanding.