This is qualitative research aimed at exploring cognitive adaptation in the construction and reconstruction of quadrilateral relations. The participants were chosen using the Quadrilateral Relations Construction Test given to 20 pre-service mathematics teachers. Based on the test results, 4 types of quadrilateral relations are obtained, namely type 1, type 2, type 3, and type 4. Next, 1 pre-service mathematics teachers with type 1 (P1) and 1 pre-service mathematics teachers with type 2 (P2) are chosen as participants. Next, participants were given a Quadrilateral Relations Reconstruction Test then an in-depth interview was conducted. The data in this study were analyzed through data condensation, data display, and conclusion drawing. This result illustrated that having a scheme is not enough to successfully solve problems. One of the important factors that determine the success of problem solving is the success of cognitive adaptation process. Cognitive adaptation in the process of construction and reconstruction quadrilateral relations takes place through assimilation and accommodation. When the information obtained is in accordance with the scheme that is owned, the cognitive adaptation that occurs is called assimilation. Meanwhile, when the information obtained is not in accordance with the scheme owned, the adaptation that occurs is called accommodation. Thus, pre-service mathematics teachers must be trained to make cognitive adaptations in problem solving process.
Cognitive adaptation, concept construction, concept reconstruction, Mathematics education, Quadrilateral relations