Construction of the Area of Rectangle Concept from the Perspective of APOS Theory
Construction of the Area of Rectangle Concept from the Perspective of APOS Theory

Summary/Abstract: This study examines seventh grade students' understanding of the concept of Rectangular Area through APOS (Action, Process, Object, and Schema) theory, previously used in various studies to improve conceptual understanding of mathematics. The literature shows that students often rely on memorising the area formula without understanding its conceptual basis, which can hinder long-term understanding of geometry. Previous research by Dubinsky and Arnon showed that APOS theory can facilitate the construction of mathematical understanding through structured cognitive stages. Based on this theory, the study hypothesised that APOS can help students develop an understanding of rectangular area through a gradual process involving internalisation and depiction of the unit square. Using a qualitative descriptive approach, this study selected participants based on their understanding of rectangular area and mathematical ability, using task-based interviews to explore their cognitive development. The sample consisted of one seventh grade student at SMP PGRI Buntudatu, Toraja. The results showed that students were able to internalise the rectangular area formula by gradually adding square units and understanding multiplication as a method of determining area. These results support the need for modification in the genetic decomposition of APOS theory, by adding specific cognitive steps to understand the unit square, in order to improve pedagogical strategies in learning geometry. The implications of this study highlight the importance of using cognitive frameworks in teaching mathematical concepts, by offering an approach that does not rely solely on procedural memorisation. This approach could potentially be applied to other mathematical concepts to improve students' understanding and long-term retention of geometry principles.

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