Students’ mental construction in cube and cuboid concepts based on mathematical ability differences

Rofiki, Imam, Anam, Ahmad Choirul, Sari, Putri Eka, Irawan, Wahyu Henky and Santia, Ika (2020) Students’ mental construction in cube and cuboid concepts based on mathematical ability differences. Al-Jabar: Jurnal Pendidikan Matematika, 11 (1). pp. 133-144. ISSN 2540-7562

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Abstract

Understanding the cube and cuboid concepts is one of the essential goals of solid geometry learning. Most studies on students' understanding of these concepts have posited a gap between the conception of the surface area and volume. This research was aimed to describe the students' mental constructions in APOS (Action, Process, Object, and Schema) theory. Three junior high school students who have differences in mathematical abilities were chosen as the research subjects. This research employed the qualitative approach. The data were collected using the task sheet and interview. The result of this research discovered that the subject with high mathematical ability could solve cube and cuboid problems correctly in the action stage. In the process and object stage, the subject could provide detailed explanations of the steps to assess the surface area and volume by comparing two shapes with different sizes. In the schema stage, the subject made a systematic understanding related to the concepts of surface area and volume of cube and cuboid. The subject with medium mathematical ability explained the mental construction in action and process stage well despite the error done in the process stage. In the next stage, she compared two different shapes of cube and cuboid to find their ratio. In the last stage, the subject could not complete the explanation. The subject with low mathematical ability could solve the cube and cuboid problems. At the process, object, and schema stage, the subject could not complete the indicators of cube and cuboid concepts

Item Type:	Journal Article
Keywords:	APOS Theory; Mathematical Ability; Mental Construction; Understanding Concepts
Subjects:	13 EDUCATION > 1302 Curriculum and Pedagogy > 130202 Curriculum and Pedagogy Theory and Development
Divisions:	Graduate Schools > Magister Programme > Graduate School of Mathematics Education
Depositing User:	Wahyu Henky Irawan
Date Deposited:	06 Apr 2026 13:37

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