The analysis of the understanding of the three-dimensional (Euclidian) space and the two-variable function concept by university students

• Published in: The Journal of mathematical behavior 2020-03, Vol.57, p.100697, Article 100697
• Main Authors: Şefik, Özgün, Dost, Şenol
• Format: Article
• Language: English
• Subjects: APOS theory; Conceptual understanding; Genetic decomposition; Mathematics education; Three-dimensional space; Two-variable function
• ISSN: 0732-3123; 1873-8028
• DOI: 10.1016/j.jmathb.2019.03.004

•Only one student constructed a three-dimensional object conception within the framework of genetic decomposition.•Some students could not relate the concept of two-variable function to three-dimensional space.•The students who could perform algebraic operations had problems as far as geometric representation was concerned. Conceptual understanding is being emphasized in mathematics education. Students often have difficulty understanding the multi-variable function, a key concept. Based on the APOS theory, which analyzes the cognitive structures formed by individuals in learning a mathematical concept and produces components related to that learning, this study analyzes the conceptual understanding of three-dimensional spaces and two-variable functions by university students. The genetic decomposition of these concepts proposed by Trigueros and Martinez-Planell is also considered. The analyzes results revealed that only one student constructed the concept of three-dimensional space as an object within the framework of genetic decomposition. Some students could not relate the concepts of two-variable function and three-dimensional space. Students who could perform algebraic operations had problems related to geometric representation. This study suggests the refinement of genetic decomposition to include, e.g., mental construction steps for writing algebraic equations of special surfaces whose graphs are given in R3.