Obstacles to Relations and Functions Concepts Learning in Terms of Theory of Didactic Situations Criteria

Abstract

Effective learning planning requires information on the obstacles to learning a given concept that students experience to create a learning flow that matches the students’ characters, including in the learning of the concepts of relations and functions. The research aims to determine the learning obstacles (LOs) that students experience in learning the concepts of relations and functions as per the criteria of the theory of didactic situations (TDS). Employing the case study method, this qualitative research was conducted with subjects that included 19 prospective teacher students who had taken a diagnostic test and participated in in-depth interviews. An analysis was conducted based on three TDS criteria, namely action, formulation, and validation. The results revealed two types of LOs that students experienced in learning the concepts of relations and functions: 1) ontogenic obstacles and 2) epistemological obstacles. The first type of obstacles included 1a) the inability to properly understand the definition of the intersection of two relations, referred to as conceptual ontogenic obstacle, and 1b) the inability to relate the concept of relations in drawing a Hasse diagram, referred to as instrumental ontogenic obstacle. Meanwhile, the second type included 2a) the difficulty in expressing relations in the forms of mapping diagrams and graphs, 2b) the difficulty in determining the range of ​​a function, 2c) the difficulty in identifying relations which are also functions, 2d) the inability to represent relations in the forms of mapping diagrams, and 2e) the inability to write a function as a set of ordered pairs. It is recommended that these LO findings be taken into consideration in designing learning tools.

Keywords

• learning obstacle
• diagnostic test
• relations and functions
• ontogenic obstacle
• epistemological obstacle