A Study on the Framework to Describe the Development of Conception of“Linear Function”: From the View Point of Example Space and Schema in APOS Theory

Abstract

　　The result of National Assessment of Academic Ability in 2018 indicates that Japanese secondary students have difficulty in identifying the type of a function which is inherent in a given situation, in particular in the case of “linear function”.  Against this issue, we’d like to stress the importance of the deep developed conception of “linear function”, rather than the reinforcement of memorizing what “linear function” is and/or how to identify them. 

　　First, from the view point of example space, we make a consideration on the actual conditions of students’ learning process of linear function in lower secondary schools.  In fact, we point out that, though the intensional definition is given explicitly, students’ learning could advance extensionally using examples.

　　Thus, to obtain deep developed conception of linear function, it is required to step into the intensional conception based on the definition.  To describe students’ changing process from extensional conception of linear function to intensional conception of that, we propose applying the framework of Schema development in APOS theory.  Finally, using this framework, we present a desirable conception of linear function for students.