A diagnostic study on functions
IND's studenterserie nr. 104. Specialerapport. Matematik.
Nicole Jonasen, 2021.
Vejledere: Mikkel Willum Johansen & Britta Eyrich Jessen
The purpose of this master’s thesis is to examine high school students’ understanding of functions. The examination of the students’ understanding of the concept of function is done on the base of Tall and Vinner’s theory about concept images and concept definitions. This master’s thesis will present a diagnostic questionnaire, which is developed on the base of diagnostic teaching and testing and cognitive theory. The diagnostic questionnaire will examine why the students are incapable of drawing linear functions. The results of the questionnaire are based on 52 first year high school students’ answers. Among other things the answers to the questionnaire revealed that students have a narrow concept definition of the concept of functions and that almost a third of the students perceived that a function is an algebraic expression. The results of the questionnaire showed that there is a relation between being incapable of drawing linear functions by hand and not understanding the conceptual blend of the Cartesian plane. Furthermore the results of the questionnaire also showed that there is a relation between not understanding and using the !(!)-notation correct and not being able to draw linear functions by hand. The relations were tested through statistical testing of several hypotheses. In addition, the answers to the questionnaire also showed that the students’ usages of CAS-tools do not have an influence on their abilities to draw linear functions by hand. These above relations suggest a change in the approach to teaching the !(!)-notation. Furthermore this thesis also suggests that a greater focus on teaching the students conceptual metaphors, conceptual blends and metonymy of mathematics could maybe improve the students’ understanding of various aspects of functions.