Grunnskolelærerstudenters forståelse av funksjonsbegrepet : En casestudie av lærerstudenters forståelse av funksjonsbegrepet før de møter begrepet i egen utdanning
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This master thesis intends to study preservice teachers at the teacher education master program grade 5-10 and their understanding of the concept of functions. The thesis attempts to answer two different research questions. The first question is: What understanding does the students at teacher education grade 5-10 hold of the concept of function, before they encounter the concept in their education? In this thesis understanding will be defined by Sierpinska (1992), Hiebert and Carpenter (1992) and Skemp (1987). To study the students’ understanding this study will use Vinner and Tall’s (1981) theory of concept image and DeMarois and Tall’s (1996) theory of layers and facets of a concept. This leads us to the second research question: To what extent is DeMarois’ and Tall’s model suitable as a tool for mapping students understanding of the concept of functions? This question will be answered based on experiences made while working on this thesis. The data collection is inspired by DeMarois (1998) and carried out by written, mathematical tests regarding the concept of function with 43 participants from a teacher education program at an institution for higher education in Norway. Interviews with four of these students were also conducted. During the interviews the students worked with further tasks regarding functions, and the tasks from the written test was undergone a second time. The results show that the students are largely able to utilize different representations of functions to find functional values and variable values, but that the students' conceptual images are not well defined. This leads to problems in determining whether the relationships between variables, presented through graphs and algebraic expressions are functional relationships or not. None of the students were able to define or describe what a function is in a correct manner. Even though the four students stated that they had no previous experience with function machines, the results from the tests and interviews showed that the students mastered this representation in line with other representations, and in some cases, better. Based on experiences gained through the work with this thesis I can determine that DeMarois’ and Tall’s model is a good tool for mapping students understanding of a concept through creating a detailed image of the concept understanding, by considering both its depth and the width dimension. Still, the model has its weaknesses through assumptions that underlies the model and the vast amount of empirical data that is needed to create such a detailed image.
Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2018