Matematikklærerstudenters matematiske ‘meanings’ om funksjonsbegrepet : En pilotstudie av hva instrumentet MMTsm avslører i forhold til norske matematikklærerstudenters matematiske ‘meanings’ om funksjonsbegrepet

Abstract

The theme for this master study is teacher students’ mathematical meanings about the function concept. Meanings are representations of cognitive schemes, which can be observed through the behavior of the person, for example through answers on tasks. This study is part of a bigger research project connected to Patrick W. Thompsons’ research about secondary mathematics teacher’s meanings. The instrument Mathematical Meanings for Teaching secondary mathematics (MMTsm), developed by American researchers, is used in this study. In my study, students’ meanings about the concept of functions have been studied by analyzing teacher students’ written answers on tasks in the instrument MMTsm addressing the research question: What does the instrument MMTsm reveal when used to explore in depth Norwegian mathematics teacher education students meanings about the concept of functions? This study is defined as a qualitative inquiry pilot study, where constructivist learning theory is used as the theoretical framework. The student’s individual thinking and meanings are in focus. Moreover, the instrument is developed within the constructivist framework. Qualitative data were collected as written answers to selected tasks in the instrument. The answers have been analyzed using an analysis tool that is developed and based on the interpretation tool that Thompson developed alongside the instrument. The findings from this master study reveal that the students expressed a diversity of different meanings about the concept of functions and that the kind of meanings expressed about concepts and ideas connected to the concept of function are highly individualistic. This master study shows that several students do not have fully developed meanings and that they therefore express themselves in an unclear and vague manner. From the analysis of the written answers, it can be argued that several of the meanings that have been expressed are likely to create confusion amongst the students they will teach in school