Gymnasielärares användning av representationer av funktioner - en intervjustudie

Abstract

Functions are an important part of the mathematics syllabuses at the upper secondary school level in Sweden, because the concept of function is connected to many other mathematical concepts, such as derivatives. A function can be represented in different ways, for example, verbally, algebraically (using mathematical symbols), graphically, and with a table of values. The ability to translate between these representations is regarded by most mathematics educators as crucial for students’ conceptual development. Aim: The aim of the study is to investigate in-service mathematics teachers’ knowledge of how representations of functions can be used in mathematics teaching. Theory: This study draws on two theoretical frameworks: the Mathematical Knowledge for Teaching framework (Ball et al., 2008), and Sfard’s framework of reification (Sfard, 1991, 1992). Method: Individual semi-structured interviews were conducted with fourteen in-service mathematics teachers. The collected data were analyzed through thematic analysis and by statistical analysis. Results: All respondents demonstrate knowledge of content and teaching when they say that they translate between representations of functions in their introductory teaching of functions. Respondents with more years of teaching experience report using a slightly greater number of representations in their introductory teaching of functions than those with less teaching experience. Furthermore, several respondents demonstrate knowledge of content and teaching when they describe the possibilities and limitations of representations in the teaching of functions. Several respondents emphasize that both graphical and algebraic representations of functions are useful in advanced mathematics courses. They express that the graphical representation is useful for visualizing functions, while the algebraic representation can be used for calculating the derivative of a function.