Variabelbegreppet i matematik : En kvalitativ studie om hur variabelbegreppet sammankopplas med andra matematiska områden såsom algebraiska uttryck i undervisningen för årskurs 4-6

Sammanfattning: The aim of this study is to investigate how elementary school teachers use conceptual understanding in the teaching of the variable concept, namely, how these teachers connect the variable concept with other areas of mathematics, such as algebraic expressions.  The empirical data was obtained by qualitative methods comprising interviews with five mathematic elementary school teachers. In addition three observations in three classrooms were made; one observation is in grade 4 and the other two are in grade 6.The theoretical framework is based on Kilpatrick et al. (2001) theories: conceptual understanding, strategic competence and procedural fluency. Furthermore the theory of representations of Bergsten et. al (1997) and Persson (2010) were used in the theoretical framework. The results of this study show that none of the five participating teachers connects the variable concept to other areas of mathematics, such as algebraic expressions. However, two of them mention the variable concept in equations, problem-solving, algebraic expressions and shapes, but without explaining the meaning of the variable concept or how that concept is used and integrated into these mentioned areas of mathematics. Furthermore the study shows that the other three participating teachers mention the variable only to one to two areas of mathematics. These areas are problem- solving and shapes. These teachers do not explain how the variable concept is used in the mentioned areas of mathematics, but they focus on how the calculation will be performed to solve the data they used. The participating teachers do not use any representations to explain the variable concept and how it’s connected to the other areas of mathematics. In conclusion, the variable concept was not explained and its connection to other mathematical areas was not addressed, which due to the absence of usage of conceptual understanding in teaching the variable concept.