VARIABELNS MÅNGFASETTERADE TVETYDIGHETER En studie kring begreppets historia, elevers svårigheter och lärares möjligheter

Abstract

In this literature study I have sought answers to the following questions: “How did today’s variable categories come into existence?” and “What difficulties do today’s students face when working with variables and what possibilities do teachers have in dealing with those difficulties?” The questions originate from the fact that the algebraic variable is found in several different contexts. Contexts which are likely to contribute to confusion arising when students, and often even teachers, are asked to motivate what the variable stands for in a given problem. The three categories that are identified comprise the variable’s three most common areas of usage: variables as unknown numbers, variables as general numbers and varying variables. This study starts off with a historical account on how today’s categories of the variable term came to form. It then brings attention to research conducted in different countries concerning common learner errors. Common difficulties include not accepting open expressions as answers, leading to a number of strategies being employed to eliminate operations from the expressions; dealing with variables in expressions and equations as if they were names or units; an inability to describe patterns using variables; and, perhaps most importantly, differentiating the different variable types. Swedish high school teachers’ possibilities in dealing with the lattermost difficulty are shown to be limited to some extent by the directives of The Swedish National Agency for Education. However, firm knowledge and awareness concerning the variable types are nonetheless indicated as absolute necessities among teachers for students to learn effectively how to deal with variables in a seamless manner.