Hur ser man bråk?

: en studie om visuella representationer av bråk

Abstract

In this study we examine mathematics teacher’s verity in their reasoning and their different perspectives about visual representations and sub-constructs of fractions. Teachers were interviewed about task that their students solved, which were the methods used in this study. Therefor we also examine if there are any correlations between the teacher’s different perspectives of visual representations and the classes results on fraction tasks. The study was based on three theoretical frameworks; Four stages through the use of representations, five sub-constructs of fraction and pedagogical content knowledge. The methodological consideration and analysis were based on these theories. The result showed that there were some similarities and differences in the teacher’s reasoning. A similarity was that all participated teachers found visual representations as a helpful tool when teaching fractions for student’s conceptual understanding. Another similarity was that all teachers were more familiar with the part-whole sub-construct than the other subconstructs of fraction. Some differences in the teacher’s reasoning were if they found fraction difficult or not for the students and in which extent visual representation should be used in the ninth grade. When the class results were analyzed some connections were found. Student have difficulties with tasks where area models are not equaled partitioned, with tasks related to number lines and to tasks were the students must change from a visual to a textual representation. According to the teachers comments these difficulties accurse due to that the students lacks a curtain mathematical understanding that is required when solving these tasks. This leads to the use of an inaccurate method. The teacher’s also comments that some tasks in this study requires a higher conceptual understanding which affects the classes’ results.