There are More Than Part-Whole Strategies at Work in Understanding Non-Equal-Parts Fraction-Area-Models

In this study, 88 Grade 6 students ’ responses to three part-whole tasks are analysed in terms of Kieren’s (1988, 1993) four-part model for fractions- measure, quotient, operator, and ratio. Using data from interviews, their strategies were also analysed using traditional part-whole explanations, including identifying the count-and-match misconception which was found to have distinct variations. Statement of the Problem If a part-whole sub-construct is used as a conceptual model to analyse students’ performance on fractions tasks, then simple categories are established: correct part-whole understanding, the count-and-match misconception, and other incorrect part-whole strategies. The intent of this paper is to examine whether analysing students ’ performance on part-whole tasks in terms of Kieren’s (1993) four sub-constructs- measure, quotient, operator, ratio- enables more precise interpretations of students ’ strategies. Context of the Problem in the Research Literature The Part-Whole Count-and-Match Misconception and Kieren’s Four-Part Model Traditional fraction instruction in the primary school often emphasises a part-whole understanding of fractions; a whole is pre-divided into equal parts and students have to identify the fractional part shaded (Carrahar, 1996; Gould, 2005). Over the last four decades researchers have developed explanations of this part-whole concept and related curriculum models. Three independent branches have developed: th