What Does Three-quarters Look Like? Students ’ Representations of Three-quarters

Forty-one students from Years 3 to 10 completed a clinical interview on the topic of fractions. Four of the questions from the 20-30 minute interview involved the fraction 3/4; students ’ responses to these questions are analysed in this paper. When asked to illustrate 3/4, the most popular model chosen by students was a circle, yet fewer than 25 % of the students knew that a circle divided into 4 parts with unequal areas (using 3 vertical lines) did not represent 3/4. Such students are unable to identify the appropriate attribute which is relevant to the given model. Understanding fraction concepts is clearly difficult for many students. For example, 69 % of the Year 8 Australian sample in TIMSS (2003) correctly chose 16/30 on this multiple choice item: In a group of children, 16 have birthdays during the first half of the year, and 14 have birthdays during the second half of the year. What fraction of the group have birthdays during the first half of the year? (Item Number M012041). Although this result compares favourably with the international average (52%) it is clear that about one in three Australian Year 8 students in this sample lacked fundamental fraction understanding after about four years of the topic being included in the school curriculum. This paper will further the research into students’ understandings of fractions by investigating the models they use to represent fractions. In addition, we wish to determine if students understand the essential features of the models they use