Fraction decision confusion – a case study among 13-year old students / Noraini Noordin, Fadzilah Abdol Razak and Nooraini Ali

Abstract— If one uses mental computation in an estimation procedure, there will be a previous selection of simple numbers to be operated on mentally. This choice of numbers will bring about approximate answers, thus, this implies that a close relationship exists between estimation and mental computation. A study was conducted in 2010 on 385 students from four selected colleges in the North Zone of Malaysia to assess the estimation and computation abilities of 13-year old students. These students had prior exposure to fractions at primary schools. Students were asked to respond to items on a Computation Test and an Estimation Test followed by a Probing Interview. The Computation and Estimation Tests have similar stem items. Analysis of the responses to the Computation and Estimation Tests was done using Rasch Measurement Model. Among issues investigated in the study was fraction confusion decision. This paper discusses the estimation problems student face when they compare fractions to another number. Items 2, 3 and 6 on the Computation Test were selected for analysis. Responses to all these three items demonstrated that majority of the students were able to convert fractions to decimal numbers, and vice versa. Majority of the selected students were also able to demonstrate their computational estimation ability by using prior knowledge on counting on or counting back sequence to decide which among the given decimal numbers in Item 3 was larger than 4 150/1000. However, responses to Items 2 and 6 indicated that students were confused. This impeded their judgments in deciding which among the given improper fractions in Item 2 was nearest to 10, and which among the given sums of fractions in Item 6 was nearest to 5. In terms of hierarchy of difficulty, Item 6 caused the most confusion to the students.