Handling mixed numbers on a number line – a problem among lower secondary students / Noraini Noordin, Fadzilah Abdol Razak and Nooraini Ali

Primary school Mathematics curriculum dictates that students will be taught to look at fractions in three different forms: proper fractions, improper fractions and mixed numbers beginning Year 3 at primary schools. Based on their four-year exposure to fractions at primary school, students should be able to determine equal intervals on a structured number line. Using the part-whole approach to interpret fractions, students will normally break up the distance between two points on the number line into equal number of parts to represent equal intervals. In a previous study done to assess the conceptual understanding of fractions among secondary students, there were three items involving students handling fractions that attracted our attention, i) item involving naming proper fractions on a number line, given two reference points, 0 and 1; ii) item involving placing a mixed number on a number line, given two consecutive proper fractions as reference points and iii) item involving naming two fractions A and B placed an interval distance to the right of the first and second reference points, respectively. Estimation is a process that needed preliminary selection of simple numbers to be worked on mentally and this choice of number will help in approximating the results. There were few shortcomings on the part of the students in the estimation processes that they went through. As a result, the previous study indicated students facing difficulties as they progressed through from items i) to iii). There is a need to understand this phenomena, thus, these three items were included as items in the Probing Interview for the current study which was conducted on random samples of students from selected colleges in the North Zone of Malaysia. It is hoped that these findings will shed some information on fraction confusion that interfered with their estimation and computation abilities.