Investigation Of Students’ Abilities In Translating Among Representations Of Fractions

The representation of fraction is a significant approach for students to understand the concept of fraction. The representations of fraction mainly include region, discrete objects, number line, symbol and so on. And representations of fraction relate to the concept of fraction. The translating among representations of fraction can help students have better understanding of fraction.This paper modified the Translations among Representations of Fractions Test(Kurt & Cakiroglu) and used it to investigate 247 fifth and 264 sixth students’ abilities in translating among representations of fractions. Besides, face-to-face interview and documents analysis were used to explore the problems students met in translating among representations of fractions. The findings of this study are presented below: 1. The current situations on students’ ability in translating among representations of fraction.1) Students have good performance in transforming tasks related to region and discrete objects, because they have good understanding of ‘part-whole’ concept.2) Students have some difficulties in transforming tasks that associated with number line. Some students cannot understand the differences between region(discrete objects) and number line.3) Students have some difficulties in transforming tasks related to improper fraction, for they have difficulties in understanding improper fraction and ‘one unit’.2. The characteristics of students’ ability in translating among representations of fraction:1) There is a significant improvement in 6 grade students’ ability in translating among representations of fraction related to number line. It is mainly because 6 grade students have deeper understanding in ‘measure’ concept, which help them better comprehend ‘number line’.2) 5 grade students have better performance in translating among representations of fraction related to improper fraction. It is mainly because there is nothing related to improper fraction and its representation in grade 6 fraction teaching, which may lead to short memories and confusion in related knowledge. 3. The typical mistakes and thinking obstacles in translating among representations of fraction:1)Students tend to regard the axis of number line as the whole and find the related point which can present the mentioned fraction based on ‘part-whole’ concept.2)Students’ mindset makes them regard improper fraction as proper fraction by mistake,they neglect the relationship between ‘1’ and improper fraction. Based on students’ performance and typical mistake in translating among representations of fraction tasks, this study proposed some suggestions for fraction teaching. Mathematics teachers should pay more attention on translating among representation of fraction tasks, especially for number line and representations of improper fraction. It can help students build a more comprehensive system of understanding of fraction and improve students’ comprehensions of fraction concept.