The Relationships between Indonesian Fourth Graders’ Difficulties in Fractions and the Opportunity to Learn Fractions: A Snapshot of TIMSS Results

Abstract

This paper reports an exploration into Indonesian fourth graders' difficulties in fractions and their relation to the opportunity to learn fractions students got at schools. The concept of 'opportunity to learn' is often considered as a framework to investigate possible reasons for students' difficulties. The data for this study was drawn from TIMSS 2015 that comprised test results and teachers' responses to TIMSS Teacher Questionnaire. The test and questionnaire data were analysed by using descriptive statistics. In addition to test and questionnaire, this study also included an analysis of Indonesian textbooks in order to get a broader scope of the opportunity to learn. Qualitative approach was used to analyse the textbooks. The analysis of the TIMSS results shows Indonesian students' low conceptual understanding of fractions. Three possible reasons for students' low conceptual understanding were revealed. First, the content of Indonesian curriculum that gave low emphasis on basic concepts of fractions and introduced operations of fractions too early. Second, the Indonesian mathematics textbooks only presented one definition of fractions, i.e. fractions as parts of wholes. Third, there is a limited use of models or representations of fractions in the classroom practices.

Incomprehension of the Indonesian Elementary School Students on Fraction Division Problem

“…In an attempt to reduce this problem, it is critical not only to focus on the meaning of the fractions as part-towhole, but also to emphasize other sub-fraction constructs in the learning process of fraction concepts (Clarke, Clarke, & Roche, 2011;Purnomo, 2015a;Siebert & Gaskin, 2006), among others fraction as division, fraction as ratio, fraction as operator, fraction as measure. This is also alluded to by Wijaya (2017) in which most mathematics textbooks in Indonesia only introduce the concept of fractions with the concept of fractions as part-to- Volume 8, No 1, February 2019, pp. 57-74 71 whole.…”

“…In Indonesia, context-based teaching is still unique because education systems still focus on performance and result (Purnomo, 2015b(Purnomo, , 2016Purnomo, Suryadi, & Darwis, 2016;Wijaya, 2017). In addition, mathematics textbooks in Indonesia tend to consist of a set of rules and the use of performance-oriented algorithms (Purnomo et al, 2014;Wijaya, 2017). Consequently, students are more likely to cope with regular problems and they encounter hardness in dealing with context-based problems.…”

“…In Indonesia and most of the international curriculum, fractions are firstly introduced in the third grade of the elementary school (Wijaya, 2017), while the divisions are introduced in the fifth grade of elementary school (see also Purnomo, Widowati, Aziz, & Pramudiani, 2017). Further, Wijaya (2017) states that the introduction of the fractional concept as parts of the whole becomes the only construct having a space to learn from both mathematical textbooks and the teacher's teaching method, while the fractional operations are dominated by rigid rules to solve problems.…”

“…In Indonesia, some previous studies have mentioned that the fractions topic becomes a difficult topic for the students and a serious concern because of the weakness of the students' performance on this topic (Purnomo et al, 2014;Trivena, Ningsih, & Jupri, 2017;Wijaya, 2017). In his study, Wijaya (2017) has analyzed students' difficulties on the fractions topic from TIMSS results in 2015 and attributed it to the students' opportunities to study the fractional at school. Based on the analysis of TIMSS results, his research has found that Indonesian students have a weakness on the understanding of fractions, particularly in story problem cases.…”

Learning to Make Sense of Fractions: Some Insights from the Malaysian Primary 4 Pupils

“…Fractions are complex, yet important concepts in mathematics. Fractions are heavily used in various measurements and calculation (Van de Walle, Karp, & Bay-Williams, 2013) as well as providing the foundations on which algebraic thinking and proportional reasoning are built (Chinnappan, 2005;Clarke, Roche, & Mitchell, 2008;Wijaya, 2017). Over the years, the teaching of fractions continues to attract the attention of mathematics teachers and education researchers worldwide.…”