Academic journal article Journal of Emerging Trends in Educational Research and Policy Studies

An Invesatigation of 5th and 6th Grade Students' Success Rates in Solving Fraction Problems Having Different Representation Formats

Academic journal article Journal of Emerging Trends in Educational Research and Policy Studies

An Invesatigation of 5th and 6th Grade Students' Success Rates in Solving Fraction Problems Having Different Representation Formats

Article excerpt


Previous studies show that students have problems with fractions. This reason was seen important make a study that related with the fractions and representation forms. The aim of this study is to investigate 5th and 6th grade students' achievement of solving fraction problems according to their representation styles in the topic of operations with fractions and to reveal ideas of the students about fraction problems according to their representation forms. A mixed method composed of quantitative and qualitative techniques was used in this research. Firstly, the quantitative data was analyzed, and then, the qualitative data was collected by interviewing with the prospective teachers in order to retrieve detailed information from them about the tests prepared according to representation types of fractions and the answers they gave to the questions placed in these tests and to support quantitative findings. "Verbal Representation Test (VERT)", "Visual Representation Test (VIRT)" and "Symbolic Representation Test (SRT)", including 4 questions and developed by the researchers, were used as quantitative data collection tools. The study was conducted with 127 students at 5th and 6th grades of a state school in Bolu-Turkey, in the academic years of 2013-2014. As a result of data analysis, it was found that the means of 6th grade students were higher than that of 5th grade students in all representation forms of problems. When the differences between achievements of the tests were examined, the difference in the symbolic test was only found to be significant. It appeared that there was a positive and significant relationship between the achievements of students in solving fraction problems presented in different representation styles. These results show that the performances of students were affected by the different representation forms.

Keywords: fractions, addition with fractions, subtraction and multiplication, verbal-visual-symbolic representation, mathematics education


The concept of natural numbers is presented to students in elementary school. Additionally; the concept of fractions, despite not a set of numbers, is taught to students in order to make an introduction to rational numbers. From the beginning of elementary school, students begin to learn what a fraction means. Towards the upper grades, fractions with different denominators, comparison and sorting in fractions, and additions, subtractions and multiplications with fractions are learnt. Examining 1st- 4th grade gains in the Primary School Mathematics Curriculum (1-5. Classes) (Ministry of Education, [IMDOP], 2009), it can be said that rational numbers are taught earlier than integers due to the presentation of the concept of fragments. This is because students are more likely to encounter with fractions and rational numbers in everyday life and in the events around them (Altun, 2002).

The word 'Fraction', in the Glossary of Turkish Language Institution, is described as 'a number expressing one or more equal parts of a divided unit" (TDK, 2014). Fractions are used to show fragmental amounts and are quite different from cardinal numbers. While natural numbers answer the question "How many?", fractions give answer to the question "How much?". Furthermore, fractions cannot be obtained by counting (Toluk and Olkun, 2002). Therefore, for elementary school students especially focusing on making operations with counting and natural numbers, fractions seem to be a highly complex and difficult issue (Charalambos and PittaPantazi, 2005). It is stated that the issues encountered here not only arise from the use of different approaches in teaching the concept of fractions but also from the structure of the fractions (Aytekin, 2012; Behr, Harel, Post and Lesh, 1993; Ertuna, 2013). In addition to the students, teacher candidates are experiencing certain difficulties in the concept of fractions as well. In a study conducted on mathematics and classroom teachers; teacher candidates' pedagogical content knowledge related to natural numbers was found to be higher than their pedagogical content knowledge related to fractions (Sahin, Gökkurt, Basibüyük, Erdem, Nergiz and Soylu, 2013). …

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