### Students’ Performance in Solving Problems Involving Fractions

Linda Vitoria, Fauzi Fauzi, Nadia Ananda

#### Abstract

The concept of fraction is a fundamental mathematics subject that is repeatedly reported to be difficult for students to learn and for teachers to teach. Various articles on strategies to teach fractions have been presented, but students’ proficiency in dealing with fractions has not improved in general. This article describes a qualitative study conducted to assess students’ performance in solving a set of problems involving addition and subtraction of fractions. The students’ performances were analyzed according to the standard competence as inscribed in the Indonesian Curriculum Version Year 2013 for fifth grade students which was: capable of solving problems involving addition and subtraction of fractions with different denominators. A set of test was administered to twenty fifth-grade students at a primary school in Aceh, Indonesia. Result showed that the students’ understanding of addition and subtraction of fractions was poor: majority of the students knew the rule of addition and subtraction of fractions but only 45% executed the computation correctly, 25% students appeared to be struggling in finding the least common denominator when executing operations with fractions, none of the students reduced their fractions to lowest terms, and understanding word problems also proved to be a challenge to many of the students. This finding necessitates the importance of meaningful learning. Students need to experience fractions in a familiar context in order to be able to grasp conceptual and procedural understanding of fractions.

Keywords:student performance, addition and subtraction of fractions.

PDF

#### References

Amato, S. (2005). Developing students’ understanding of the concept of fractions as numbers. Paper presented at the 29th Conference of the International Group for the Psychology of Mathematics Education. 10-15 July, Melbourne, Australia.

Charalambous, C. Y., Delaney, S., Hsu, H., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117-151.

Idris, N., & Narayanan, L. M. (2011). Error patterns in addition and subtraction of fractions among Form Two students. Journal of Mathematics Education, 4(2), 35-54.

Jan, S., & Rodrigues, S. (2012). Students’ difficulties in comprehending mathematical word problems in English language learning contexts. International Researcher, 1(3), 152-160.

Johar, R., Patahuddin, S. M., & Widjaja, W. (2017). Linking pre-service teachers’ questioning and students’ strategies in solving contextual problems: A case study in Indonesia and the Netherlands. The Mathematics Enthusiast, 14(1), 101-128.

Lamon, S. J. (2005). Teaching fractions and ratios for understanding (2nd ed.). Mahwah: Lawrence Erlbaum Associates.

Major, T. E., & Mangope, B. (2012). The constructivist theory in mathematics: The case of Botswana primary school. International Review of Social Sciences and Humanities, 3(2), 139-147.

Ndalichako, J. L. (2013). Analysis of pupils’ difficulties in solving questions related to fractions: The case of primary school leaving examination in Tanzania. Creative Education, 4(9), 69-73.

Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26, 400-417.

OECD. (2016). Programme for International Student Assessment (PISA): Results from PISA 2015. Retrieved from https://www.oecd.org/pisa/PISA-2015-Indonesia.pdf

Piaget, J. (1968). Quantification, conservation, and nativism. Science, 162, 976-979.

Sadi, A. (2007). Misconceptions in numbers. UGRU Journal, 5, 1-7.

Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM Mathematics Education, 40, 927-939.

Siebert, D., & Gaskin, N. (2006). Creating, naming and justifying fractions. Teaching Children Mathematics, 12, 394-400.

Siegler, R., et al. (2010). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE, 2010-4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, US Department of Education.

Wong, M., & Evans, D. (2011). Assessing students’ understanding of fraction equivalence. Fractions: Teaching for Understanding (pp. 81-90). Adelaide: The Australian Association of Mathematics Teachers Inc.