DOI: 10.14704/nq.2018.16.10.1699

Using Cooperative Learning to Overcome Students’ Misconceptions about Fractions

Elizabeth Julius, Abdul Halim Abdullah, Ting Yann Yann, Mahani Mokhtar, Sharifah Nurarfah S. Abd Rahman


The purpose of this study was to identify misconceptions about Fractions among Year 4 students. In addition, the study also investigated effectiveness of Cooperative Learning in correcting students’ misconceptions about Fractions. This study was conducted among Year 4 students from two classes in a primary school in Johor Bahru. Sixty students (30 students for experimental group and 30 students for control group) of heterogeneous academic levels were involved in the study. Descriptive quantitative design was used in this study. A pre-test was given to students before treatment to investigate their misconceptions about Fractions. Students in the experimental group were taught for four weeks using STAD strategy which is a Cooperative Learning approach. However, students in the control group were taught for four weeks using a traditional method. A post-test was given after the treatment to investigate the effectiveness of Cooperative Learning in correcting students’ misconception about Fractions. The quantitative data were presented in percentages. Results of the study show that there are four misconceptions about Fractions among Year 4 students. First, the bigger the number of denominators, the bigger the Fractions; second, the students viewed whole number as numerator in Fractions; third, the students viewed numerator and denominator as separate numbers and fourth, students failed to find a common denominator. In addition, the findings of this study also show that cooperative learning is effective in correcting students’ misconceptions about Fractions. Therefore, Cooperative Learning is recommended to be used as a teaching strategy to overcome students’ misconceptions about Fractions.


misconception; Cooperative Learning; Fractions

Full Text:



Alder J. Setati, M. Pedagogy and Diversity in Maths Classroom: Using and Expressing Mathematics. School of Education, 2001.

Artzt AF, Newman CM. How to use cooperative learning in the mathematics class. National Council of Teachers of Mathematics, 1906 Association Drive, Reston, VA Virginia, 2006.

Anthony RA. Cooperative learning effects on the classroom. Masters Thesis, Northern Michigan University, 2013.

Aksu M. Student performance in dealing with fractions. The Journal of Educational Research 1997; 90(6): 375-80.

Bednar J, Coughlin J, Evans E, Sievers T. Improving Student Motivation and Achievement in Mathematics through Teaching to the Multiple Intelligences. Saint Xavier University, Chicago, 2002.

Battista MT. A research-based perspective on teaching school geometry. InSubject-specific instructional methods and activities 2001: 145-85

Bernero J. Motivating students in math using cooperative learning. Saint Xavier University, Chicago, 2000.

Bennett BB, Rolheiser-Bennett NC, Stevahn L. Cooperative learning: Where heart meets mind: An interactive resource book. Educational Connections, 1991.

Christou KP, Vosniadou S. What kinds of numbers do students assign to literal symbols? Aspects of the transition from arithmetic to algebra. Mathematical Thinking and Learning 2012; 14(1): 1-27.

Cheng HA. Case study of cooperative learning in mathematics: middle school course design. Journal of Mathematics Education 2011; 4, (1): 79-91.

Dunzenli GN, Sharma MD. A study on the addition and subtraction of fractions: The use of Pirie and Kieren model and hands on activities. Procedia Social and Behavioral Sciences, 2010.

DeTurk D. Out in the left field: Why teach fractions? Skeptic Ring Publisher, 2008.

Empson SB, Levi L. Extending children’s mathematics: Fractions and decimals. Mathematics Education 2011; 27(4): 403-34.

Fazio L, Siegler R. Teaching Fractions. Educational Practices Series-22. UNESCO International Bureau of Education, 2011.

Gould P, Mitchelmore M. Conference proceedings of the 2006 meeting of the Mathematics Education Research Group of Australia (MERGA): Australia, 2006.

Gabriel FC, Coché F, Szucs D, Carette V, Rey B, Content A. A componential view of children's difficulties in learning fractions. Frontiers in Psychology 2013; 4: 715.

Gillies RM, Haynes M. Increasing explanatory behaviour, problem-solving, and reasoning within classes using cooperative group work. Instructional Science 2011; 39(3): 349-66.

Gardner H. The disciplined mind. New York: Simon & Schuster, 1999.

Hallett D, Nunes T, Bryant P, Thorpe CM. Individual differences in conceptual and procedural fraction understanding: The role of abilities and school experience. Journal of Experimental Child Psychology 2012; 113(4): 469-86.

Hecht SA, Vagi KJ. Patterns of strengths and weaknesses in children’s knowledge about fractions. Journal of Experimental Child Psychology 2012; 111(2): 212-29.

Hackenberg A, Lee M. Pre-fractional middle school students’ algebraic reasoning. InProceedings of the 34th annual meeting of the north American chapter of the international group for the psychology of mathematics education 2012: 943-50.

Rittle-Johnson B, Schneider M. Developing conceptual and procedural knowledge of mathematics. Oxford handbook of numerical cognition, 2016.

Johnson DW, Johnson RT, Holubec E. Cooperation in the classroom, 8th ed., Minneapolis: Interaction Book Company, 2008

Khan GN, Inamullah HM. Effect of student’s team achievement division (STAD) on academic achievement of students. Asian Social Science 2011; 7(12): 211.

Kagan M, Kagan S. Advanced cooperative learning. San Clemente: Kagan, 2000.

Keramati M. The Effect of Cooperative Learning On Academic Achievement of Physics Course. In T. Bastiaens et al. (Eds.), Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education 2009: 2751-56.

Luneta K, Makonye PJ. Learner Errors and Misconceptions in Elementary Analysis: A Case Study of a Grade 12 Class in South Africa. Acta Didactica Napocensia 2010; 3(3): 35-46.

Martinie S. Assessing conceptual understanding of rational numbers and constructing a model of the interrelated skills and concepts, 2005.

Ni Y, Zhou YD. Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist 2005; 40(1): 27-52.

Narzoles DG. Student Team Achievement Division (STAD): Its effect on the Academic performance of EFL Learners. American Research Journal of English and Literature.(1). 2015; 1.

National Mathematics Advisory Panel. Foundations for success: The final report of the National Mathematics Advisory Panel. US Department of Education, 2008.

Ojose B. Common misconceptions in mathematics: Strategies to correct them. University Press of America, 2015.

Pinzker V. Increasing the Engagement and Understanding of Concepts in Mathematics. Saint Xavier University, Chicago, 2001.

Rai N, Samsuddin S. STAD vs Traditional teaching, Redesigning Pedagogy, 2007.

Siemon D. The missing link in building fraction knowledge and confidence. Australian Mathematics Teacher 2003: 411-15. (Proceeding).

Siegler RS, Thompson CA, Schneider M. An integrated theory of whole number and fractions development. Cognitive Psychology 2011; 62(4): 273-96.

Siegler RS, Fazio LK, Bailey DH, Zhou X. Fractions: The new frontier for theories of numerical development. Trends in cognitive Sciences 2013; 17(1): 13-19.

Lamon SL. Rational Numbers and Proportional Reasoning: Toward a Theoretical Framework. In Lester (Ed.), Second handbook of research on mathematics teaching and learning: Chalotte, NC: Information Age Publishing 2007, 629-668.

Slavin RE. Using Student Team Learning. Revised Edition. Baltimore: Center for Social Organization of Schools, The Johns Hopkins University, 1980.

Slavin RE. Synthesis of Research on Cooperative Learning. Educational Leadership 1981; 38(8): 655.

Slavin RE. Cooperative Learning, Success for all and evidence-based reform in education. John Hopkins University, 2008.

Stafylidou S, Vosniadou S. The development of students’ understanding of the numerical value of fractions. Learning and İnstruction 2004;14(5): 503-18.

Slavin RE. Cooperative learning: Where behavioral and humanistic approaches to classroom motivation meet. The Elementary School Journal 1987; 88(1): 29-37.

Slavin RE. Cooperative learning: what makes group-work work?. The Nature of Learning 2010:161-78.

Sarwadi HR, Shahrill M. Understanding students’ mathematical errors and misconceptions: The case of year 11 repeating students. Mathematics Education Trends and Research 2014; 2014: 1-0.

Slavin RE. Research on cooperative learning: Consensus and controversy. Educational Leadership 1990; 47( 4): 52-54.

Schneider M, Siegler RS. Representations of the Magnitudes of Fractions. Journal of Experimental Psychology. Human Perception and Performance 2010; 36( 5): 1227–38.

Tan IGC, Sharan S, Lee CKE. Group Investigation and Student Learning. An Experiment in Singapore Schools. Marshall Cavendish Academic, 2006.

Vamvakoussi X, Vosniadou S. Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction 2004; 14(5): 453-67.

Way J. Developing Fraction Sense Using Digital Learning Objects. Fractions: Teaching for Understanding. The Australian Association of Mathematics Teachers (AAMT) Inc, 2011: 153-66.

Wong M, Evans D. Assessing Students’ Understanding of Fraction Equivalence.. Australian Association of Mathematics Teachers 2011; 81-90.

Purnomo YW, Kowiyah K, Alyani F, Assiti SS. Assessing number sense performance of Indonesian elementary school students. International Education Studies 2014; 7(8): 74.

Supporting Agencies

The authors would like to thank University Technology Malaysia and Ministry of Education for their financial support. This work was supported by the research Universiti Grant (GUP) Tier I grant no QJ130000.2531.19H09.

| NeuroScience + QuantumPhysics> NeuroQuantology :: Copyright 2001-2018