Handling Fractions and Errors in Fractions

Devika R*
Assistant Professor, Department of Education, NSS Training College, Ottapalam, Kerala, India.
Periodicity:July - September'2016
DOI : https://doi.org/10.26634/jmat.5.3.8223


The concept of fractions seems to be very challenging, at the same time interesting to the students. It is introduced to the fourth graders in the school level. The concept of fragmentation from the 'whole' part becomes a real challenge for the teacher as well as for the students. There are enormous ways beginning from the concept of 'Numerator' and 'Denominator' by which students start generating errors while trying to conceptualise it. Teachers should understand and except a good number of errors while practicing the topic fractions. The anticipation of errors while learning like fractions, unlike fractions, mixed fractions, addition and subtraction of fractions, all needs to be attended properly as 'fractions' which is an important area in mathematics and the basics needs to be handled well. Thus when teaching fractions, teachers need to be on the lookout for errors as this may cause errors in the computation also. Some of the most common misconceptions that occur in the classrooms while teaching fractions and handling those errors are discussed in this paper.


Fractions, Numerator, Denominator, Mixed Fractions

How to Cite this Article?

Devika,R. (2016). Handling Fractions and Errors in Fractions. i-manager’s Journal on Mathematics, 5(3), 1-7. https://doi.org/10.26634/jmat.5.3.8223


[1]. Armstrong, B.E. & Larson, C.N. (1995). “Students' use of part-whole & direct comparison strategies for comparing partitioned rectangles”. Journal of Research in Mathematics Education, Vol.26, No.1, pp.2-19.
[2]. Bezuk, N. S. & Bieck, M. (1993). “Current research on rational numbers and common fractions: Summary and implications for teachers”. In D. Owens (Ed.), Research Ideas for the Classroom: Middle Grades Mathematics (pp.118-136). New York: Macmillan Publishing Company.
[3]. Behr, M., Harel, G., Post, T. & Lesh, R. (1993). “Rational numbers: Toward a semantic analysis-emphasis on the operator construct”. In T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.), Rational Numbers: An Integration of Research, pp.13-47. Hillsdale, NJ: Erlbaum.
[4]. Brown, G., & Quinn, R. J. (2006). “Algebra students' difficulty with fractions: An error analysis”. Australian Mathematics Teacher, Vol.62, pp.28-40.
[5]. Brown, G.B., & Quinn, R.J. (2007). “Investigating the relationship between fraction proficiency and success in algebra”. Australian Mathematics Teacher, Vol.63, pp.8-15.
[6]. Carpenter, T., Corbitt, M., Kepner, H., Lindquist, M., & Reys, R. (1980). “National assessment: A perspective of students' mastery of basic mathematics skills”. In M. M. Lindquist (Ed.), Selected Issues in Mathematics Education (pp.215-227). Chicago: National Society for the Study of Education and Reston, VA: National Council of Teachers of Mathematics.
[7]. Clarke, D.M., & Roche, A. (2009). “Students' fraction comparison strategies as a window into robust understanding and possible pointers for instruction”. Educational Studies in Mathematics, Vol.72, pp.127-138.
[8]. Empson, S. & Levi, L. (2011). Extending Children's Mathematics: Fractions and Decimals: Innovations in Cognitively Guided Instruction. Portsmouth, NH: Heinemann. pp.178-216.
[9]. Gould, P., Outhred, L. N., & Mitchelmore, M. C. (2006). “One-third is three-quarters of one-half”. In P. Grootenboer, R. th Zevenbergen & M. Chinnappan (Eds.), Identities, Cultures and Learning Spaces (Proceedings of the 29 Annual Conference of the Mathematics Education Research Group of Australasia, Vol.1, pp.262-269). Adelaide: MERGA..
[10]. Groff, P. (1996). “Is teaching fractions a waste of time?” Clearing House, Vol.69, pp.177-179.
[11]. Hasemann, K. (1981). “On difficulties with fractions”. Educational Studies in Mathematics, Vol.12, pp.71-87.
[12]. Hecht, S.A., Close, L., & Santisi, M. (2003). “Sources of individual differences in fraction skills”. Journal of Experimental Child Psychology, Vol.86, No.4, pp.277-302.
[13]. Huinker, D. (1998). “Letting fraction algorithms emerge through problem solving”. In L. J. Morrow and M. J. Kenny (Eds.), The Teaching and Learning of Algorithms in School Mathematics (pp.198-203). Reston, VA: National Council of Teachers of Mathematics.
[14]. Huinker, DeAnn (2002). “Examining dimensions of fraction operation sense”. NCTM 2002 Yearbook: Making Sense of Fractions, Ratios and Proportions, (pp.72-78).
[15]. Hiebert, J. (1988). “A theory of developing competence with written mathematical symbols”. Educational Studies in Mathematics, Vol.19, pp.333-355.
[16]. Jigyel, K., & Afamasaga-Fuata'i, K. (2007). “Students' conceptions of models of fractions and equivalence”. Australian Mathematics Teacher, Vol.63, pp.17-25.
[17]. Kamii, C. & Clark, F.B. (1995). “Equivalent fractions: Their difficulty and educational implications”. Journal of Mathematical Behavior, Vol.14, pp.365-378.
[18]. Kieren, T. (1995). “Creating spaces for learning fractions”. In J. T. Sowder & B.P. Schappelle (Eds.), Providing a Foundation for Teaching Mathematics in the Middle Grades, (pp.31-65). New York: State University of New York Press.
[19]. Kilpatrick, J., Swafford, J., Findell, B., (2001). Adding it Up: Helping Children Learn Mathematics. The National Academics Press, Washington, DC.
[20]. Kong, S. C. (2008). “The development of a cognitive tool for teaching and learning fractions in the mathematics classroom: A design-based study”. Computers & Education, Vol.51, No.2, pp.886-899.
[21]. Lipkus, I. M., Samsa, G., & Rimer, B. K. (2001). “General Performance on a Numeracy Scale among Highly Educated Samples”. Medical Decision Making, Vol.21, No.1, pp.37-44.
[22]. Mamolo, A., Sinclair, M., & Whiteley, W. J. (2011). “Proportional reasoning with a pyramid”. Mathematics Teaching in the Middle School, Vol.16, No.9, pp.544-549.
[23]. Moss, J. & Case, R. (1999). “Developing children's understanding of the rational numbers: A new model and an experimental curriculum”. Journal for Research in Mathematics Education, Vol.30, No.2, pp.122-147.
[24]. Niemi, D. (1996). “Instructional influences on content area explanations and representational knowledge: Evidence for the construct validity of measures of principled understanding”. CSE Technical Report 403, Los Angeles: National Center for Research on Evaluation, Standards, and Student Testing, University of California.
[25]. National Assessment of Educational Progress, (2005). The Nation's Report Card: Mathematics 2005. Retrieved from http://nces.ed.gov/nationsreportcard/pdf/main2005/2006453.pdf
[26]. Orpwood, G., Schollen, L., Leek, G., Marinelli-Henriques, P., & Assiri, H. (2011). College Mathematics Project. Ministry of Education and the Ontario Ministry of Training, Colleges and Universities. Toronto: Seneca College of Applied Arts and Technology. Retrieved from http://collegemathproject.senecac.on.ca/cmp/en/pdf/FinalReport/2011/CMP_2011_Final_ Report%20-%2002Apr12%20pmh.pdf
[27]. Petit, M., Laird, R., & Marsden, E. (2010). A Focus on Fractions. New York, NY: Routledge.
[28]. Pitkethly, A., & Hunting, R. (1996). “A review of recent research in the area of initial fraction concepts”. Educational Studies in Mathematics, Vol.30, pp.5-38. Retrieved from http://dx.doi.org/10.1007/BF00163751
[29]. Reyna, V. F., & Brainerd, C. J. (2008). “Numeracy, risk communication, and medical decision making”. Learning and Individual Differences, Vol.17, pp.147-159.

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