The Use of Concrete Contexts for Conceptual Change in Addition Of Fractions

08 Nov

Addition of fractions is one of mathematics topics which are learned by elementary school students. However, in general, students’ achievement on this topic is not good enough. The possible cause is because students find some difficulties when they are learning the domain of fractions. As Prediger (2006) wrote that in many different countries, empirical studies on students’ competencies and conceptions in the domain of fractions have shown enormous difficulties. In term of addition as one of operations applied in fractions, the relationship between integers and fractions is sometimes dangerous to students as they tend to analogize the concept. They often choose the easiest way to solve addition of fractions problems by using this following rule. 

Hart (1981) found that 30% of 13 year olds students were making this error, and notes that 15 year oldsstudents were almost as likely to make this error as 13 year olds (see Sadi, 2007). In this case, conceptual change is needed to overcome both students’ misinterpretation and misconception. Furthermore, it leads students to the right conceptual knowledge. The use of context, specifically concrete context might be a promising solution for this problem since according to Gilbert (2007), the function of context is to describe such circumstances that give meaning to words, phrases, and sentences. Contexts using concrete problems are possible to make students’ learning more meaningful and relieve their misinterpretation and misconception. However, the question is what kinds of concrete contexts which are appropriate and useful for conceptual change in addition of fractions?

To answer the question, mathematics textbooks and observations in mathematics classroom which have been done by teachers can be used as references. Firstly, the idea is using pizza contexts which further symbolized by pie charts (PDST, 2010) and using loaves context which further symbolized by bar charts (Fosnot & Dolk, 2002). However, teachers will find that it is difficult to apply these contexts in solving addition of fractions with different denominators as this following problem:

Secondly, according to Fosnot and Dolk (2002), an idea of using time measurement can be possible used as an alternative context. Yet, it has a weakness since teacher can only apply this context for certain denominators. Therefore, as the third context, the idea of using length measurement of a hundred basis numbers might also be another alternative solution. Both the second and the third contexts work in a cycle which is started by converting fractions to measurement and continued reconverting measurement to fractions. The idea of using these contexts is parallel with the principle of Realistic Mathematics Education (RME), “conceptual matematization” which said that a general concept is extracted from several more concrete instantiations (de Lange, 1987; Gravemeijer, 1994, Bock, et all, 2011). The expectation is that students can understand the substance of addition of fractions since they experience kinds of real problems. Hence, their prior knowledge which is assuming that the concept of addition of fractions is by adding the numerators and denominators will be changed to the correct conceptual knowledge.


Bock, et all. 2011. Abstract or Concrete Examples in Learning Mathematics? A replication and Elaboration of Kaminski, Sloutsky, and Heckler’s Study. Journal for Research in Mathematics Education. 42 (2), 109 – 126.

Gilbert, John K. 2006. On the Nature of “Context” in Chemical Education. International Journal of Science Education. 28 (2), 957 – 976.

Prediger, Susanne. 2006. Continuities and discontinuities for fractions, a proposal for analyzing in different levels. Published in Novotna, J. et al. (eds.): Proceedings of the 30th PME, 4-377-384. Germany: Bremen University.

Fosnot, C. T. and Dolk, M. 2002. Constructing Fractions, Decimals, and Percents. United States of America.

Professional Development Service for Teachers (PDST). Fractions: Teacher’s Manual. A guide  for teaching fractions in Irish primary schools. (Assesed February 2013).

Sadi, Amar. 2007. Misconceptions in Numbers. UGRU Journal. 5, 1 – 7.


This is the first trial essay which was submitted for an Introduction to Science Education and Communication course. Yah, there will always a first time in everything you do. And it is normal if you need a lot of improvement. Semangattt!!!



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Posted by on November 8, 2013 in Papers


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