According to the National Center for Education Evaluation (2010), a large number of U.S. students lack the conceptual understanding of fractions even after having had the opportunity to study them for several years. Because these students lack this understanding, their ability to solve fraction problems and learn and apply mathematical procedures that include fractions is limited. This is supported by Yanik, Helding, and Baek (2006) who report that students' understanding of fractions reflects most difficulties with conceptualizing fractions, and that this is true not only nationally but also globally. According to Barnett-Clarke, Fisher, Marks, and Ross (2010) teachers need to help students conceptualize fractions as an extension of how we use whole numbers. They argue that measurement opportunities offer a simple evolution from understanding whole numbers to understanding fractions. This leads educators to ask what the measurement model of fractions is, what the measurement activity that serves as a conduit to rational numbers consists of, and what elements a quality measurement lesson should include to help students see the relationship between integers and rational numbers. The fraction measurement model described by Lamon (2012) states that a fraction is usually the measurement assigned to an interval or region. In a one-dimensional interval the fraction measures length and in a two-dimensional interval the fraction measures area or volume. As explained by Chapin and Johnson (2006), a rational number is the measure of some distance or region which is often referred to as points on a number line and these points are actually a measure of distance. Lamon (1999) goes on to cite......middle of paper......achers of Mathematics, 335-339.Moyer, P.S., & Mailley, E. (2004). Worm and a Half: Developing Fraction and Measurement Concepts Using Mathematical Representations. Teaching mathematics to children, 244-252. National Center for Educational Evaluation. (2010). Developing effective fraction instruction for kindergarten through eighth grade. Washington DC: US Department of Education. Wong, M., & Evans, D. (2008). Fractions as measures. Proceedings of the 31st annual conference of the Australasian Mathematics Education Research Group (pp. 597-603). Brisbane: MERGA inc. 2008.Yanik, H. B., Helding, B., & Back, J. M. (2006). Student difficulty understanding fractions as measures. 28th annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education (pp. 323-325). Merida, Mexico: Universidad Pedagogica Nacional.
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