Teaching Measurement and Fractions Essay

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According to the National Center for Education Evaluation (2010), a high number of U.S. students do not possess conceptual understanding of fractions even after they have had the opportunity to study about them for several years. Because these students lack this understanding they are limited in their ability to solve problems with fractions and to learn and apply mathematical procedures that include fractions. This is supported by Yanik, Helding, and Baek (2006) who report that students’ understanding of fractions reflect that most struggle with conceptualizing fractions, and that this is true not just nationally but also globally. According to Barnett-Clarke, Fisher, Marks and Ross (2010) teachers need to help students conceptualize fractions as an extension of the way in which we use whole numbers. They contend that measurement opportunities offer an effortless evolution from understanding whole numbers to understanding fractions. This leads educators to ask, what is the measurement model of fractions, what is it about measurement activities that serves as a conduit to rational numbers, and what elements must a quality measurement lesson include to help students see the relationship of whole numbers to rational numbers?
The measurement model of fractions as described by Lamon (2012) declares a fraction is usually the measure assigned to some interval or region. In a one dimensional interval the fraction measures length and a two dimensional interval the fraction measures area or volume. As imparted by Chapin and Johnson (2006), a rational number is the measure of some distance or region that is often referred to as some point on a number line and these points actually are a measure of distance. Lamon (1999) goes on to sa...

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...eachers of Mathematics, 335-339.
Moyer, P. S., & Mailley, E. (2004). Inchworm and a Half: Developing Fraction and Measurement Concepts Using Mathematical Representations. Teaching Children Mathematics, 244-252.
National Center for Education Evaluation. (2010). Developing Effective Fractions Instruction for Kindergarten Through 8th Grade. Washington D.C.: U.S. Department of Education.
Wong, M., & Evans, D. (2008). Fractions as Measures. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia (pp. 597-603). Brisbane: MERGA inc. 2008.
Yanik, H. B., Helding, B., & Back, J. M. (2006). Students' Difficulties in Understanding Fractions as Measures. 28th Annual meeting of the North American Chapter of the Internation Group for the Psychology of Mathematics Education (pp. 323-325). Merida, Mexico: Universidad Pedagogica Nacional.

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