1332 words - 5 pages

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 say that a measurement understanding of fractions is defined as one that is able to be seen and uses a given unit to measure any distance from the origin.

Knowing the definition of the measurement model of fractions one might ask what is it about measurement activities that facilitate a better understanding of fractions? Barnett-Clarke, Fisher, Marks and Ross (2010) declare that when people engage in measurement activities they are using a tangible method to realize that whole numbers are not precise enough to designate an accurate quantity no matter if measuring volume, length or weight. They contend that when students are given real world experiences that require them to make more precise measurements learners will discover for themselves the need for rational numbers. By providing these hands on activities teachers are fostering students’ innate awareness of fractions to recognize and analyze about the units represented. They also suggest that a number line is an excellent mathematical model that provides deep experiences for students to understand and reason about rational numbers. According to Flores, Samson, and Yanik (2006) number lines that can be presented in ruler, yardstick, or meter stick form early can...

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