Fraction Assessment Analytic 1: Fourth Graders’ Argumentation about the Comparison of 1/2 and 1/3
Creators: name: Van Ness, Cheryl
Publisher: name: No Publisher Supplied
Year: 2015

description: The events depicted in this analytic were taken from a larger data set gathered as a result of a year-long research intervention involving fourth graders’ exploration of fractions. The events depicted here occurred on September 29, 1993 and are taken from the first month of the intervention during the fifth session. (For a detailed analysis of the student reasoning during this intervention, see Maher &amp; Yankelewitz, 2017; Yankelewitz, 2009).The students’ investigations in this VMCAnalytic build on their explorations in the prior sessions, during which they constructed Cuisenaire rod models to support ideas about basic relationships among whole numbers and fractions. During these sessions, students assigned number names to individual rods and also to trains constructed of more than one rod based on a specific rod, or train of rods, given the number name 1 and assigned as the “unit." During the sessions prior to this one, students compared 1/2 and 1/3 and developed Cuisenaire rod models to support their claim that 1/2 was greater than 1/3 (Steencken, 2001; Steencken &amp; Maher, 2003; Yankelewitz, 2009; Maher &amp; Yankelewitz, 2017). During Session 3, Researcher Carolyn Maher contextualized the idea of the unit by describing an actual situation in which she used chocolate candy bars as a metaphor for thinking about fractions. Students agreed that 1/2 of a larger candy bar (unit) was bigger than 1/2 of a smaller candy bar (unit) and so they should keep the same "candy bar" or the same unit when assigning number names to rods during their Cuisenaire rod explorations (Alston &amp; Van Ness, 2017). In Session 5, depicted here, students revisit the comparison of 1/2 and 1/3 and are asked to quantify the difference. The argumentation described here supports solutions to the task, "Which is greater 1/2 or 1/3, and by how much?" It is important to note that, other than this research intervention, students in this analytic had not had any formal instruction on operations with fractions. Researchers have found that given certain learning environments, students, even young children, can develop convincing arguments (Krummheuer, 1995; Weber, Maher, Powell, &amp; Lee, 2008; Conner et al., 2014; Whitenack &amp; Yackel, 2002; Ball, 1993; Ball et al., 2002; Stylianides, 2006; 2007; Zack, 1997; 1999; Maher &amp; Martino, 1996; Maher, 2009). The original purpose of this analytic was to access viewers understanding of argumentation. The current purpose is to outline the argumentation in each event. For a detailed analysis of the argumentation in each event, including students’ claims, data, warrants, and backing and accompanying diagrams that show the elements and structure of the argumentation in these events, see Van Ness (2017). For a more detailed discussion of students’ exploration of the unit, see VMCAnalytic Comparing Models and Justifying the Choice of Unit, (http://dx.doi.org/doi:10.7282/T3XW4MQT) (Van Ness &amp; Alston, 2015) and Switching the Unit (Alston &amp; Van Ness, 2017), Justifying the Choice of the Unit (Van Ness &amp; Alston, 2017) and Establishing the Importance of the Unit (Van Ness &amp; Alston, 2017). For a more detailed discussion of the events that come after the ones presented here, see the VMCAnalytic Comparing 1/2 and 1/3: Confusion about the Unit, (http://dx.doi.org/doi:10.7282/T3ZW1NS9) (Van Ness &amp; Alston, 2015) and Switching the unit (Alston &amp; Van Ness, 2017). ReferencesAlston, A. S., &amp; Van Ness, C. K. (2017). Switching the Unit. In C. A. Maher &amp; D. Yankelewitz (Eds.). Children’s Reasoning While Building Fraction Ideas (pp. 65-81). Rotterdam, The Netherlands: Sense Publishers.Ball, D. L. (1993). 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Journal for Research in Mathematics Education, 38(3), 289-321.Van Ness, C. K. (2017). Creating and Using RUAnalytics for Preservice Teachers’ Studying of Argumentation. Doctoral dissertation, Rutgers, The State University of New Jersey, New Brunswick.Van Ness, C. K. &amp; Alston, A. S. (2015). Comparing 1/2 and 1/3: Confusion about the Unit. [video]. Retrieved from http://dx.doi.org/doi:10.7282/T3ZW1NS9Van Ness, C. K. &amp; Alston, A. S. (2015). Comparing Models and Justifying the Choice of Unit. [video]. Retrieved from http://dx.doi.org/doi:10.7282/T3XW4MQTVan Ness, C. K. &amp; Alston, A. S. (2015). Which is Larger, 1/2 or 1/3? An Introduction to Comparing Unit Fractions. [video]. Retrieved from http://dx.doi.org/doi:10.7282/T3V40X3RVan Ness, C. K., &amp; Alston, A. S. (2017). Establishing the Importance of the Unit. In C. A. Maher &amp; D. Yankelewitz (Eds.). Children’s Reasoning While Building Fraction Ideas (pp. 49-64). Rotterdam, The Netherlands: Sense Publishers.Van Ness, C. 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