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theses

This study uses RUanalytics to examine the representations created by fourth and eighth grade students' work in solving open-ended activities of comparing and ordering fractions on a number line and finding surface area and volume of various models of stacked Cuisenaire rods. This research study has developed from data collected from a longitudinal and cross sectional study of two focus groups of students, conducted at Rutgers University. The research reported here builds on this earlier work by using video clips and full video to construct video narratives of student learning. The methodology of this study is based on the viewing and analysis of archived video data, student transcripts and the creation of three RUanalytics, two showing problem solving of fourth graders and a third of eight graders. The video data were analyzed according to the model by Powell, Francisco and Maher (2003). The methodology was extended to include building video narratives with the RUanalytic tool. The study was guided by a single research question: What representations do fourth and eighth grade students use to express their ideas in problem solving? As the fourth-grade students transitioned from operator to number understanding of fraction, they used a variety of representations in their problem solving: manipulatives, pictorial, written, symbolic, imagistic and spoken language. Eight-grade students also used manipulative, pictorial, written, symbolic notation, imagistic, experiential and spoken language to represent their data when working to find a formula for the surface area and volume of rods and stacked rods. By using a variety of representations and moving between and among them, students uncovered important mathematical ideas and relationships in their problem solving. This research provides evidence of the importance of open-ended problem solving tasks in which students have an opportunity to call upon a variety of personal representations to explore their ideas prior to formal instruction. By tracking student representations in problem solving, the RUanalytics show, students growing understanding of rational number ideas and early algebra concepts.

ETD_7091

Ed.D.

Includes bibliographical references

by Kenneth A. Horwitz

doi:10.7282/T3Z60R73

ETD doctoral

The author owns the copyright to this work.