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ETD_2540

http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052900

theses

This study examined how Milin, a nine-year old student, justified his solutions to towers of a variety of heights over a 13 month period. Specifically, it sought to identify heuristics, strategies, and forms of reasoning and argumentation used by Milin in building and supporting his reasoning by partial cases, cases, and then an inductive argument. The research also traced how Milin's ideas traveled to other students. Videotape recordings of Milin's work on towers task and its extensions were analyzed along with his written work, written assessments and the researcher's field notes. The video data consisted of two problem-solving sessions, three individual task-based interviews, a small group assessment, and a whole class discussion. As Milin searched for and sought to justify a global solution for the towers problem, he constructed mathematical ideas by continuously evolving the heuristics and strategies employed. He started by making random towers using a "guess and check" method, where he would randomly create a tower and then compared it with existing towers to identify duplicates. He then proceeded to use local organization strategies to create pairs of towers. This included opposites by color, opposites by inverting and a hybrid strategy. Later, Milin moved towards more refined local organizations such as staircase patterns. When these schemes also proved inadequate to justify a complete solution, Milin developed a family strategy, based on a doubling pattern he had uncovered. This strategy gave him a global organization method. The progression to the global solution was an iterative process in which Milin revisited earlier strategies. Milin also used various forms of reasoning to account for all towers. These included amount of time elapsed between building towers, the concept of "partner" towers, justification by contradiction, cases, doubling rule, and the family strategy. Milin shared his inductive argument with three other students during a small group assessment session. Almost one year later, he re-explained his inductive argument to his partner, Michelle, while working on another task. In turn she shared this argument with other class mates, culminating with one student presenting it to the entire class. The students appeared to understand and retain Milin's strategy better when involved in solving the problem themselves. This case study contributes the body of research in several ways. It documents strategies used by young students to build models of reasoning and argumentation. It also provides support for Davis and Maher's idea that building understanding is not a linear process in that new ideas are built from previous ideas. Finally, this study contributes to the broader collection of case studies from the longitudinal study at Rutgers University.

Ed.D.

Includes abstract

Includes bibliographical references

by Manjit Kaur Sran

doi:10.7282/T34Q7V2G

ETD doctoral

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ETD

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