Dissertation/Thesis Abstract

Children's Mathematical Understandings of Tessellations: A Cognitive and Aesthetic Synthesis
by Eberle, Robert Scott, Ph.D., The University of Texas at Austin, 2011, 336; 3530288
Abstract (Summary)

Tessellations have a rich mathematical structure and are especially appropriate as a context for teaching geometry in the middle grades. Few studies have researched how children conceptualize and learn tessellations in spite of their international use in educational contexts. This exploratory study looks at how fourth grade students conceptualize tessellations before instruction. The analysis is done from a Piagetian, cognitive viewpoint and from an aesthetic viewpoint. It is argued that the aesthetic viewpoint is crucial and foundational to children's mathematical understanding, just as it is for mathematicians. A series of clinical interviews was conducted with six fourth grade children. The results identified common themes of children's understanding, strategies, reasoning, and aesthetic criteria for tessellations. Children's ontology varied between object and process conceptions of tessellations. Children struggled especially with the infinite space of mathematical tessellations. Children's aesthetics, including symmetry, influenced their choices in creating tessellations and are shown to have played a cognitive role in children's mathematical exploration of tessellation structures. Mathematics influences studentsā€˜ aesthetic appreciation of tessellations and, more importantly, aesthetics drives the study of the mathematical structure of tessellations. Children's aesthetic criteria were the same as mathematiciansā€˜, but with much different emphases. Other results are discussed, including the mathematical content elicited by the tasks, the influence of the tools used to create tessellations, the children's epistemology of their tessellations, and the role symmetry played in giving children confidence. Recommendations for future research and possible implications for curriculum and instruction are noted.

Indexing (document details)
Advisor: Carmona-Dominguez, Guadalupe
School: The University of Texas at Austin
School Location: United States -- Texas
Source: DAI-A 74/02(E), Dissertation Abstracts International
Subjects: Mathematics education
Keywords: Aesthetics, Geometry, Infinite space, Symmetry, Tessellations, Tiling
Publication Number: 3530288
ISBN: 978-1-267-68443-1
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