Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis

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...

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Main Author: Eberle, Robert Scott
Format: Others
Language:English
Published: 2012
Subjects:
Online Access:http://hdl.handle.net/2152/ETD-UT-2011-12-4815
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spelling ndltd-UTEXAS-oai-repositories.lib.utexas.edu-2152-ETD-UT-2011-12-48152015-09-20T17:06:01ZChildren's mathematical understandings of tessellations : a cognitive and aesthetic synthesisEberle, Robert ScottTessellationElementary educationMathematics educationGeometryAestheticsTilingSymmetryInfinite spaceTessellations 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 students' 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 mathematicians', 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.text2012-04-02T15:02:11Z2012-04-02T15:02:11Z2011-122012-04-02December 20112012-04-02T15:02:36Zthesisapplication/pdfhttp://hdl.handle.net/2152/ETD-UT-2011-12-48152152/ETD-UT-2011-12-4815eng
collection NDLTD
language English
format Others
sources NDLTD
topic Tessellation
Elementary education
Mathematics education
Geometry
Aesthetics
Tiling
Symmetry
Infinite space
spellingShingle Tessellation
Elementary education
Mathematics education
Geometry
Aesthetics
Tiling
Symmetry
Infinite space
Eberle, Robert Scott
Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
description 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 students' 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 mathematicians', 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. === text
author Eberle, Robert Scott
author_facet Eberle, Robert Scott
author_sort Eberle, Robert Scott
title Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
title_short Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
title_full Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
title_fullStr Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
title_full_unstemmed Children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
title_sort children's mathematical understandings of tessellations : a cognitive and aesthetic synthesis
publishDate 2012
url http://hdl.handle.net/2152/ETD-UT-2011-12-4815
work_keys_str_mv AT eberlerobertscott childrensmathematicalunderstandingsoftessellationsacognitiveandaestheticsynthesis
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