Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders
Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islande...
Published in: | Journal of Humanistic Mathematics |
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Claremont Colleges Library
2019
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Online Access: | https://acuresearchbank.acu.edu.au/download/d5679596eee6918f8701d540f2a7ab46f2ac82d93323e446109d5eadf1a0e217/2903013/OA_Lipka_2019_Symmetry_and_Measuring_Ways_to_Teach.pdf https://doi.org/10.5642/jhummath.201901.07 |
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ftaustraliancuni:oai:acuresearchbank.acu.edu.au:8vz79 2023-09-05T13:19:15+02:00 Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders Lipka, Jerry Adams, Barbara Wong, Monica Koester, David Francois, Karen 2019 application/pdf https://acuresearchbank.acu.edu.au/download/d5679596eee6918f8701d540f2a7ab46f2ac82d93323e446109d5eadf1a0e217/2903013/OA_Lipka_2019_Symmetry_and_Measuring_Ways_to_Teach.pdf https://doi.org/10.5642/jhummath.201901.07 unknown Claremont Colleges Library https://acuresearchbank.acu.edu.au/item/8vz79/symmetry-and-measuring-ways-to-teach-the-foundations-of-mathematics-inspired-by-yupiaq-elders ISSN:2159-8118 https://acuresearchbank.acu.edu.au/download/d5679596eee6918f8701d540f2a7ab46f2ac82d93323e446109d5eadf1a0e217/2903013/OA_Lipka_2019_Symmetry_and_Measuring_Ways_to_Teach.pdf https://doi.org/10.5642/jhummath.201901.07 Lipka, Jerry, Adams, Barbara, Wong, Monica, Koester, David and Francois, Karen. (2019). Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders. Journal for Humanistic Mathematics. 9(1), pp. 107-157. https://doi.org/10.5642/jhummath.201901.07 CC BY journal-article 2019 ftaustraliancuni https://doi.org/10.5642/jhummath.201901.07 2023-08-11T14:21:13Z Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry and measuring provide a systematic and integrative way to teach the foundations of mathematical thinking? We illustrate how the fundamental structures of symmetry, measuring, and comparison-of-quantities, starting with the embodied orthogonal axes, form a basis for properties of equality, aspects of numbers and operations (including place value), geometry and number line representations, functions, algebraic reasoning, and measurement. We conclude by embedding the earlier geometric constructions of triangles and squares within the unit circle and making explicit connections to trigonometric functions. Article in Journal/Newspaper eskimo* Alaska Australian Catholic University: ACU Research Bank Journal of Humanistic Mathematics 9 1` 107 157 |
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Australian Catholic University: ACU Research Bank |
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description |
Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry and measuring provide a systematic and integrative way to teach the foundations of mathematical thinking? We illustrate how the fundamental structures of symmetry, measuring, and comparison-of-quantities, starting with the embodied orthogonal axes, form a basis for properties of equality, aspects of numbers and operations (including place value), geometry and number line representations, functions, algebraic reasoning, and measurement. We conclude by embedding the earlier geometric constructions of triangles and squares within the unit circle and making explicit connections to trigonometric functions. |
format |
Article in Journal/Newspaper |
author |
Lipka, Jerry Adams, Barbara Wong, Monica Koester, David Francois, Karen |
spellingShingle |
Lipka, Jerry Adams, Barbara Wong, Monica Koester, David Francois, Karen Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders |
author_facet |
Lipka, Jerry Adams, Barbara Wong, Monica Koester, David Francois, Karen |
author_sort |
Lipka, Jerry |
title |
Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders |
title_short |
Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders |
title_full |
Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders |
title_fullStr |
Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders |
title_full_unstemmed |
Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders |
title_sort |
symmetry and measuring: ways to teach the foundations of mathematics inspired by yupiaq elders |
publisher |
Claremont Colleges Library |
publishDate |
2019 |
url |
https://acuresearchbank.acu.edu.au/download/d5679596eee6918f8701d540f2a7ab46f2ac82d93323e446109d5eadf1a0e217/2903013/OA_Lipka_2019_Symmetry_and_Measuring_Ways_to_Teach.pdf https://doi.org/10.5642/jhummath.201901.07 |
genre |
eskimo* Alaska |
genre_facet |
eskimo* Alaska |
op_relation |
https://acuresearchbank.acu.edu.au/item/8vz79/symmetry-and-measuring-ways-to-teach-the-foundations-of-mathematics-inspired-by-yupiaq-elders ISSN:2159-8118 https://acuresearchbank.acu.edu.au/download/d5679596eee6918f8701d540f2a7ab46f2ac82d93323e446109d5eadf1a0e217/2903013/OA_Lipka_2019_Symmetry_and_Measuring_Ways_to_Teach.pdf https://doi.org/10.5642/jhummath.201901.07 Lipka, Jerry, Adams, Barbara, Wong, Monica, Koester, David and Francois, Karen. (2019). Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders. Journal for Humanistic Mathematics. 9(1), pp. 107-157. https://doi.org/10.5642/jhummath.201901.07 |
op_rights |
CC BY |
op_doi |
https://doi.org/10.5642/jhummath.201901.07 |
container_title |
Journal of Humanistic Mathematics |
container_volume |
9 |
container_issue |
1` |
container_start_page |
107 |
op_container_end_page |
157 |
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1776200065503723520 |