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...
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ftclaremontcoir:oai:scholarship.claremont.edu:jhm-1534 2023-05-15T16:07:24+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 2019-01-31T17:32:31Z application/pdf https://scholarship.claremont.edu/jhm/vol9/iss1/7 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1534&context=jhm unknown Scholarship @ Claremont https://scholarship.claremont.edu/jhm/vol9/iss1/7 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1534&context=jhm default Journal of Humanistic Mathematics mathematics education Indigenous Knowledge symmetry measuring Anthropology Arts and Humanities Indigenous Education Logic and Foundations of Mathematics Mathematics Science and Mathematics Education text 2019 ftclaremontcoir 2022-06-06T07:42:07Z 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. Text eskimo* Alaska Claremont Colleges: Scholarship@Claremont |
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mathematics education Indigenous Knowledge symmetry measuring Anthropology Arts and Humanities Indigenous Education Logic and Foundations of Mathematics Mathematics Science and Mathematics Education |
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mathematics education Indigenous Knowledge symmetry measuring Anthropology Arts and Humanities Indigenous Education Logic and Foundations of Mathematics Mathematics Science and Mathematics Education Lipka, Jerry Adams, Barbara Wong, Monica Koester, David Francois, Karen Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders |
topic_facet |
mathematics education Indigenous Knowledge symmetry measuring Anthropology Arts and Humanities Indigenous Education Logic and Foundations of Mathematics Mathematics Science and Mathematics Education |
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 |
Text |
author |
Lipka, Jerry Adams, Barbara Wong, Monica Koester, David Francois, Karen |
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 |
Scholarship @ Claremont |
publishDate |
2019 |
url |
https://scholarship.claremont.edu/jhm/vol9/iss1/7 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1534&context=jhm |
genre |
eskimo* Alaska |
genre_facet |
eskimo* Alaska |
op_source |
Journal of Humanistic Mathematics |
op_relation |
https://scholarship.claremont.edu/jhm/vol9/iss1/7 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1534&context=jhm |
op_rights |
default |
_version_ |
1766403499365498880 |