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Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders
Lipka, Jerry Adams, Barbara Wong, Monica Koester, David Francois, Karen
Lipka, Jerry
Adams, Barbara
Wong, Monica
Koester, David
Francois, Karen
Abstract
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.
Keywords
Date
2019
Type
Journal article
Journal
Journal for Humanistic Mathematics
Book
Volume
9
Issue
1
Page Range
107-157
Article Number
ACU Department
School of Education
Faculty of Education and Arts
Faculty of Education and Arts
Collections
Relation URI
Source URL
Event URL
Open Access Status
Published as ‘gold’ (paid) open access
License
CC BY
File Access
Open