# Symmetry and Measuring: Ways to Teach the Foundations of Mathematics Inspired by Yupiaq Elders

Journal article

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

Authors | Lipka, Jerry, Adams, Barbara, Wong, Monica, Koester, David and 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. |

Year | 2019 |

Journal | Journal for Humanistic Mathematics |

Journal citation | 9 (1), pp. 107-157 |

Publisher | Claremont Colleges Library |

ISSN | 2159-8118 |

Digital Object Identifier (DOI) | https://doi.org/10.5642/jhummath.201901.07 |

Open access | Published as ‘gold’ (paid) open access |

Publisher's version | License File Access Level Open |

Publication process dates | |

Deposited | 06 May 2021 |

https://acuresearchbank.acu.edu.au/item/8vz79/symmetry-and-measuring-ways-to-teach-the-foundations-of-mathematics-inspired-by-yupiaq-elders

## Download files

###### Publisher's version

OA_Lipka_2019_Symmetry_and_Measuring_Ways_to_Teach.pdf | |

License: CC BY | |

File access level: Open |

##### 267

total views##### 149

total downloads##### 0

views this month##### 1

downloads this month

*These values are for the period from 19th October 2020, when this repository was created.*

## Export as

## Related outputs

##### Developing profession ready teacher education graduates through school-university partnerships : An Australian study

Tanti, Miriam, Monteleone, Chrissy and Wong, Monica. (2023). Developing profession ready teacher education graduates through school-university partnerships : An Australian study.*Asia-Pacific Journal of Teacher Education.*pp. 1-18. https://doi.org/10.1080/1359866X.2023.2227842

##### Symmetrical measuring :An approach to teaching elementary school mathematics informed by Yup'ik Elders

Wong, Monica, Lipka, Jerry and Andrew-Ihrke, Dora. (2014). Symmetrical measuring :An approach to teaching elementary school mathematics informed by Yup'ik Elders. In J Anderson, M Cavanagh and A Prescott (Ed.).*Curriculum in focus: Research guided practice (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia).*Australia: Mathematics Education Research Group of Australasia. pp. 661 - 668

##### Isotonic resistance jaw exercise alters jaw muscle coordination during jaw movements

Wirianski, Alexander, Deall, Simon, Whittle, Terry, Wong, Monica, Murray, Gregory and Peck, Christopher. (2014). Isotonic resistance jaw exercise alters jaw muscle coordination during jaw movements.*Journal of Oral Rehabilitation.*41(5), pp. 353 - 366. https://doi.org/10.1111/joor.12153

##### Alaska native Indigenous knowledge opportunities for learning mathematics

Lipka, Jerry, Wong, Monica and Andrew-Ihrke, Dora. (2013). Alaska native Indigenous knowledge opportunities for learning mathematics.*Mathematics Education Research Journal.*25(1), pp. 129 - 150. https://doi.org/10.1007/s13394-012-0061-4

##### Mathematics curriculum in the schooling years

Anderson, Judy, White, Paul and Wong, Monica. (2012). Mathematics curriculum in the schooling years. In In B Perry, T Lowrie and T Logan, A MacDonald & J Greenlees (Ed.). pp. 219 - 244 Sense Publishers.##### Developing an Alternative Learning Trajectory for Rational Number Reasoning, Geometry, and Measuring Based on Indigenous Knowledge

Lipka, Jerry, Wong, Monica, Andrew-Ihrke, Dora and Yanez, Evelyn. (2012). Developing an Alternative Learning Trajectory for Rational Number Reasoning, Geometry, and Measuring Based on Indigenous Knowledge. In In S. Mukhopadhyay and W. M. Roth (Ed.).*Alternative Forms of Knowing (in) Mathematics*pp. 159 - 182 Sense Publishers. https://doi.org/10.1007/978-94-6091-921-3_8

##### Teacher subject matter knowledge of number sense

Briand-Newman, Hannah, Wong, Monica and Evans, David. (2012). Teacher subject matter knowledge of number sense. In J Dindyal, L P Cheng and S F Ng (Ed.).*Mathematics education: Expanding horizons. Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 130 - 137

##### Assessing students' understanding of fraction equivalence

Wong, Monica May Dze and Evans, David. (2011). Assessing students' understanding of fraction equivalence. In pp. 81 - 90 Australian Association of Mathematics Teachers.##### Adapting assessment instruments for an Alaskan context

Wong, Monica May Dze and Lipka, Jerry. (2011). Adapting assessment instruments for an Alaskan context. Australia: AAMT and MERGA. pp. 821 - 829##### Fractions as a measure

Wong, Monica and Evans, David. (2008). Fractions as a measure.*Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 597 - 603

##### Assessing students' understanding of fraction equivalence

Wong, Monica and Evans, David. (2007). Assessing students' understanding of fraction equivalence.*East Asia Regional Conference on Mathematics Education (EARCOME).*Malaysia: Asian Academy of Management and Universiti Sains Malaysia. pp. 119 - 127

##### Improving basic multiplication fact recall for primary school students

Wong, Monica and Evans, David. (2007). Improving basic multiplication fact recall for primary school students.*Mathematics Education Research Journal.*19(1), pp. 89 - 106.

##### Examining number sense: an exploratory study of students with additional learning needs

Evans, David, Strnadova, Iva and Wong, Monica. (2007). Examining number sense: an exploratory study of students with additional learning needs.*International Symposium Elementary Mathematics Teaching.*Czech Republic: Charles University. pp. 101 - 109

##### Students' conceptual understanding of equivalent fractions

Wong, Monica and Evans, David. (2007). Students' conceptual understanding of equivalent fractions.*30th annual conference of the Mathematics Education Research Group of Australasia.*Wrest Point Hotel Casino, Hobart, Tasmania, Australia 02 - 06 Jul 2007 Mathematics Education Research Group of Australasia. pp. 824-833

##### Teaching common fractions in primary school: teachers' reactions to a new curriculum

Anderson, Judy and Wong, Monica. (2007). Teaching common fractions in primary school: teachers' reactions to a new curriculum.*Annual Conference of the Australian Association for Research in Education (AARE).*Australia: Australian Association for Research in Education. pp. 1 - 12