Teaching Registration - Teachers Council Registration Criteria 3

Demonstrate commitment to bicultural partnership in Aotearoa New Zealand.

Key Indicator: to demonstrate respect for the heritages, languages and cultures of both partners to the Treaty of Waitangi

Reflective Question: In my teaching, how do I take into account the bicultural context of teaching and learning in Aotearoa New Zealand?

Why teach about Kowhaiwhai in mathematics?

The geometry of Kowhaiwhai patterns is part of mathematics called ethnomathematics. Ethnomathematics is the mathematics that is involved in the art and culture associated with different civilisations.

IB International Mindedness

Education for international-mindedness relies on the development of learning environments that value the world as the broadest context for learning. IB World Schools share educational standards and practices for philosophy, organization and curriculum that can create and sustain authentic global learning communities. In school, students learn about the world from the curriculum and from their interactions with other people. Teaching and learning in global contexts supports the IB’s mission “to develop inquiring, knowledgeable and caring young people who help to create a better and more peaceful world through intercultural understanding and respect”.

See the following readings about ethnomathematics.

NZ Curriculum Documents for Levels 3-6

Teaching in the context of Kowhaiwhai is specifically mentioned in the NZ Curriculum documents at each level.


NZMaths Website

The New Zealand Ministry of Education promotes the use of realistic contexts by providing the “Figure It Out” series free to all schools. This series of Mathematics books (supported by extensive teacher notes) caters for all of the mathematics curriculum strands. All the activities are based on contexts familiar to New Zealand students, as in the following extracts on kowhaiwhai.

1. http://www.nzmaths.co.nz/resource/k-whaiwhai
2. http://www.nzmaths.co.nz/resource/i-spy-symmetry

Series of articles on Kowhaiwhai and Geometry
Knight, G. (1984). The geometry of Maori Art-rafter patterns. NZ Mathematics Magazine, 21(2), 36-41.

Article about the Art and Geometry of Kowhaiwhai

Teacher/Student Resource Booklet from the Auckland Museum


The long repeated pattern of the kowhaiwhai is called a frieze. Mathematicians have found that there are only 7 ways to make a frieze pattern and all 7 ways can be found in Kowhaiwhai. Transformations include reflection, rotation, translation, enlargement, glide reflection and shear.

Powerpoint on Kowhaiwhai in Transformation Geometry

Visual Resources - Photos of Kowhaiwhai

Note: I have placed the links to photos or images where there is copyright.
My Pinterest Board of Photos of Kowhaiwhai ( http://www.pinterest.com/msmathnz/kowhaiwhai/)
Other websites with photos
1. http://natlib.govt.nz/photos?i%5Bcentury%5D=1900&i%5Bcollection%5D%5B%5D=Drawings+and+Prints+Collection&i%5Bcollection%5D%5B%5D=Godber%2C+Albert+Percy%2C+1876-1949+%3A%5BDrawings+of+Maori+rafter+patterns+or+kowhaiwhai%5D+%5B1939%3F%5D-1947&i%5Bprimary_collection%5D=TAPUHI
2. http://www.maori.org.nz/whakairo/default.php?pid=sp55&parent=52
3. http://mp.natlib.govt.nz/search/?l=en&q=kowhaiwhai&t=items
4. http://beta.natlib.govt.nz/photos?i%5Bsubject%5D=Kowhaiwhai&il%5Bsubject%5D=New+Zealand+Centennial+Exhibition+(1939-1940+%3B+Wellington)
5. http://kohatu.connemarapony.co.nz/kohwhaiwhai.html
6. http://homepages.paradise.net.nz/gabriell/TW%20200710%20Kowhaiwhai%20Desc.html
7. http://ahikakariki.com/kowhaiwhai.htm
8. https://pinterest.com/maxibaby/kowhaiwhai/
9. Primary School Kowhaiwhai http://glsjacksonpotter.blogspot.co.nz/2012/02/room-11s-kowhaiwhai.html
12. http://whakaahua.maori.org.nz/cats.php?CatID=103&ParentID=3

Other Print Resources on the internet

Student Kowhaiwhai

Blank Graph grids for drawing kowhaiwhai

For students:
There are lots of ways for students to use this site. They will be able to:
  1. See photos of Kowhaiwhai
  2. Find the geometrical patterns in Kowhaiwhai
  3. Construct their own geometrical Kowhaiwhai patterns using correct techniques
  4. Download files that they need.
  5. Contribute their own work and see other students' work.
  6. Prepare for the tests and exams related to this unit of work.