Mathematics talent abounds in Indigenous communities


By Veselin Jungic, Simon Fraser University

On the occasion of National Indigenous Peoples Day, I would like to show how ubiquitous mathematics — and mathematics talent — is within Indigenous cultures. As a mathematician who immigrated to Canada, and who has worked at universities for most of my adult life, my teaching and learning experiences have shown me this first hand.

After attending the First Nations Math Education Workshop in Banff in 2009, I launched the Math Catcher Outreach Program at Simon Fraser University (SFU), which uses the model of the Indigenous storytelling as a tool to attract youth to the study of mathematics.

The main goal of the program is to encourage both Indigenous and non-Indigenous students to discover the joy and appeal of mathematics in the hope that they may better understand the presence of math and its importance in everyday life, and consider mathematics as a field of study and vocation.

Inspired by Indigenous storytelling traditions, the program has created animated films in several Indigenous languages. We also coordinate a volunteer tutoring activity between the Native Education College and SFU.

Small Number and the Basketball Tournament.

We regularly visit First Nation communities across B.C. and Alberta to hold workshops for students and teachers, or to collaborate with the community members on math-related projects.

Through the Math Catcher Program, I’ve had the privilege to interact with hundreds of Indigenous students and their parents, elders, teachers and community members, both in urban and rural settings. These interactions have made it clear to me that talent and interest in mathematics abound among Indigenous learners.

It has also become clear to me that there is a profound mathematical presence in various Indigenous traditions, from art to weaving patterns in cedar root and birch bark baskets, to canoe designs, the strategies of the salmon harvest and the ways of managing resources.

Mathematical presence in Indigenous traditions

A recent Math Catcher visit to Tla’amin Nation included a community event built around several hands-on mathematical activities. In one activity, we explored the properties of the Möbius strip, a surface with only one side and one edge.

In another, we examined a challenging puzzle that required making a braid with six crossings and with no free ends from a piece of paper with two slits. The underlying mathematics of both of these activities is quite complex.

Sosan, a young woman who came to the workshop with her two children was among the event participants. I told her how impressed I was with how quickly she grasped the activities and she answered with something that I regularly hear: “I was never good at math.”

The following morning, after a Math Catcher workshop in the neighbourhood school, a teacher handed me a small package from Sosan containing two objects.

One was a small Möbius strip masterfully woven from cedar inner bark. Sosan’s creation captured the true essence of the Möbius strip: It is impossible to find where the strip begins and where it ends.

The other was a solid braid with twelve crossings and no free ends made from a long piece of bark. To create this braid one needs a great deal of skill and ingenuity because solving this puzzle requires both braiding and unbraiding. Sosan had to process the bark to make it pliable, then braid it, and then return the bark back to its solid state.

Small Number and the Old Canoe.

As a longtime university math instructor, I felt almost certainly, that no one had considered that solution until that moment. What kind of knowledge, talent and inspiration were needed to find a method and to execute it so precisely by creating a model of a complex mathematical object?

I wonder when Sosan came up with the braid in bark problem? During our event? While driving back home? While putting her children to bed?

In my career as a mathematician, I have been fortunate to collaborate with some of the most talented mathematicians in my area of study, Ramsey theory. My encounter with Sosan’s creativity and her deep understanding brought back that same dizzying feeling of witnessing something very special when I had worked with some of the finest mathematical minds.

Sosan’s gifts are now two of my most valued possessions.

This experience also describes what I consider a great challenge for my teaching and academic communities. What can we do, collectively and as individuals, to further challenge ways of thinking about mathematics? How can we create and sustain an environment for learning mathematics in which Indigenous learners can share their knowledge and skills with the broader community?

In other words, we need an environment for learning mathematics where we, as part of the school system as a whole, will listen and learn from our Indigenous learners about mathematical forms and the applications of mathematics that may be outside of what the current math curriculum prescribes.

How can we urge and support Indigenous students to further explore and develop their talents in mathematics?

The ConversationFor me, for now, it is one Math Catcher event at a time.

Small Number and the Old Totem Pole in Sliammon.

Veselin Jungic, Professor, Simon Fraser University

This article was originally published on The Conversation. Read the original article.

Explainer: the seasonal ‘calendars’ of Indigenous Australia


File 20171221 17712 1iuedf4.jpg?ixlib=rb 1.1
Lalin in Western Australia is ‘married turtle season’
Brian Gratwicke/Flickr, CC BY

Alice Gaby, Monash University and Tyson Yunkaporta, Monash University

On Wangkumarra land, in the corner-country near the borders of Queensland, New South Wales and South Australia, stands an ancient stone arrangement. It has been placed to the side of a huge complex, rivalling Stonehenge, featuring megaliths polished, carved and placed to balance precariously on each other.

Ancient stone arrangements on Wangkumarra land.
Tyson Yunkaporta

They should fall, but they don’t, as this is a place where time runs differently. In contrast to the Western “arrow of time”, the small rock formation pictured shows the non-linear, infinitely interconnected cycle of time followed by the First People who built the site and used it over millennia. It is a stone calendar, aligned within a fraction of a millimetre to the points of the compass.

The stone calendar on Wangkumarra land.
Tyson Yunkaporta

The key to understanding this temporal reality is the shape of the stone calendar. It is round, not a continuum. There is no beginning or end, and as such, there is no “New Year”. Seasons do not serve as a basis for linear metaphors of new life in spring to death in winter.

Instead, both seasons and humans are viewed as components of cycles. Around Australia, Indigenous languages vary in both the number of season words in their lexicon and their precise meaning. This is at least partly due to the very different kinds of weather experienced around the year in different parts of the country.

A tour of the seasons

In the Tiwi islands just to the north of Darwin there are three major seasons named in the Tiwi language: Kumunupunari (the dry season of fire and smoke); Tiyari (the season of hot, humid weather); and Jamutakari (the wet season of daily rain and full rivers). These three seasons subsume 13 overlapping, more precisely defined seasons.

For example, in the Mumpikari season (which overlaps with the start of the Jamutakari “wet season”) the first rains after the dry time make the ground soft and muddy enough to retain the footprints left by possums returning to their trees, which makes the possums easier to track when hunting.

Understanding the meaning of a word like Mumpikari “season of muddy possum tracks” entails knowledge of the type of weather experienced at that time (first rains following a long dry spell), consequent changes in the local ecology (muddy ground), as well as changes in human behaviour and potential sources of food (it’s a good time to hunt and eat possums).

In the Tiwi Islands Mumpikari is ‘season of muddy possum tracks’
Marcia Cirillo/Flickr, CC BY-NC

The changes in weather, ecology and potential food sources over the course of the year are dramatic, but vary significantly across a continent as large as Australia. The season experienced in tropical Cape York in January is very different to January in Tasmania. Likewise, the middle of the year brings radically different weather patterns to the tropical north, temperate south and central desert regions respectively.

The definitions of seasonal terms tell us a lot about the ecology that a language is spoken within and how speakers interact with it. In the Warlpiri language of the Tanami Desert, for example, several seasonal terms (such as karapurda) make reference to the prominent westerly winds that blow at the onset of the hot season.

Common food sources also feature prominently in the definitions of season terms, such as mangkajingi, “season of year when goannas are easily found in shallow burrows”. In the Bardi language of the Dampier Peninsula (WA), the build up to the wet season is named Lalin and colloquially referred to as “married turtle season”, because the mating turtles are a prized food source at this time.

In Gulumoerrgin (Larrakia) language group, spoken around Darwin, the year is divided into seven named seasons. Each of these seasons is associated with distinctive patterns of weather, but also changes in flora, fauna, and human activity. The Gurrulwa season, or “big wind time”, is heralded by the flowering of wattles, which in turn indicates that the local stingrays are plentiful and good to eat. The flowering of the Yellow Kapok at this time in turn indicates that it is the time for important traditional ceremonies to be held.


These connections between species are often cemented in language by using a single word. In the Dalabon language of Arnhem land, the word yawok has two meanings: (1) a species of yam (Dioscorea bulbifera); and (2) a species of grasshopper (Caedicia spp.). To the untrained observer, the yam and grasshopper might appear to have little in common.

In Arnhem Land, when the yawok (grasshopper) calls, the yawok (yams) are ready for harvesting.
Wikimedia/JJ Harrison, CC BY-SA

But for Dalabon speakers, this naming practice is a useful mnemonic that helps them remember that the yam is ripe for harvest precisely at that time of year when the grasshopper’s mating call can be heard. Similar principles have been found to underpin the naming of plant and animal species in languages such as Bininj Gun-Wok and Ndjébbana.

The words of any language tell us a lot about the history of its speakers; who they’ve been in contact with, where and how they have lived. This is certainly true of the English calendar months. It is also seen in the number and nature of the seasons named by different Indigenous communities, from the tropical north of Australia to the chillier climates down south.

The ConversationWith around 370 languages and many hundreds more dialects originally spoken in Australia, it is impossible to do justice to the wealth and variety of traditional systems of tracking time and seasons. But a recurrent theme is the interconnectedness of human activities and the cycle of changes in flora and fauna that attend the tilting of the earth’s axis.

Alice Gaby, Senior Lecturer in Linguistics, Monash University and Tyson Yunkaporta, Senior Lecturer Health, Monash University

This article was originally published on The Conversation. Read the original article.