-Part 1 (Numeracy): Using Gale’s lecture, Poirier’s article, and Bear’s article, identify at least three ways in which Inuit mathematics challenge Eurocentric ideas about the purpose of mathematics and the way we learn it.
Gale’s lecture “Curriculum as Numeracy” asserts that human beings are naturally mathematical, and that from birth they are able to understand such concepts as addition, subtraction, etc. Even though children don’t necessarily know the formal, socially constructed terminology and systems of math, through ‘relationships’ and ‘context’ they grasp the essence of the fundamentals, including decimals and division. To demonstrate this argument, Gale points to a class of 5-year-old students at Harvard, where the teacher let the students take charge of their own education–to see how far they could go without substantial guided instruction. The youngsters were given only small pointers, such as ‘what is between zero and one?’, and after some time the students came to understand that there can be a half between 0 and 1, essentially 0.5. Also, they came to recognize that there are many numbers between 0 and 1, some lower and some greater than 0.5. Gale goes on to argue that the Euro-centric model of math instruction is by no means necessary or required for successful classroom instruction in math. Quite the contrary. According to Gale, Inuit students often under-perform on mathematical tests carried out in English or French. However, in tests that are oral and in Inuktitut, they perform even better than non-Inuit children. According to Gale, the explanation for this is that Inuit culture has a different way of approaching mathematics. First, instead a base 10 numeral system, it uses a base 20. Second, the Inuit have 6 contexts for numbers. For example, having 5 dots on a dye is spoken of differently than having the number 5 on a playing card. Also, when the Inuit do math, they mostly do it orally. For these and other reasons, Inuit cultural approaches to math are different from Euro-centric norms.
Louise Poirier delves deeper into Inuit traditions of math instruction in her “Teaching mathematics and the Inuit community”. As indicated by Poirier, Inuit children begin learning Math and English in Grade 3, learning that is built upon the base knowledge and traditions of Inuktitut. Math being a social construction, what is defined as math and not math is cultural. The same applies to what is deemed ‘more important’ and ‘less important’. In the case of the Inuit, the number 420 is deemed important whereas 100 is less so. Furthermore, the Inuit calendar is not number-based but event-based, with cyclical happenings like deer shedding their horns, the arrival of fish, etc. being the means by which to track cyclical time. Inuit measure by a variety of culturally relevant means, such as using body appendages for the length and size of clothing. They also don’t count a pineapple as a singular thing but rather by its slices, because they are used to seeing pineapples in pieces. Taking these various factors into consideration, Poirier argues that imposing a ‘southern’ mathematics system upon the traditional Inuit one is fraught with problems—most notably, it creates confusion. Accordingly, Poirier advocates for collaborative research between Inuit and non-Inuit educators to determine the best possible educational methods for Inuit schools. Among the ideas that Poirier proposes is an activity-oriented approach to mathematics education, for example telling mathematical riddles to the children and having them answer them through class discussion.
Leroy’s article “Jagged Worldviews Colliding” compares the Euro-centric worldview with those of North-American Indigenous Nations. Leroy explains that First Nations have a cyclical view of time where everything is seen as a process. Contrastingly, the European worldview is fundamentally linear, and it looks upon everything in the world as products. While First Nations peoples believe in renewal, honesty, cognitive diversity, and loving one’s own children, the colonial settlers valued quantity, materialism, specialization, and singularity. As a result of this clash of worldviews and ideologies, and the eventual domination of western ones, First Nations ideas and concepts were devalued. Indigenous groups were discouraged and even barred from practicing their traditional beliefs. This struck a debilitating blow to First Nations identity and history. They were caught between their own devalued traditions and unfamiliar, ‘unnatural’ western ones, a predicament that was culturally destructive. Leroy stresses that he does not frame settlers as ‘evil’ or ‘bad’, but rather seeks to show the effects of their arrival and establishment in North America. Such a recognition and understanding represents steps towards positive change for First Nations communities.
-Part 2 (Literacy): Which “single stories” were present in your own schooling? Whose truth mattered? What biases and lenses do you bring to the classroom? How might we unlearn / work against these biases?
As mentioned by Chimamanda Adichie in her TED Talk “The Danger of a Single Story,” stories are powerful and people are impressionable. Accordingly, stories can both empower groups and diminish them. One story that hovered over my K-12 education in a very general way (represented in movies, on TV, in novels, and even in class) is that ‘good’ students are rewarded with happy, successful lives, and ‘bad’ ones with the reverse. The story, and my desire to be happy and successful, meant that I sometimes thought that I was better than peers who misbehaved. It was as if each good deed represented a step up a long staircase of excellence. In contrast, those who misbehaved were stepping down into a pit of despair. The story thus led me to compare myself to others, and to judge them. As I reflect on it now, the problem with this way of thinking is that often people who behave ‘badly’ are not necessarily bad or unmotivated; rather, they simply do not fit into the educational system. There are so many strict rules in school, and it is difficult for some children to navigate them. Often the ‘square pegs’ turn out to be highly creative and unique. In the article “Examples from English Literature,” Kumashiro asserts that sometimes books that try to be culturally sensitive, and are recognised as such, express hidden racism or make damaging appropriations. The same goes for teaching: sometimes teachers try to teach without having any bias or preconceived notions about their students; however, unconscious biases might nevertheless exist. The reductive idea of ‘good’ and ‘bad’ students has deep roots in the history of education. It is encouraging that recent research suggests that there really is no such thing as a ‘bad’ student. The best way to avoid such a categorisation is for teachers to take an interest in each of their students, and to do their best to understand them as they are. Teachers should also be generous and share a bit of themselves with their students. Such approaches will help establish meaningful relationships between teachers and students. With relationships comes respect and appreciation of individual gifts, talents, and interests.
Chimamanda Adichie, “The Danger of a Single Story”: The Danger of a Single Story
Chapter 7 from Kumashiro’s Against Common Sense: here
Leroy Little Bear from Reclaiming Indigenous voice and vision, “Jagged Worldviews Colliding”: Jagged worldviews colliding
Curriculum as Numeracy: Gale Russell’s Guest Lecture for ECS 210: Watch this lecture by Gale Russell on Curriculum as Numeracy