FNMI Ways of Knowing in Mathematics

In my own experience in learning Math, I cannot say that I remember one meaningful application of FNMI ways of knowing. Maybe the problem was the textbooks, or maybe it was that teachers felt overwhelmed with the amount of material that needed to be covered. Whatever the reason, there was no instance in my time learning Math 9, Foundations and Pre-Calculus 10, Workplace 10, Foundations 20, Pre-Calculus 20, Foundations 30 or Pre-Calculus 30 that I ever learned anything but the dominant discourse about math. What are the causes of this? How could I have gone through thirteen years of learning math, all different kinds of math used for all kinds of purposes, and never once encountered one word problem or equation that displayed any way of knowing other than what Math Makes Sense says are appropriate applications of math? Is this discrimination, oppression even? That’s hard to say, but I do know that it was a majorly missed opportunity on the part of every math teacher I ever had to introduce students to FNMI ways of knowing in Math.

Three ways in which Inuit mathematics challenge Eurocentric mathematic ideas:

  • Firstly, students learn mathematics in their own language. This can challenge the ways in which students understand concepts, such as using a word meaning “indivisible” for the number “0”. “Their tradition being essentially an oral one, the Inuit have developed a system for expressing numbers orally.”, this means that they have had to adopt European ways of representing written numbers.
  • Second, the traditional Inuit calendar challenges Eurocentric ways of knowing by characterizing months based off of natural events. For example, September’s number of days fluctuates depending on how long it takes a caribou’s antlers to shed their velvet.
  • Third, traditionally, the Inuit use their bodies for measurement in contrast to the Metric or even Imperial systems used worldwide today.

 

Louise Poirier, Canadian Journal of Science, Mathematics and Technology Education, http://www.tandfonline.com/loi/ucjs20, Teaching mathematics and the Inuit community.

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Week 8- Mathematics

At the beginning of the reading, Leroy Little Bear (2000) states that colonialism “tries to maintain a singular social order by means of force and law, suppressing the diversity of human worldviews. … Typically, this proposition creates oppression and discrimination” (p. 77). Think back on your experiences of the teaching and learning of mathematics — were there aspects of it that were oppressive and/or discriminating for you or other students?

Unfortunately, I attended a Caucasian dominated school with limited diversity. With that being said, my whole grade consisted of Caucasian students, thus there were few notions of oppression or discrimination directed at individual students, as we were all white. However, I can confirm that the manner in which mathematics was taught revolved around Eurocentrism. Consequently, if my grade was more diverse, then those students with different cultures would have experienced the oppressive nature of a bias math class. Essentially, mathematics was taught using the English language and was supported by westernized values. In that regard, if we had students who emigrated from non-English speaking countries, they would have had to adjust to our procedures as math was practiced from one perspective.

However, there were English speaking students, including myself, who did not understand mathematics. Unfortunately, since it was only taught in one way, I never fully comprehended nor succeeded in math. It would have been useful to incorporate other ways of knowing.

After reading Poirier’s article: Teaching mathematics and the Inuit Community, identify at least three ways in which Inuit mathematics challenge Eurocentric ideas about the purposes mathematics and the way we learn it.

There exist multiple ways in which Inuit mathematics challenge Eurocentric ideas regarding its value and instructions. Firstly, we must address that Inuit often begin learning math in their own language called, Inuktitut. Of course, this obviously challenges Eurocentrism as their mathematics involves a dramatically different language. Moreover, the Inuit, similar to other cultures, have adopted their own set of “mathematical tools” based on the demands of their environment. As a result, they have developed a base-20 numerical system, as opposed to our western base-10 numerical system. Additionally, while our culture stresses that a basic sense of math is required for everyday issues, the Inuit argue otherwise. Next, the notion of spatial representation in relation to geometry differs as well. Poirier’s article addresses that Inuit children and westernized children develop different spatial representations, resulting in the skills and abilities of Inuit children being undervalued. Lastly, it is crucial to acknowledge the differences in how we teach mathematics. In western cultures, teaching often involves a structured classroom, supported by resources such as technology and paper. Conversely, Inuit children traditionally learned from their elders by observing them and listening to enigmas. Clearly, our practices of teaching greatly differ, as Inuit mathematics challenge our own perspectives and values of mathematics.

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Curriculum as Numeracy – Martina

Think back on your experiences of the teaching and learning of mathematics — were there aspects of it that were oppressive and/or discriminating for you or other students?

  •          For me there personally was not. I am caucasian and I had been thinking mathematically since I could talk. My mathematical thinking followed the colonial pattern of base ten and all of the things that were taught throughout school. I was taught the Western style of thinking that is very quantitative. So for me my mathematics in school were nothing out of the ordinary and considering all 17 of my classmates had had the same upbringing as me and were all caucasian I don’t think any of them felt oppressed either.

Identify at least three ways in which Inuit mathematics challenge Eurocentric ideas about the purposes mathematics and the way we learn it.

1) They do not have a written number system. Their numbers are stated orally up to three and from there they see no need for quantity as they use things like “many” or “enough.”

2) They do not quantify space, rather they have a strong sense of how far away from something they are.

3) Instead of making a calendar with a certain number of days per month they make “months” out of the animal activity that happens during that time. “When baby caribou are born,” for example.

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Mathematics-Week: 8

I, having had grown up in the white settler society have never really felt oppressed by colonialism- especially not in mathematics. My father is a business man and my mother is a nurse therefore, they use math everyday. My father uses statistics, currency conversions and simple counting in his day to day life and my mother uses dosage calculations on a regular basis. Traditional math is common to me. It is my common sense.

It was strange for me to hear that other societies do not use our methods of mathematics and counting. I went to a francophone school, as I am francophone, we put the dollar amount behind the entire number and we use commas instead of dots to indicate decimal marks (e.g. 25,00$ or $25.00). These are simple conversions that I have picked up in my day to day life that have not affected me as a learner.

 

2. Inuit counting, localization and measuring are areas of study for comparison between Inuit math and Eurocentric math. Inuit people do math in their heads and orally, it was just recently that written math was developed to aid the instruction of their math. Their methods of measurement are also very different. They look at seasons, common sense “enough”, and corporal measurements to help them determine measurement. It is not standardized, it is common sense. Their base system and their general outlook on math is different as it is based on necessity and common sense. written math based on diagrams is needed, not numbers.

We can learn a lot from the way other cultures do math as math is often one of those “non-negotiable” subjects, where 2+2=4 every time. As for the Inuit, they may have a better way of doing math.

 

 

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Week 8: October 26, 2018

 

 

1. At the beginning of the reading, Leroy Little Bear (2000) states that colonialism “tries to maintain a singular social order by means of force and law, suppressing the diversity of human worldviews. … Typically, this proposition creates oppression and discrimination” (p. 77). Think back on your experiences of the teaching and learning of mathematics — were there aspects of it that were oppressive and/or discriminating for you or other students?

The only recollected memories from my high school math days were all awful. Math was a class that I dreaded and struggled with throughout high school, therefore, turning me off from math courses. In my classes, the “lecture only” style was intolerable. 45 minutes of lecture, 15 minutes of silent work time where everyone sat in confusion staring at their Math Makes Sense textbooks until the bell dismissed us. This style of teaching is oppressive because, as we have learned, this transmission style teaching does not work for everyone. Our teachers believed they had the only answer, and that they would lecture the content into our heads to a point where we could sit immediately after the lecture and do work. Majority of math classes function this way, and I have not ever heard of another one where the teacher uses a transformative and constructivist approach to teach formulas and terms. For myself, math was designed so students could fit in a particular mold, and I did not fit in that mold.

 

2. After reading Poirier’s article: Teaching mathematics and the Inuit Community, identify at least three ways in which Inuit mathematics challenge Eurocentric ideas about the purposes mathematics and the way we learn it.

Inuit mathematics is challenging Eurocentric mathematics, and because of this, math is not universal as much as everyone thought. Inuit children speak Inuktitut in school from Kindergarten until Grade 3, challenging the Eurocentric ways of doing math in English (Poirier, 2007, p. 54). Inuit math uses the “base-20 numeral system,” with the numbers 20 and 400 being pivotal since the other numbers are built from these (Poirier, 2007, p. 54 & 57). The different number system from ‘southern’ mathematics is challenging it in a new way. Their spatial relations and geometry are much different due to the use of space in their communities and how they use space in their everyday lives compared to Eurocentric ways. They use space to orient themselves as they travel, as well as building an inukshuk for safety from the elements and to let others know they were/are there (Poirier, 2007, p. 59). These practical ways of understanding space are never taught in a classroom or through a textbook. Another way they challenge Eurocentric ideas of math is through their form of measurement and the traditional calendar. They began by measuring with parts of the body, such as a finger or foot, and today, they use their palms when making “atigi (parkas),” further challenging Eurocentric measurements (Poirier, 2007, p. 60). Their calendar is based on “natural, independently recurring yearly events,” such as “when baby caribou are born,” opposite to the lunar or solar calendars (Poirier, 2007, p. 60). Finally, their teaching methods differ since they base their learning on “observing an elder or listening to enigmas,” rather than the traditional “paper-and-pencil exercises” (Poirier, 2007, p. 55).

 

 

 

Resources

Bear, L. L. (2000). Jagged worldviews colliding. In M. Batiste (Ed.), Reclaiming Indigenous voice and vision (pp. 77-85). UBC Press.

Poirier, L. (2007). Teaching mathematics and the Inuit community, Canadian Journal of Science, Mathematics and Technology Education, 7(1), p. 53-67.

 

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Colonialism in Mathematics…

  1. I struggled in math throughout my school career. This was partly because I was uninterested, and partly because I was simply not naturally good at it like I was in subjects such as english and art. My experience, as I am sure is similar to many others, was that there was only one way math was ever taught to me. I was taught this in a very traditional and lecture type format. I often felt so behind and confused in math, that I did not even know what questions I should have been asking. When getting extra help, the teaching did not change, but rather I was pulled aside and explained it the same way individually. I found that there was always one way math was taught, and if you did not learn this way, then you consequently got left behind. I also found that math teachers seem to be less creative in their teaching strategies. This is another way that math does not accommodate others. Many other subjects attempt to include indigenous education in its methods, however, I have never seen this in the math I was ever taught. Due to this, I believe I have been turned off from math for the rest of my life. I avoid it at any costs, as I am not confident in any way with it. These are just a few ways that math discriminates and works against people.
  2. The article states that the first ways of measuring were with the fingers and feet. The Inuit peoples use their body to measure things rather that standard tools like rulers and tapes. This is one way that they challenge Eurocentric ideas of mathematics. Another way they challenge traditional Eurocentric ways of mathematics is how they express math orally, rather than in written from. In Inuit terms, the meaning changes due to context of what one is talking about. This makes the language of math much more complex, but precise. Lastly, they challenge these traditional terms of mathematics by their incorporation of real life objects and places to help with comprehension and understanding. This is quite unique in comparison to Eurocentric ways of teaching. This method is useful to people because the skills transfer into numerous environments such as hunting for example. The ways that the Inuit communities teach are for transferable understandings. This is often more useful than the ways we teach here.
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Week 6 and 7

Week 6:

1. List some of the ways that you see reinhabitation and decolonization happening throughout the narrative.

Throughout the reading, I noticed many ways in which reinhabitation and decolonization are conducted. This was done mainly through a 10-day river trip with youth, adult and elder participants traveling together on their traditional waters and lands learning about many different aspects of traditional ways of life. For example, at one point the group discovers the importance of listening to the animals in nature to know if water is safe or what type of weather is approaching (Restoule, p. 76). Ways of knowing such as these have been lost to the culture, and by relearning them, it helps Indigenous people’s reclaim their culture. This is, in essence, a tool of decolonization, by giving youth the information of their traditional knowledge, and the language they keep the connection with their culture.

2. How might you adapt these ideas to considering place in your own subject areas and teaching?

As a future History and English teacher place play a massive part in both subjects. For History, the understanding of place is extremely important. When teaching students about the signing of the treaties, it is essential that they can grasp the importance of area where it concerns the Indigenous peoples. A failure to understand the Indigenous people’s way of knowing does their culture a disservice by not accurately representing how they saw the land as a place to be shared and treated with respect. Understanding the importance of “place” provides an incredible aid to understanding history.

Week 7

1. What is the purpose of teaching Treaty Ed (specifically) or First Nations, Metis, and Inuit (FNMI) Content and Perspectives (generally) where there are few or no First Nations, Metis, Inuit peoples?

The purpose of teaching Treaty Ed especially in a class such as Social 30 is to show a complete history that is inclusive to all students. Just because there are few Indigenous people in the class does not make Treaty Ed any less important, on the contrary, it makes it all that more important. Through the use of Treaty Ed, the teacher is performing decolonization through the use of retelling the story of the colonization in its real truth. Its non-Indigenous students that need to hear this truth the most. It is unlikely that they would have heard it outside the classroom. If a teacher chooses not teach Treaty Ed, they are stating that they do not believe these truths to be important. They are making an active decision to continue the oppression towards the Indigenous peoples. The oppression that has been here for a long time.

2. What does it mean for your understanding of curriculum that “We are all treaty people”?

To me being a “treaty people” is an honor, to be blessed enough to live on these lands with so much history behind it is incredible. At the same time, there is an understanding of all the damage that was done to the peoples who originally inhabited these lands and those that still do. To be a “treaty people” involves understanding the intent of treaties from both sides perspectives. Being a treaty person along with being a future teacher places an additional role on me. It is my job to help educate my prospective students the importance of Treat Ed and teach them the entire truth of Canada’s history.

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Challenging Eurocentric Ideas in Math

While reading the article, it turns out that there are many ways that Inuit mathematics challenges Eurocentric ideas of learning. To begin, they take language into consideration. From kindergarten to grade 2, the students learn in their language; however, when they hit grade 3, they switch to either English or French. This can cause confusion with an overload of information. There is also confusion on if the numerical system in Inuktitut is the same as French or English. Next, the Inuit use their senses as a way or orientation. Instead of compassing or using traditional use of degrees, they use their noses to smell the saltiness of the air to know how far away they may be from the bay. They also make Inukshuks to signify a good fishing spot. Lastly, measuring is different. Instead of using a ruler as a measuring tool, they have traditionally used body parts, especially while making clothing.

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Curriculum as Numeracy

1. At the beginning of the reading, Leroy Little Bear (2000) states that colonialism “tries to maintain a singular social order by means of force and law, suppressing the diversity of human worldviews. … Typically, this proposition creates oppression and discrimination” (p. 77). Think back on your experiences of the teaching and learning of mathematics — were there aspects of it that were oppressive and/or discriminating for you or other students?

My experience with math class varied from teacher to teacher. My high school had three math teachers, and they all taught very differently. I experienced classes with two of these teachers, one was great and the other was not-so-great. I found that there was only one “right” way of teaching math in high school, so students who did not understand the “only way” were left behind hating math. Some math teachers would offer extra help to the students who were struggling, though when this offer was taken up, the result of the process did not change. By receiving this one-on-one help, the teacher would just explain the “only way” in a more personalized manner. In this sense, my experience with math class in high school was definitely discriminating against a certain group of students.

2. After reading Poirier’s article: “Teaching Mathematics and the Inuit Community”, identify at least three ways in which Inuit mathematics challenge Eurocentric ideas about the purposes mathematics and the way we learn it.

This article states that one-way Eurocentric ideas are being challenged is through measurement. Rather than using rulers or measuring tape, Inuit people use their bodies as a way of measurement. The article states that the first measuring “tools” used were the fingers and the feet. Teaching methods differ as well. The traditional “pencil-and-paper” is not the “natural” way of learning for Inuit students. Rather, “traditional Inuit teaching is based on observing an elder or listening to enigmas” (55). In addition to this, students are not asked questions that they will not know the answer to. Lastly, the number system is quite different between the two. The Inuit use a base-20 number system. They view “the numbers 20 and 400 [as] pivotal, as other numbers are built from these two numbers” (57).

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Week 8-Curriculum as Numeracy

1) At the beginning of the reading, Leroy Little Bear (2000) states that colonialism “tries to maintain a singular social order by means of force and law, suppressing the diversity of human worldviews. … Typically, this proposition creates oppression and discrimination” (p. 77). Think back on your experiences of the teaching and learning of mathematics — were there aspects of it that were oppressive and/or discriminating for you or other students?
Math was very much a ‘one way’ subject. I believe that it still is. In my mind, it is considered a ‘right and wrong’ subject. Students either are right or wrong in math because the subject entails students to work out a problem or question until they either get a right or wrong answer. English however, provides students with more room for analysis, perceptions, and opinions/thoughts. I feel now looking back on my math class, it was oppressive in 2 ways. 1. it did not incorporate TreatyEd (if referring to culture inclusion). 2. If students were struggling there was very little diversity in learning in new ways to help students make sense of what the math lesson is teaching them. Therefore, leaving students who needed different ways of learning to struggle moving forward.
2) After reading Poirier’s article: Teaching mathematics and the Inuit Community, identify at least three ways in which Inuit mathematics challenge Eurocentric ideas about the purposes mathematics and the way we learn it.
1) Universal terms is a Eurocentric idea challenged by Inuit mathematics. Inuit mathematics is  expressed orally whereas Eurocentric mathematics is mainly expressed in written form. . In learning Eurocentric mathematics, something as simple as “δ” can refer to several equations and measurement. In Inuit mathematics terms need to be logical and related to things that are well known. Therefore, visual forms of mathematics go against what Inuit mathematics is. This connects to diverse learning and how we as teachers need to incorporate many forms in the classroom for students who have needs to understand differently whether its culturally, visually, kinaesthetically, orally, etc.
2) Another way Inuit mathematics challenges Eurocentric mathematics is in reference to measurements. Measurements of time such as months directly relate to common events. I found this incredibly useful considering if there is no access to a calendar you can get a time estimation by natural events. For example, if you see rabbits changing their color closer the middle of fall then we can assume that winter is coming soon.
3) In Eurocentric mathematics terms are often descriptions that are helped by the use of diagrams in the classroom. However, Inuit mathematics focus on terms, definitions, descriptions, and examples. This helps students who learn best by practising questions and have good attention spans and memory.

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