Different Perspectives on Mathematics

In math class, there could be concerns with the phrasing of word problems. If there were EAL students in the class, and they didn’t understand one of the terms in the question, then it could make the difference if they were to get the answer right or wrong. Just like that math professor was telling us during lecture today. The one time there was a student who failed her math test (or got one of the questions wrong, I forget which) and one of the questions had to do with a circus and well she didn’t know circus jargon so she got the question wrong. The math professor in class today also talked about how differently the Inuit people were doing math. It wasn’t a wrong way of doing it, but it was just different than what the western, European way of math was like. Aspects of mathematics that could be discriminating would be the underrepresentation of different cultures and different students, as well as not being inclusive enough in its language so that all students would be able to understand it. As I was growing up and taking math in school, the course usually wasn’t oppressive/ discriminating towards me, but I could see how it could negatively impact other students.

 

One of the ways that Inuit mathematics challenge Eurocentric ideas is with their base-20 numeral system. This numeral system is totally different than the Eurocentric base-10 numeral system, and it still works for the Inuit people which shows how they’re challenging the Eurocentric way of even just counting. In Poirier’s article, she discusses how some people consider math a “universal language,” but it actually isn’t. Poirier states that “different cultures have developed different mathematical tools according to the needs and their environment, and the Inuit community is no exception”. Another way that Inuit mathematics challenges Eurocentric ways is through spatial relations. Poirier gives the example of a student who was raised by a traditionalist grandfather who didn’t send him to school. This particular student wasn’t good at the math that was being pushed through the current curriculum, but his spatial representations had been developed greatly. This shows how the Inuit community/ culture places emphasis on different aspects of mathematics. Another way that the Inuit community is challenging Eurocentric ways is through the way that their culture has developed certain aspects of mathematics to suit their needs. Such as counting, oral numeration, and sense of space.

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ECS210 Reading Response #8: Curriculum as Literacy

  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?

In my Elementary school, I did not hard on math because the math was easy in lower grades, I never reviewed for math because I was able to understand it in the class time. For writing the assignments and the exams, I just needed to remember the ways to solve questions and I could get high marks. After I went to middle school, math started getting harder, we were no longer deal with the simple computation problems and the topic of trigonometry became the most difficult topic for students to learn. I realized math is not as easy as the elementary school one, so I concentrated in the class and studied harder. I had math assignments every single day, which helped me to keep practicing the new questions and reviewing the old questions. Although our math teachers warned us that math in middle school would not be as easy as before, I could still get good marks for assignments and exams. Until we had a new math teacher, he thought to do so many questions was not good for middle school students, so he only gave us a few typical questions to practice every day. I was not doing quite well on math at that time because I did not spend much time reviewing old questions and I could barely understand what my math teacher was talking about in the class. I was upset about my marks because I thought I did not have talent in math and I could only solve mathematics questions by reviewing the ways to solve questions.

After I graduated from grade 9, I went to Canada and I started grade 10 in a Canadian high school. On the day to schedule my courses, I said to the councillor that I want to pick mathematics course, but my Chinese friend and his mum laughed at me because there’s no point to study hard on math since we are in Canada, there were so many fun courses to learn rather than mathematics this boring subject. And my mum came to heel, she said why would I pick it, there’s no point. I was upset at that moment because my mum did not support on my side. But I still insisted to pick the math course, and I did so well in mathematics in my entire high school life. And now I am a second-year mathematics major student, I did not regret the decision I made in grade 10.

 

  1. 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.

First, language is a big issue for Inuit students to through in an English or a French speaking classroom.

Second, the Inuit people believe that math is originated from our daily life, so they may not understand some mathematics topics due to a lack of real-life applications.

Third, the traditionally Inuit teaching of mathematics was “based on observing and elder or listening to enigmas” (page 55), and I did not see it perform well in the Canadian classrooms.

 

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Eurocentrism in mathematics

My Story;

I grew up in whitehorse, and for me mathematics has a history. in whitehorse we did not have a strong focus on mathematics and rather focused on practical mathematics. I knew how to count my cash and I knew how to do my basic basic multiplications and divisions, as these only were useful to a grade 4 student every once in a while. in grade 5 I moved to Saltcoats, and before even going to school I was a little behind in my mathematics. I had not learned long division. and that was a hurdle to jump over. mathematics became somewhat easier until high school. in high school my math took a dive. I started to feel trapped by the equations and threatened by the numbers. in grade 11 however math became oppressive, mostly thanks to a bad teacher who could have cared less about their students and held no intention of actually educating students. grade 11 math was a fight. I was nearly failing and I could not keep up in such heavily product based classroom. math became very discriminative at this time as I became stuck in a constant turmoil with my parents over why my math marks were in the 50s where I was an 80s student everywhere else. this led to constant fights on if I was actually trying or not. but in the end I graduated grade 12, and that teacher is one of the reasons I cited for becoming a teacher last year during my ECS 100 class.

The Reading;

it is not surprising that there is Eurocentric oppressions in mathematics as the systems we use in Canada are a European idea. but it was very surprising to learn about the Inuit way of mathematics. the first thing that battles the Eurocentric view of math was their base – 20 with a sub base- 5 system. this intrigued me because its difficult to understand what reasons things are made for. the second idea was the use of body parts to measure. I have been taught by a stranger in a clothing store that if you can wrap a pair of jeans around your neck, then they will fit relatively well. I tried this and it worked. but I never understood where that idea came from. now I do. The 3rd thing that battled the euro belief was the names of direction based on what is easiest to hardest to see rather than north east south west. or the 12 hour clock system for telling direction like we do.

 

I really appreciated the reading on Inuit mathematics because it challenged my ideas and show me different ways of thinking in a course that I have grown to despise.

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Blog #9- ECS 210

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ECS 210- Viewing Mathematics

I’m not going to lie, math and I and do not get along. For as long as I can remember, I have always struggled with math. I think the reason I struggled so much is because math is a class where your work and answer is either right or wrong, you know it, or you do not and that really intimidated me. Everything we learned was based around the textbook that was being used (Math Makes Sense was the most common) and if you did not understand the textbook and teacher, you often did not succeed. As I got older, there were some units in math where the teacher would show us various ways to solve the problem and that is where I did best because I got to pick what worked best for me. Unfortunately, I did not get that option often and some students in other schools did not get that at all. Every student learns differently, and I know that math is one of those subjects where it is difficult to use various teaching strategies but encouraging hard work and being open to the idea that students learn differently is a great start.

The article “Teaching Mathematics and the Inuit Community” by Louise Poirier suggest various ways that Inuit mathematics challenges Eurocentric mathematics. Three that stuck out to me include

  1. Learning math in their mother tongue
    • Inuit children go through the first three years of school learning math in their language. Poirier states that “Furthermore, Inuit mathematics is quite different. For example, theirs is a base-20 numeral system.” (pg. 54)
  2. Measuring techniques
    • The first tools used to measure were body parts (fingers, foot, etc.). Today, there are still Inuit people that use body parts as a form of measurement.
  3. Different teaching methods
    • Traditional Inuit teaching involves bringing in and elder and having students observe and listen. Questions are not often asked when using traditional teaching methods unless they know for sure that the students will have the answer.
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Curriculum as Literacy

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?

Personally, in my own experience with mathematics, the curriculum lined up well with my world view, ways of knowing and my language. However, for other students who didn’t come from the same culture as myself, or didn’t grow up having English as their first language, the math classes could be quite difficult. The language barrier caused difficulties for students who were trying to learn English but also learning math concepts at the same time. These students may not have struggled with math if it was taught in their first language but because math was taught in English, they would fall behind. For people with different cultural backgrounds, math speaks in a language that is very Eurocentric. It follows a base-10 number system and the currencies the curriculum uses in many examples are ones created by Europeans. Telling time is another example of how math is Eurocentric based. Also, the fact that in any word problems regarding days, months, hours, or years, it is all based on the assumption that the individual is familiar and follows the North American calendar.

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.

The first way Inuit mathematics challenged Eurocentric ideas about the way we learn math was when the article mentioned that Inuit people run off a base 20 system. This is something that had never occurred to me and I’m guessing, had never occurred to many others. Everything students learn in North America in math revolves around a base 10 system so it makes sense that there is such a lack of relevancy to Inuit students when it comes to the “standard” mathematics. The second way the Inuit math challenges European math is in the language it is taught. Because math is taught in Inuktitut until grade 3, these students gain a whole difference learning experience in their math classes that would seem abnormal to those who grew up learning in a “normal” European fashion. There is also challenges that arise when these students transition to learning math in English or French at grade 3 onwards. There is not only a language shift but also a cultural shift. The third way Inuit math challenges Eurocentric ideas is through the seasons and months. I found it astounding that each month each year can be different for Inuit people because of the structure around their months. I think it is really neat but also unfortunate that I’ve never learned about this before. Im sure others, like myself, unconsciously go about their days with an assumption that everyone follows the same months or season patterns that I do, and for those that do follow a different calendar, they are those who live far away on a different continent. This article really challenged my thinking in regards to even different approaches I can take to teach mathematics.

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Math: The Sixth Sense

  1. 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?

As Leroy Little Bear states in the reading, “Singularity manifests itself in the thinking processes of Western Europeans in concepts such as one true god, one true answer, and one right way.” This was prevalent in my learning of mathematics throughout grade school. Math is a subject, I was taught, that has one correct answer and one correct way of getting that answer. The problem with this, as Little Bear mentions, is that “it is these assumptions that make it hard for a person to appreciate an alternative way of thinking and behaving.” Therefore, the Western approach to mathematics having one solution would have been oppressive and discriminating for my classmates who adopted and practiced other ways of knowing, especially Indigenous ways of learning and seeing the world. Further, in his TED talk, Eddie Woo makes the comparison of someone saying they are “just not a math person” to the ridiculous statement “I guess I’m just not a seeing kind of person.” When we compare the two statements, it is clear that the philosophy that some people are just not cut out to do math can be damaging to students who struggle with mathematics. This was relevant in my schooling, as some of my teachers adopted this philosophy which discouraged kids from pursuing higher education in mathematics.

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 of mathematics and the way we learn it.

After reading Poirier’s article, it is clear that Inuit ways of teaching and learning challenge Eurocentric ideas about the teaching methods of mathematics. For instance, Inuit teaching strategies do not include pen to pencil work and instead, focus on “observing an elder or listening to enigmas. These enigmas can be clues for problem solving in mathematics.” This concept of learning about problem-solving through experiential learning is especially intriguing because it illustrates mathematics through real-world applications. Further, Inuit ways of thinking about spatial relations challenge the Euro-centric understanding of measuring distance because, again, the Inuit perspective is developed from life experiences. For instance, “Space in the North is an ever-changing space, changing with the season, the time of day, the temperature, and so on.” Additionally, calendars (especially days in a month) are heavily included in Western mathematics. However, Inuit mathematics have a different understanding of the length of calendar months: “How long one month is depends on how long it takes for a natural event to take place.” Therefore, a concept that is correct in an Inuit understanding of mathematics would be incorrect on a mathematics test because of the Western or “Southern” understanding of the calendar. Thus, Inuit perspectives on mathematics propose a way of learning about math through real-life applications which makes math more meaningful to students. Further, this raises challenges for Inuit students who are forced to learn math from a “southern” perspective later in their lives.

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Does Math Make Sense?

Thinking back on my education of mathematics, it was a very positive experience all around. Since I can remember, I have always loved math and I think part of it was because I was able to understand it really easy. I could take the numbers and equations and work through them rather quickly. In elementary school I can remember the teacher following the Math Makes Sense textbook like it was the only thing that could teach us anything about math. For a long time, I honestly didn’t think any other textbook existed. Back then, I never thought anything about it but now I am realizing that those textbooks were potentially discriminating against or oppressive to my fellow students. With only learning from the same textbook for most of your life, you learn to solve problems the way that THEY want you too. Some teachers would even mark others differently depending on how you got the answer, rather than if it was correct or not. I myself have even struggled with  trying to change my ways of problem solving to fit what the textbook (and my teacher) wanted from me. This can be problematic because not everyone will understand the one method of solving a specific type of problem. Still up to this day, I have not learned anything about how math is taught and viewed through Indigenous perspectives and I know that I am really missing out. I hope that I can experience some of this teaching while at the university, as well as be able to transfer it to my future classroom. Being a math major, I think it would be beneficial to break this cycle and introduce new ways of teaching so that all y students can understand to the best of their ability. 

Within Poirier’s article about teaching mathematics within the Inuit community, challenges the way Eurocentric ways of viewing math. The first mentioned is learning math in their own language. This can be transferred into classrooms all around because math can be a very complex subject. If students don’t fully understand English or French (depending on where they are learning math) then it can make figuring out the problem 10 times harder. This will also help students stay in touch with their culture and who they are. If they are coming to school and are speaking English, but go home and speak a different language, it can be difficult to connect what you are learning and get help from parents if you don’t know how to translate the terms into their own language. Even some of my friends who are in French Immersion school, do not know how to do math in English because the terms and symbols are different. Another way that Inuit mathematics challenges the Eurocentric view of math is through seeing the purpose for math. Although I am a lover of math (most of the time), I often question when I am going to use the derivative to determine velocity, or when I am going to need to know the rate of change of a ladder sliding down a wall in the future. However, the Inuit community believes that math being taught should be transferable to everyday life needs. This would definitely help me as a future math teacher to explain to my students why what we are learning is important. Finally, another way that the Inuit teachers math that differs from the Eurocentric view is through the teaching styles. One style would be through oral learning. Oral learning is important to their community because most learning is done through storytelling and would be another close connection to their culture. 

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Gaining Pedagogical Insight of How to Teach Mathematics for Meaningful Learning

            As I did my curriculum critique assignment on the grade 6 mathematics curriculum, the article “Jagged Worldviews Colliding” by Leroy Little Bear (2000) was really interesting to me because I was thinking about this topic extensively. I chose grade six mathematics as a focus to challenge myself to step out of my Arts Education comfort zone. I know from my schooling experience mathematics was not my favourite subject and I saw with my peers it often gave many students stress, anxiety, and frustration. In elementary school I did not really consider if the teaching and learning of mathematics was oppressive or discriminating of any students. As I got older I started to become more aware about different learning styles and how cultural bias and oppression are embedded into society in many different ways, and how you can see this in classrooms. For example, in grade nine, students were placed in modified, regular, or pre-AP math classes. The pre-AP math class was almost completely higher socio-economic white students. These class sections were organized by the high school teachers in conjunction with the grade eight teachers as we registered in grade nine. Although the people in these different class groups changed a bit in my four years of high school, they mainly stayed the same even though I know there were many students who were in the regular classes that could have benefitted from faster paced AP math classes. Additionally, most math instruction followed a teacher facilitated, product based curriculum model which only benefitted certain learners. In the readings, Leroy Little Bear discusses how the “education and socialization of a child . . . is a collective responsibility” (Little Bear, 2000, p. 81). I think moving towards this mentality would be a positive shift towards a praxis model and be more supportive of diverse learners.

            In the article “Teaching mathematics and the Inuit community” by Louise Poirier (2007), this view of the collective responsibility of education is elaborated with suggestions of a community centered model for teaching mathematics. One way this is exemplified is how traditionally Inuit teaching of mathematics was “based on observing and elder or listening to enigmas” (Poirier, 2007, p. 55). Another example of Inuit mathematics challenging Eurocentric ideas for mathematics is the land or place-based pedagogy of ‘localization’ which is outlined to be “the exploration of one’s spatial environment and the symbolization of that environment with the help of models, diagrams, drawings, words, or other means” (Poirier, 2007, p. 56). This is such a positive and inclusive way of learning for many different learning styles and abilities. Another interesting traditional Inuit mathematics skill passed down from many generations was using body parts as measuring tools (Poirier, 2007). This has been done by many different cultures for centuries and is still often employed as an easy math tool to this day. I myself sometimes use the length of my arm or hand to measure things. This is a valuable skill for children to realize that some of their best measurement tools are their bodies. This definitely challenges the ruler and compass measuring tools of Eurocentric ideas for mathematics.

            Finally, I just want to say how much I enjoyed the TED Talk video about how math is a sense. Being in Arts Education, I am always considering how to turn lessons into aesthetic experiences and connect to the senses for deeper learning. Many people think about math being an all left brain focused subject area. However, this video inspired me to see the art of math and how it can connect to the beauty of nature and our lives in a meaningful way. This motivates me to continue to find ways to love math more and more so I can be a positive role model for students to find their own love for math.

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MATH EXPERIENCES

My overall experiences with math in grade school were very positive. I found that I was overall very good at the content and I put in a lot effort to ensure I understood the material. In terms of the class being oppressive I find that the subject matter is built around right and wrong answers for the most part. In my opinion math is a class that a teacher can limit themselves to explaining the material in one way and that is that. Great math teachers find multiple different ways to explain concepts so their students will remember the material. I understand that one might say that math can simple be too hard because of the tests where you need a desired outcome and this can be oppressive. However this can lead to helping students realize that in life sometimes there are right answers, as surely many university students would agree. An example of this would be when engineers are creating bridges or buildings there is not more than one answer to their calculations. This is why I find that Math can lead to improving one’s work ethic because I studied more for it than I did for my other classes. I would learn tricks and easier ways to remember how to do difficult questions. Also, for the students that do still struggle they are usually reviews and other assignments that you could work hard to get a good mark on to improve your overall grade if you struggled with tests. My teacher would always be there to help and answer any questions that we had. The math program is built around hard work especially if you struggle with the content and I’m not sure how it would work without having students test out the formulas that are taught.

After finishing Poirier’s article: Teaching mathematics and the Inuit Community, three ways that Inuit mathematics challenge Eurocentric ways of math include counting, localization, and measuring. Counting which is when systematic using of methods compare and arrange sets of different objects. Localization is based around using models, diagrams, drawings, and words to explore the environment. Lastly, measuring is built around the idea of using different tools or objects to understand dimensions. These are only three of the ways that Inuit mathematics challenges Eurocentric ways.

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