ECS 210 – Different Perspectives of Math

When I was in elementary and high school, I did not notice that my education was very exclusive and only presented certain perspectives. I did not notice that many of my classmates simply did not have their perspectives represented in the work they were doing. As a white person and someone who benefits from white privilege the curriculum, even in a math class always, catered to my perspectives. White, Eurocentric perspectives were constantly presented in the material we used in math class, especially in the heavily used textbooks. I have learned that the math material was specially meant to be taught in English. This made it almost impossible for to use the math material in other languages or French classes. EAL students found it very difficult to understand the material when they did not fully proficient in English yet. Looking back, I can see that the math was made by white people for white people and mainly used white perspectives. Indigenous ideas and perspectives maybe got a page or two in the material and the knowledge shared was not from a local Indigenous perspective. Indigenous perspectives about math were completely left out. My school had a higher proportion of Indigenous students and I think my math classes were oppressive in that they did not teach any Indigenous math perspectives and instead only focussed on a white Eurocentric perspectives I remember my math classes being very dull and always following the textbook very closely which simply do not include many differing perspectives.

Poirier’s article points out some interesting ways in which Inuit Mathematics challenges the Eurocentric Ideas of the purpose of mathematics. First, Poirier challenges the Eurocentric idea that math must be represented by the traditional numerical symbols. Instead, the Inuit people have their own unique ways of presenting mathematical symbols saying “the Inuit have developed a system for expressing numbers orally. They do not have other means of representing numbers” but “each number has different forms according to the context” (Poirier 57). Another challenge presented was the idea that we must use math and numbers in all aspects of our daily lives. Months, days, times, calendars and distances are all ways in which we use math everyday. However, the intuit people use landmarks and occurrences to describe calendars and distances. Thirdly and possibly most importantly Poirier challenges the idea that mathematics is a universal language which is understood the same throughout the world. Poirier discusses how there and many different cultural interpretations of math that are vastly different than the Eurocentric perspective of math.

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My Single Story

My “single story” blossomed from the separation of my parents when I was five. My mom moved us out of my biological fathers’ house and we then lived full-time with her, only seeing our father a few times a year. My mom worked two jobs to make ends meet and sometimes once all the bills were paid, groceries were bought, hockey and dance were paid for among other monthly expenses… my mom would have no more than 9 or 10 dollars in the bank account. We lived in low-income housing for a very long time until my mom saved up enough money to buy her own house when I was going into grade 9. I watched my mom hustle HARD my whole entire life and I knew that the world was extra hard for my small family. When I was in elementary school, I brought the bias that told me that my family and I are the only ones struggling. Lots of kids in my class had both moms and dads under one roof and were wealthy compared to me. Despite the struggles that my family faced, school always gave me hope. I was a good student who always got good marks and felt like school was my second home- I still feel this way in university. My mother raised us to believe that we could do whatever we wanted in life, no matter what. We could be doctors, lawyers, famous celebrities if we so desired and all we had to do was “dream big” as she would say. This saying drove me to further pursue school and getting good marks as I knew if I could succeed in school, then I could maybe succeed in other things too and hopefully not have to struggle in the same way my mom did. Now, as an adult and a future teacher I know that everyone struggles in one form or another. I hope as a teacher that I can create a space for students to feel adequate and like they are enough, no matter their socio-economic class. I also hope that being honest with my students and sharing my personal experiences will give hope to some of them.

It was powerful to watch the TED Talk by Chimamanda Adichie when she brings up the idea of ‘nkali’. Nkali, she says is the idea of being better than someone else and I think the influence that teachers have on young students’ minds and thoughts can in some ways be corrupted by the power that comes from our political, economic and societal climate. The world we live in right now is guided by mass-media, big corporations and in many cases corrupt leaders who get to call the shots as to what is popular and what is not. The power that these people and organizations hold allow them to continue to be in a place of power and delegate which stories are cared about and told to the world. In my case, I grew up in Prince Albert which is in Treaty 6 Territory and has a high population of Indigenous people- and I won’t lie, a good part of their peoples’ population is poor, drug addicts involved in gang activity. That being said, I think back to Adichie’s part of her TED talk where she says something like: tell people who they are, over and over again and that is who they become. I think this is especially true in Prince Albert… Indigenous people have been held at a place of inferiority for so long now and heard the same negative story about their people one too many times, that they perhaps have given up and fell into the mold that has been pre-destined for them due to the shots being called by White, Western people in power. Now being an adult, I can look back to my upbringing and recognize that it was in fact these same people whose truth mattered most, despite it not being accurate truths at all.

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Reflection #8- Curriculum and Treaty Education

According to the Levin Article, school curricula are developed by a surprisingly large and diverse group of people, ranging from academics, to teachers and business representatives. I found this to be a very strange fact, as I would've expected academics and teachers to be the ones to develop our provinces curricula since they are the... Continue Reading →

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Inuit Mathematics

  • In my schooling I excelled, I got good grades, I profited from the lessons, I learned the way my teachers taught and was able to pass all my classes with good marks, and easily fulfilled the requirements I needed to graduate. I recognize that there is a privilege in passing a math class; being able to physically come to class, sit in a desk and listen attentively, take notes, and then do the assignments, and then the hand-in and then the test. One must be able to read English and use its number system. This is difficult if you have an attention disorder, if your second or third language is English, or if you struggle to learn the way that math is taught. All these things make it difficult to learn math in the current system that is in our schools. If the system was changed in order to accommodate people with differences or to teach math in a different type of way, then it will be easier for everyone to learn math.

 

  • The three challenges that the Inuit community faced were as follows: Localization, counting and measuring. Localization is a way of using the area and space around you to understand things, such as using a snowbank to measure/understand which direction the wind is going and perimeter, area, and volume, whereas a Euro-centric math system would use numbers to solve for area, volume, and perimeter. Counting is an issue of base numbers. The Inuit use a number system with a base of 20, whereas a European system uses a base of 10. This causes issues for students when trying to solve problems that require rounding, or fractions. Next, Counting is an issue because in the Inuit language, there is context needed, and because there is no written language, therefore no word for the digit of 3. The Inuit language has words for ‘three things in something’ or ‘three groups’, and more. But because their words always revolve around context, the students struggle to learn European based math system in a non- European language. Lastly, measuring can be confusing because the Inuit measure things in relation to themselves, which creates self-awareness better than English has in my experience. The Inuit also use nature to measure things, such as time. The duration of one natural cycle might equate to a month for English speakers.
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Curriculum: Its’ Creation and Implementation

While reading the work titled Curriculum Policy and The Politics of What Should Be Learned in Schools by author Ben Levin, we learn that curricula is developed and implemented during a long, drawn out process that involves many people and often depends on governance systems that are in place at the time. Curriculum creation happens when a group of people come together to develop and/or renew certain curricula. The group in session usually consists of heads of post-secondary institutions, expert teachers, principals and/or senior admin personal, and some government officials such as people from the ministry of education. These people will look at the curriculum that already exists, collect some data and discuss what should be done in terms of a new curriculum. In some cases, there are piloted trials done for new curricula which will come back into the hands of the creators for suggestions or revision and in other cases the new courses are simply released freely for teachers to begin teaching.

I found it very surprising that this process can sometimes take several years to be complete. It seems interesting that it takes such a lengthy amount of time as some of the issues that are brought up in the first place, may be totally different than the issues facing teachers or the curriculum by the time it is all over and done with. In this context, I think of the History 30: Canadian Studies curriculum which is twenty-two years old and my professor of ESST 300, Heather Findlay, says that she has heard of a renewal of this curriculum for about five years now and it still hasn’t happened. The world is constantly changing, and so is the way that teachers teach… so why shouldn’t what teachers are teaching change and develop with the rest of the world too? I’m not suggesting that curriculum be looked at every year or two, I know that is an unattainable goal. However, I think that there should be attention given to making sure that curriculum is relevant to the students of today and maybe that means curriculum creators meet every five or seven years to check on curriculum and its’ implementation.

I also found the reading engaged me when the author brought up fact that teachers who are experts in some subjects are part of designing curriculum and yet it is only those few teachers may be the only ones in the province who can successfully teach it. I think that there should be some data and research done on what kind of supports teachers need to implement curriculum in their classrooms and that information should be taken into direct account when creating or renewing curriculum. If majority of teachers- excluding the experts on that subject- cannot properly teach the content simply because they don’t have the expert knowledge that is needed, then the education is doing a disservice to both teachers AND students. There has to be some sort of way to include necessary content and an effective way to teach it that is relatable to the majority of teachers so that the curriculum can be instructed properly.

When looking at the Saskatchewan Treaty Education Document I can see all of the key players that were involved in the developing process. Those individuals include Indigenous elders, post-secondary representatives, members of FSIN, federal government officials and Ministry of Education personal. I can imagine that since this was a brand-new concept and only introduced in 2007, that there may have been some tensions among the people of the public asking why this is important for their children to learn. I would even go as far as to say there was possibly even some backlash from teachers who were questioning how or why they had to teach this when there is already so much on their plates.

There is no doubt that curriculum development and implementation is a hefty process that is complex in many different ways!

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Teaching Treaty Ed: It’s More Than Just ‘Building Tipis’

While working a summer job in 2018, I had one of my co-workers (who is white) tell me that they were thinking of transferring their children from one school to another. When I asked why, they said: “Well, because all they do at this school is build tipis”. At the time, I knew that this comment was wrong on so many levels- however I did not feel as if I were in a position to respond. This person was a superior of mine in the workplace and who was I, a summer student, to come in and start a conversation that would surely rock the boat?

After consuming all of the information for this blog- Claire’s work, Dwayne’s’ lecture and the reading I think there is significant importance in teaching Treaty Ed in terms of creating a space for First Nations, Metis and Inuit peoples voices to hold power and be heard, even if there is an absence of those bodies in the classroom. I liked when Claire pointed out that this is not an issue for Indigenous people, this is an issue for white people and somehow white people still project onto people of colour. The purpose for teaching Treaty Ed is to educate the young people of today so that they can make beneficial change for ALL Canadians in the future. Being honest and sharing the facts, just like Claire does will never hinder a student’s learning but rather help it to grow and develop into deeper understandings of other perspectives. Personally, I would tell this intern that despite how the kids react or what your coop teacher says, continue to teach about Treaty Ed in an honest and respectful way because it is our duty as teachers… and like Mike said if we aren’t doing this, then we’re not actually doing our job. The curriculum documents will back you up and serves as evidence as to why you are teaching this. Acknowledging that “we are all treaty people” means that we in fact are all in this together and it involves people of different races coming together to unite in hopes of creating a better world. It is safe to say that teaching Treaty Ed means more than just “building tipis” but honouring the relationship between Indigenous and European settler people for what it was in the past and for what it has the potential to be in the future.  Everyone has to recognize this relationship like Dwayne said, and honour it through constant work and effort- that’s where our jobs as teachers comes into play. I don’t doubt that it is challenging, maybe sometimes uncomfortable and tedious work… but it has to be done. I honestly found it a bit relieving to see a teacher like Claire doing this work with such truth and love in her practice, and I hope that someday I can do that too.

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How We Read The World.

Moose Jaw is home to me, I spent all my entire schooling in one city between two different schools. I grew up in a white middle class family with two loving parents until they divorced and gave me the opportunity to have four loving parent figures in my life. Looking at my life now, I would consider having been very privileged in my upbringing.

As I went through my schooling I understand now that I was not exposed to a lot of diversity growing up. The students I started learning with in grade one was the vast majority of the students I graduated with in grade eight. We were considered a community school, but as far as I was aware, most of my classmates came from a white, middle-class family as well just like myself. All of my teaches were white, and in elementary all but one were females. As I started high school, I was able to notice more diversity with the students in my classes, coming form different homes and having different backgrounds, however there were still only white, majority females that were my teachers.

Throughout my learnings in school, we started talking about First Nations and Aboriginal culture in about grade four, but we never got into the depth of what really happened until about grade nine and ten. That is a long time to be taught strictly the European way on living. Although we may not have been the most diverse class you might have seen, I still believe that it is almost more important to discuss and talk about the good and bad about many different cultures. I also recently discovered that the majority of the books that I read in elementary and in high school, I could picture it being my life. They were stories that could resemble my own life and how I grew up. Many of these ideas I did not see until I started university, and I only now realize that there were so many ideas I was taught in school that were ‘single stories’.

As teachers we can use our power and position to try and reverse these biases that people may have. We should be teaching our students that there are more than just ‘single stories’ within our world, there are so many different views and perspectives that we should share with them. The classrooms I am see now are way more diverse that what I grew up with, so I think that being more aware of the book and resources we bring into the classroom is a great way to start working against these biases. Tying to make sure that all students can see themselves being represented within the classroom is our goal. I still believe that I personally have a long way to go to unlearn some of the ‘single stories’ that I have been taught in school, but I am prepared and excited to continue to grow and change my view on life and the world around me.

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Curriculum as Numeracy – Atausik + Atausik = Marruuk

After reading this week’s assigned readings and viewing regarding Curriculum as Numeracy, my thoughts immediately went to the cultural diversity that exists in our school systems.  It made me think of my future classroom and the possibility that an Inuit student from Nunavik, (as discussed in “Teaching mathematics and the Inuit community” by Louise Poirier) might one day be sitting in one of the desks in my classroom.

As the immigrant population is steadily increasing in Saskatchewan, Regina is definitely becoming a melting pot of cultures. In fact, according to research documented regarding the English as a Second Language (EAL) program in Regina, I was surprised to read, “At the start of the 2018-19 school year, there were nearly 4,700 students whose first language was not English. That’s grown from 1,560 EAL students in 2012 to now representing about one fifth of the 24,000 students in Regina’s public school system.” This number represents “118 countries and 121 different languages” (Shepherd).

These statistics are staggering and justify why upcoming teachers need to be cognizant of the fact that learning styles and understandings might conflict even in subjects where “two plus two equals four” (Poirier, 54).  Not that teachers would do this intentionally, but I have to admit that it would be easy to assume a superior Eurocentric mindset of ‘your way is the only way.’  Changing our lens of perspective and recognizing that this wide diversity exists, even from Canadian students as close as the northern part of Quebec, is imperative.

The statements by Leroy Little Bear, “Language embodies the way a society thinks.  Through learning and speaking a particular language, an individual absorbs the collective thought processes” (78) resonate with me.  Relating this to my math schooling, I recollect my Grade 7 math teacher who, in a matter-of-fact way, announced the first day of math class that she refused to use the commercial program Math Makes Sense but instead would be using resources that she personally created. She continued to say that she did not agree with the approaches set forth in this program and that discovery-based math does not produce mathematicians.  That year, I absorbed her “language” of math and pushed aside the last three years of being immersed in Math Makes Sense methodology and went back to the basics. Without a doubt, I connected to her math “language” and learned more that year than I did any other year.  Her methodology and “language” is the reason why I love math today and wanted (past tense) to become a math teacher.  Fast forward to Math 221 – Introduction to Proofs and Problem Solving at the University of Regina.  Up until this class, I was all gung-ho to be a math teacher and then the “language” of my prof squashed my desire.  He taught the class with one mindset…his way or no way.  I remember standing in his office, trying to get math clarification on a problem where I ended up with the same answer but just generated the answer using a different approach. His words linger in my subconscious, “Your way is wrong.” “You will never get math.” and “Even if you work for it, you will fail.”  Just because my way, wasn’t his way, I was considered a failure.  Needless to say, I am proud to say that I didn’t fail that class but it did; however, affect my desire to become a math teacher. Language…what you say when you teach a concept, and language…what you say when you talk to your students, definitely does impact “thought processes of people” (Little Bear, 78).

After reading Poirier’s article, “Teaching Mathematics and the Inuit Community,” there are ways in which Inuit mathematics challenge Eurocentric ideas. One such way is how western civilization pedagogy is to approach teaching primarily on a theoretical level where knowledge is separated into isolated compartments rather than showing the interrelatedness to the real world.  These “paper-and-pencil exercises are not based on the ‘natural’ ways of learning of Inuit children.  Traditional Inuit teaching is based on observing an elder or listening to enigmas” (55).  One domain is “localization: the exploration of one’s spatial environment and the symbolization of that environment with the help of models, diagrams, drawings, words, or other means” (56).  Reading the snow banks and assessing the direction of the winds is a great example of another way to look at perimeter, area, and volume.  Whereas, we have been taught the numerical values; they internalize the mathematical concepts through every part of their senses.

The second domain is “counting: the systematic use of methods to compare and order sets of objects” (56).  European cultures use a base 10 incorporating the numerals 0 through 9 in different combinations to represent the desired number. Whereas, the Inuit uses a base 20 approach where they assign 20 different symbols or characters to represent the base combinations.

The third domain is “measuring: the use of objects or measuring tools to quantify dimensions” (56). Measuring objects with their body parts shows the importance of how math is related to their own personal space and experiences.  By incorporating their body parts into measurement, they come to understand more about reality, culture, society, and themselves. Another example of measurement is measuring calendar months by events occurring in nature, with September being the duration it takes the caribou to lose the velvet from its antlers.  I find this very intriguing. This connection to nature is significant because it is repeatable every year, at the same time, and supports the fact that mathematics should be discovered, not constructed.

I personally find the discussion of mathematical concepts of other cultures very fascinating. Exposing students to a variety of mathematical concepts through the lens of different cultural contexts, not only offers alternative methods of approaching conventional mathematical operations, but it increases one’s social awareness.

 

References

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 communityCanadian Journal of Science, Mathematics and Technology Education, 7(1), p. 53-67.

Shepherd, Andrew. “Diversity in the School: The Growth of Regina’s EAL Program.” 980 CJME, 6 Nov. 2018, https://www.cjme.com/2018/11/06/diversity-in-the-school-the-growth-of-reginas-eal-program/.

 

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Week 8- Schooling is Discriminatory???

After reading this, I wish I would have before I wrote my essay. A paragraph in my essay talks about the discriminatory school curriculum against Indigenous youth. My focus was math and talked about the Western style of teaching is so linear and straight forward where First Nations is not. It is about embodying human and mother nature together as one. While learning calculus 30, all we did was sit in a classroom and learn math which may have no use to many people. So looking back at this, yes math could have been discriminatory due to cultural and regional differences.

The First Nations way of learning to the European way of learning is different worlds. As stated above, they are about embodying human and mother nature together as one in their learnings. Some key differences can be described as setting, time, and strategy. The setting would be where it is taking place. Math is taught in a boring classroom, in rows, listening to a teacher. Where First Nation people would have been outside learning. They also would have been learning from both the teacher and fellow students. Time is a big thing too. There is a time limit in Math so you must finish and stress and crunch time to get it done. While on the other side, it is a more free way to learn. Finally, we have a strategy. This can encompass both setting and time but most importantly how the teacher gives information. Usually, it is from a textbook. The questions are from a textbook, etc. This may not be the best way to educate.

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What is Math?

Growing up, I did not see how my education was not entirely inclusive. As someone with white privilege from a privileged background, I didn’t always notice when my classmates weren’t represented in the curriculum or if some of the course material was discriminatory, since it didn’t seem to affect me. I now know I was wrong, and I work not only to notice oppression (and to work against it), but to bring awareness to other people about this discrimination. One thing I did notice, especially in high school, was that math was really designed to be done in English and when translated to another language, there were always some difficulties. My high school offered a French immersion program, and my friends who opted for that program had to take math classes in French. They always complained about how confusing their terms were and how hard it was to understand concepts that I had easily grasped in an English classroom.

When first thinking about whether my experience with mathematics was discriminatory, I couldn’t see how it was, my first thought was ‘math is math, how can that be discriminatory’? However, upon reflection, I realize that this is a result of a Eurocentric worldview that is privileged over Indigenous worldviews. As well, my math lessons promoted the idea that there was only one right way of thinking. I often interpreted things a little bit differently in my head than what was explained in class (but I would still get the right answers, just by my own process). Whenever I would try to explain my thinking to the teacher, they would say I was wrong and couldn’t wrap their way around another way of thinking. 

Poirier’s article challenges the Eurocentric idea that mathematics is its own “universal language”, there are many different cultural interpretations of math that use their own tools “according to their needs and their environment” (Poirier 54). Another Eurocentric idea that Inuit mathematics challenges is the idea that math is something that needs to be represented by numerical symbols, “the Inuit have developed a system for expressing numbers orally. They do not have other means of representing numbers” but “each number has different forms according to the context” (Poirier 57). As well, the idea that math is something we must use in our everyday life is also challenged by Inuit mathematics, they don’t use numbers to describe distance or months, instead they use natural landmarks and occurrences (such as inukshuks or the amount of time it takes for a caribou’s antlers to lose their velvet).


This post references the following works:

https://drive.google.com/file/d/1XgvnbwyV2EoU7Uj9I7U7nrIwBPHyrHwy/view

https://drive.google.com/file/d/1sIDgjwf9qCdqjhNNhV_GOmlxal1d_ZJM/view

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