From Gale’s lecture, Little Bear’s article, and Poirier’s article, it was easy to see the ways by which Inuit mathematics challenge the Eurocentric conceptions of the purpose of mathematics. The biggest I could pull was the importance of context in Inuit math. The way they speak about numbers, and the number of words for each number in Inuktitut highlight this importance. Little Bear notes that in the Eurocentric vision there is a heavy focus on objectivity, and he makes reference to the artificial context of science labs. Inuit mathematics through their language challenges this notion, and in citing Collignon, Poirier points out how the subjectivity of the language does not allow for discussion of abstract concepts outside of context. It must always be applied to reality. Gale’s lecture also shows that there is a benefit of teaching and learning in context by demonstrating the difference of the test scores when the students were taught in a familiar context versus when they were not.
Inuit mathematics also challenges the eurocentric vision of numbers and how they ought to be grouped. Using the base 20 system instead of a base 10 system shows a completely different and equally valid way to think about the organization of numbers. It displays the Indigenous value of diversity and acknowledges multiple ways of knowing, and it challenges the eurocentric notion that in all things there is only one correct way to do things.
Third and final point I will mention, the Inuit tradition of learning mathematics orally through storytelling and enigmas challenges the eurocentric idea that math is best learned theoretically and on paper. Enigmas teach students how to be critical and how to solve puzzles whereas the theoretical learning at a young age only teaches students how to compute and to follow procedures. Often students of this western teaching style do not actually understand what they are doing with the numbers; they are just doing as they were told.
Looking back at my school experience, one of the main ‘single stories’ that was that there was always “one right answer,” or one way to do everything. While I would say that this is not uncommon in mathematics, I had a number of teachers when teaching stories or poetry who would only accept one interpretation of the story or the poem (usually their own) and no one was allowed to think any differently. In the stories we read, there was no room to discuss grey areas; if the protagonist (who was usually a young white boy) did not live up to the standards of what it meant to be good (honest, courageous, sincere, etc.) then they had erred unmistakably. White truth mattered; nothing else was really considered.
I know that I see the world through a white middle-class male lens. That is my lived experience, and I acknowledge that it impacts the way I teach. I know I am less patient with boys than I am with girls; I know that I tend to favour those who are keen to speak up in class; while I know that a person’s race or socio-economic level does not have any bearing on their ability to engage with content, I catch myself focusing my attention on those who are similar to me. Unlearning these habits is a long process of making myself more and more aware of how I teach and how I see my students. I requires me to go beyond my comfort zone and to show myself time and again how my thoughts are not indicative of the reality, until hopefully eventually I see things more clearly from multiple perspectives.
Reflecting back on my K-12 experience, my citizenship education was very strongly rooted in Westheimer and Kahne’s personally responsible conceptualization of what it means to be a good citizen. In elementary school, I remember that there was always a “virtue of the month” that we focused on developing, and at the end of the month the teachers always chose someone to receive a merit certificate for their “outstanding demonstration” of that virtue. Each year we were taught and encouraged to contribute to the food hampers at Christmas time and to the penny drive (because we still had those in abundance) in the spring to raise funds for the neonatal intensive care unit. In high school, the principal of my grade 9 and 10 years would go on and on at school assemblies about the “Three R’s” – Respect for self, respect for others, and responsibility (by which he meant show up, be on time, and do your homework). At multiple points we were taught that we need to “exercise our democratic right and go vote,” but we were not taught how to get involved in politics or how to pressure politicians to make social change.
While it is good to strive to grow and virtue and to give back to our community and to be respectful, it is a very surface level form of citizenship. It keeps us happy and pleasant on the outside; it makes us feel good about ourselves, but ultimately, it makes it next to impossible to inspire any form of change. It does not address the systemic concerns. If I were to make a medical analogy: it suppresses the symptoms instead of healing the disease.
If I were to highlight one main aspect of how citizenship education reflects the values of a certain place, it would be how open that place is to change. Personally responsible citizenship encourages the maintenance of the status quo. It seeks to avoid conflict by instilling in the students a sense of loyalty and obedience, and a duty to always be kind and generous to their neighbours. In doing so, in perpetuates the hegemony of a white male society that has no desire to be any different. Participatory citizenship places a stronger emphasis on working together as a community to fix the issues in society. It teaches students not only to do their own little thing, but to help organize initiatives and to collaborate and to get involved on a deeper level. This type of citizenship, while it does not directly call for social change, certainly can lead toward it. Finally, justice-oriented citizenship directly calls for social change. It teaches students to not just treat the symptoms of the failing aspects of our society, but to attack the root of the problem. In this model, it important to really seek out the injustices in society and to rectify them in a meaningful and lasting way, even if it means a little bit of conflict will be necessary.
In response to an email from an intern directed to Dr. Mike Cappello:
“Treaty education can certainly be a hard a difficult topic to cover, especially when you are faced with opposition and resistance. Nonetheless, it is very important and needs to be taught. In my eyes, there are two foundational aspects to living and teaching Treaties from which all other parts branch off: relationship and story.
The signing of the Treaties were the forging of new and enduring relationships between sovereign nations. They were a relationship that looked to share and to live on the land together. Since we live on this land, we are a part of this relationship whether or not we desire to be. As Dwayne Donald discussed in this address, to neglect the Treaty is to neglect our relationship. We benefit from the Treaty be living on the land, the least we can do is learn to develop our relationship with our Indigenous brothers and sisters.
Contrary to the common teaching in the textbook, the story of this land and this place did not start with the arrival of European settlers. There is so much we can learn from those who have lived here for centuries, and it is such a valuable perspective. It is full of wisdom and knowledge that my settler ancestors never knew. Cynthia Chambers talks about how these perspectives of Indigenous peoples are so connected to the land on which we live, it is important to learn them since it gives us a more complete view of our natural history. Once settlers did arrive, there became two sides of a story. Specifically relating to the signing of Treaties, the story from the point of view of the First Nations who signed them is too often neglected. As we learn, we should always be searching for truth, and we cannot come to the truth by completely ignoring one of the parties involved. We all hear stories growing up and some of them need to be disrupted. It is difficult, but it is worth it.
As teachers, we need to learn to grow in our relationship with students so we can demonstrate the importance of the relationship of the Treaties, and we need to teach them to strive for the truth in all stories by listening to all sides. Currently, there is a cycle of ignorance because too many people just do not know the story. Parents often pass down their misinformed mentalities to their children, and through Treaty education, we aim to shed some light on this history and to attempt to start mending the relationship that has been broken time and time again. We are all Treaty people on this land, and we have a duty to make sure our students understand what this means. We have a duty to truly share the land as brothers, to make good relationships, and to learn the truth.”
According to the Levin article, there are multiple groups, interests and practices at play when it comes to developing and implementing curricula. Because curricula are a matter of public policy, to a certain extent, they are intertwined with politics in both a broad sense – who gets what – and a narrow sense – specifically dealing with government bodies.
When it comes to curriculum review or renewal, there are multiple groups of people with varying levels of authority who are involved in the process. Educators by and large are central to curriculum development as ultimately they will be the ones required to use the curriculum on a day to day basis. Researchers in their respective fields and university professors also contribute to the conversation by providing input as to what students would require for further education. Curriculum writers have an important role as well to ensure that the new curricula are accessible in the way their are written and presented. Sometimes the public, including parents and students, is involved directly and asked to contribute their thoughts, but often their impact comes more from pressure on the government as voters. The government has a lot of power in the process because they need to please the public that elected them. The government decides what programs are to be focused on and tries to make sure the new curriculum still lines up enough with the thoughts of society.
When new curricula are developed, it can be time consuming and take years to complete from start to finish. There are often trials and pilot programs before a new curriculum completely takes over, giving it an opportunity to make adjustments and improvements.
I found it very surprising how often research has to take the back seat in arguments compared to the existing beliefs of the people. Levin was clear about how changes can cause conflict and how that conflict is often not good for the government or for those that wrote the curriculum if it is not accepted by the people. It does explain a lot about why curriculum and practice always seem to be so far behind theory and research.
It was also interesting to see just how much the government is limited in what they can do for curriculum and development based on other factors like time, money, and opposition. It must be so hard to try to find a way that pleases the majority in the time that they have.
In reading the beginning of the Treaty Education document, I see that it was developed as a response to a need in the community, even though like all things it faced opposition. There was an issue that we were not meeting the rights of the Indigenous Peoples, and there was need for development and the creation of new relationships. Thus, the government collaborated with the Indigenous communities, elders, and education communities to use schools as a means to better this relationship. I imagine their were a lot of tensions caused by this development because it was a change and a shift from what people understood education to be about and from what people understood about Indigenous Peoples.
Often times when we talk about what makes a good student, the commonsense answer provides us with a narrow list of qualities. A good student is punctual; they complete their assignments to the best of their ability and submits them on time. A good student is well behaved; they sit quietly in their desk and wait to be called upon before speaking; they do not start conflicts with other students; they do not back talk the teacher or question their instruction; they listen to the authorities in the school. A good student is intelligent and inquisitive; they soak up new knowledge like a sponge; they excel in assessments; they ask questions to learn more. This is the kind of image that is presented by Painter as he talks about the ideal Christian male who attains his best potential, and by Kumashiro by his anti-examples of students M and N. I think that most of us can agree that most of these qualities are inherently good to possess; however, this “commonsense” description of a good student is incredibly limited and does not account for a myriad of outside factors that influence a student’s behaviour at school.
With its definition of a “good” student, the commonsense privileges a handful of students. These students usually come from white middle-class homes whose parents hold the same notion of what makes a good student. They are neurotypical with a stable family life and a good support system. In contrast, the definition puts many other students at a disadvantage, especially those who have difficulty conforming to the system. For example, children of immigrant families whose parents espouse a different idea of what makes a good student have trouble adjusting to the north american thought. Students with learning disabilities are also compromised as they do not learn in the same ways as their neurotypical counterparts and often struggle. There are also children who suffer from the trauma of adverse childhood experiences who can have difficulty not lashing out.
Historically, the idea of the good student is rooted in the British mindset of creating dutiful and law-abiding citizens who will do well when they enter the work force or continue into academic life. Being a good student is strongly linked to espousing British values and continuing a “tradition of excellence.” We all know how much the British though their values, methods, and practices were superior to all others, and Painter’s perspective very clearly follows this colonial attitude. Despite the recent changes in education, our commonsense definition of what makes a good student continues to perpetuate these colonialist ideals from when the British began establishing schools in North America. We see many of the same white, eurocentric values and practices in our schools today.
According to Kumashiro, “commonsense” refers to the mentalities, practices and approaches that everyone should know. Through the historical repetition of these aspects, they have become unquestioned, common place and generally accepted in a particular society. It is important to pay attention to the “commonsense” because people form their judgements about others based on their relation to what is “commonsense,” and a person’s inclusion or exclusion in a society can be incredibly dependent on how they follow the social norms. For example, Kumashiro gives the example about how the Nepali people thought he did not know how to cook because his meals did not align with their “commonsense” diet.
The “commonsense” curriculum model in Nepal, as described by Kumashiro, is heavily rooted is the lecture-practice-exam approach. Teachers are expected to give their lessons following the textbook as a lecture; students listen and respond to questions as a chorus; they practice using more questions from the textbook; and they are evaluated solely by exams. In Nepal, group work and enquiry learning are rare and face resistance. Kumashiro even makes a remark about how some American approaches he tried were considered “fun” but not real teaching by his students.
In Canada, we have a wide array of “commonsense” curriculum models. Among many older people, the concept that school should be “lecture-practice-exam” is still preminent, especially in regards to math and science classes. This is why we see all the parents and grandparents online complaining about how “they changed math” and how “math should still be taught how I learned it”. In this model, the teacher is the focus. The teacher holds all the knowledge and transmits it to the students. The major downfall to this model is that it generally leads to a lack of conceptual understanding. While students can do the computations or recite the facts, they often don’t actually know what they are doing, why they are doing it, or why it is important.
The newer commonsense models that are being established in Canada are rooted in inquiry learning. These models go beyong the product and into the process and praxis of curriculum. They use a student-centered approach, and the teacher is there as a guide to help lead them in their learning. These models capitalize on alternative forms of continuous assessment, and students constantly receive feedback to inform their learning. The benefits to this model are that students tend to gain a deeper understanding of what they have learned because they have engaged with the content and process on another level. It allows students to be creative and engage with topics that pique their interests. It pushes students outside of their comfort zones, and it teaches them how to become lifelong learners. The challenges to this commonsense model are that sometimes older members of society have a hard time understanding it because this is not what education looked like when they were in school, and they can provide some pushback. Also, not every teacher has been eager to adopt this curriculum model and still prefer to teach as they did 25 years ago.