Colonial Influences in Mathematics Education

The Saskatchewan mathematics curriculum presents one single method to learning. It has been quite a few years since I’ve been in a high school classroom but, to the best of my recollection, the Saskatchewan mathematics curriculum offers a single approach to find particular answers. It is highly regimented, rigid, linear, and wooden in its approaches. I remember the teacher having an answer key for each question and if you did not apply the exact same methods and show your work in the exact same way that the key depicted you lost marks and, in some cases, would receive no marks at all for that question. If students brought forward or asked about different approaches to solving questions in class the teacher was often impatient and would get back to their assigned method as quickly as possible. The textbook was king and their answer key derived from the questions in the textbook. Their own answers to those questions served as the answer key, and that key was viewed as infallible.

Poirier’s article brought three challenges to my attention in terms of the purpose of Mathematics and the way we learn it:

The Inuit numbering system is base 20, sub-base 5 as opposed to base 10. This counting style is drastically different from Euro-centric counting methods and has been developed to suit the needs of the Inuit.

Similarly, the Inuit counting system was developed orally, not in written form. As a result, there are a number of ways to refer to quantities based upon context. The word for three objects is different than the word for three of something inside of something else. Likewise, having a group of three of something demands its own word. This system runs completely contrary to the Euro-centric system which has one word and symbol for each amount (eg. ‘three’ and ‘3’).

Finally, Euro-centric measuring systems champion complete accuracy above all else. Years are divided into months with a precise amount of days and each day is split into a precise amount of hours and hours are split into minutes, and minutes into seconds, etc. The Inuit do not use this same method. They have developed a system based around natural phenomena which fluctuate from year to year, but remain consistent in the yearly cycle. ‘January’ is ‘the coldest of all months,’ while ‘February’ is ‘when baby seals are born but are born dead.’ These events happen in the same order every year, but the duration of each event will inevitably vary from year to year. For Euro-centric understanding of measurements, this is challenging. The Inuit have developed something that works for them and though it is challenging to Euro-centric understandings, their lifestyles and landscapes demand a unique approach to many areas of life.

Learning From Place

The article Learning From Place by Restoule et al. records the events of a river excursion in which youth, adults, and elders from Fort Albany First Nation attempted to rediscover traditional Mushkegowuk ways of knowing and to rebuild their relationship with the land. The group hoped to accomplish this by reinforcing the notion of Paquataskimik which is the understanding that “the land…is a complex being – a spiritual and material place from which all life springs.”

In order for this shift in mindset to take place, the group sought to both decolonize and reinhabit the land. Restoule et al. defines reinhabitation as the ability to “identify, recover, and create material spaces and places that teach us how to live well in our total environments” and decolonization is defined as the ability to “identify and change ways of thinking that injure and exploit other people and places.”

Throughout the excursion, the group participated in reinhabitation through:
-Identifying key locations of cultural, geographical, or historical significance to the people of Fort Albany First Nation
-Sharing the traditional Cree names for those locations
-Acknowledge that traditional ways of knowing and relating to the land were not restricted by colonial, political, or industrial boundaries and demarcations
-Identify various tributaries of the river and discussing the importance the river played in a social context (i.e. a pathway for communication and travel between communities)

The group also participated in decolonization through:
-Acknowledging traditional methods of relating to and living off of the land and waterways
-Discussing land management and governance
-Addressing the implications of colonial and industrial dividing and parceling of land and waterways into Crown land, treaty, and reserve spaces and discuss how that has disrupted traditional ways of life
-Address the impact of residential schools and the loss of language and traditional ways of knowing that they caused
-Through arranging course credit for the excursion, thereby reinforcing and acknowledging the significance of traditional ways of knowing

So, how can these examples of reinhabitation and decolonization be adapted to my teaching methods and practices?

I would say my first task is to get to know the history of any particular school and community in which I find myself living and teaching. Place is significant. There are entire generations of history within any one physical location and, whether we are aware of it from day to day or not, that history plays a significant role in the everyday lives of its inhabitants. Every location has their own way of doing things, their own culture, and their own history. These factors work together to create a local “commonsense” way of living that is crucial to understand when entering into a community, especially as a teacher.

The ways in which I implement decolonization and reinhabitation will no doubt vary from place to place, but in general I would say the act of exploring local history with students and community members is vital. This could take the shape of meeting in retirement homes with elderly residents and simply listening to their stories of how and where they lived. It could look like field trips to local historic sites and museums to explore the physical landscape and collections of historic stories and items. Depending on the location, it could look like partnering with local First Nations and elders and having them share their histories and perspectives in regards to the land and its significance. It could look like addressing local environmental and ecological concerns through visiting wildlife federations; further exploring the impacts of agriculture and industry as well as the effects of dividing the land and altering habitats and landscapes through the establishment of political or agricultural boundaries and infrastructure.

There are many ways in which teachers can implement the concepts of reinhabitation and decolonization into their local contexts. The only real restriction in doing so is the dedication and imagination of the teacher and the willingness of the parents, students, administration, and community to allow such learning to take place.

The Lenses Through Which I’ve Learned

How has your upbringing/schooling shaped how you “read the world?” What biases and lenses do you bring to the classroom? How might we unlearn / work against these biases?

The literature I was exposed to in school was predominantly written by American or British authors speaking from their American or British perspectives. These perspectives, while different than my own, were still similar enough that I was comfortable. I was not faced with anything overtly counter-cultural. To the credit of these authors, I was challenged by deep and troubling political, economic, and social issues, but these works rarely if ever touched on issues of racism, ability, or sexual identity. There were a handful of Canadian and First Nations authors and perspectives read and discussed in high school which gave me a perspective that hit a little closer to home. We read about the Japanese internment camps in British Columbia and about a First Nations boy who found himself lost and alone, searching for his home and his family. Stories like this helped me to view the world around me as a more complicated landscape than those from the predominantly white, male American/British perspectives.

My biases and lenses stem largely from who I am and what I was exposed to growing up. As an able-bodied, straight, white male who was exposed to writings from predominantly able-bodied, straight, white, American/British males, I was not exposed to many examples of people different than myself. This has led to a lack of understanding of those who are different than myself. There is much about the world around me and the people around me that I simply do not know. I feel the best way to combat this is to continue to learn more and more of the stories of those around me. By exposing myself to multiple stories, I hope to avoid the narrow-minded “single story” approach to those who are different than me.

Which “single stories” were present in your own schooling? Whose truth mattered?

The truths and stories of white, British/American males made up the majority of the stories that I heard growing up. I was exposed to very few examples of stories of people different than myself and as such the few that I did hear became my understanding of different peoples, cultures, and countries. This “single story” mindset has led to a level of ignorance within me that I did not know existed. Now that I am aware of this fact, I am better able to combat it in day to day life and ensure that the truths of those around me are heard.

It is also important that I ask probing questions in the classroom. It is not enough to simply share multi-cultural literature with my students, I need to challenge them to think deeply about who they are and why they view the works the way that they do. I need to facilitate a learning environment that discusses the importance of viewing the “others” around us through a multi-story lens; one that does justice to the people groups, races, or cultures about whom we are reading.

Development of Curriculum

Part 1) According to the Levin article, how are school curricula developed and implemented? What new information/perspectives does this reading provide about the development and implementation of school curriculum? Is there anything that surprises you or maybe that concerns you?

According to Levin’s article, curriculum is developed by a key group of actors: national, local, and provincial levels of government; teachers, administrators, business interests, community members, post-secondary subject experts, post-secondary institutions, and the Minister of Education.

These actors work together to assess the efficiency of the current curriculum as well as posit potential revisions or re-workings of the current curriculum. Research is brought forward for consideration as well as the requirements for post-secondary institutions and subjects and competencies that employers are looking for in their employees. The process of curriculum revision can take years and undergo a number of pilot periods before a version is reached that is accepted by the majority of reviewers. Ultimately, final decisions for curriculum revision fall before the mercy of government bodies.

I was surprised to learn just how much influence politics has over policy changes in education. Teachers are literally at the mercy of government bodies vis-a-vis the policies that dictate how they teach, what they teach, when they teach, etc. Of course this is concerning, but at the moment this is the nature of the beast. Increased weight from the perspectives of teachers as well as students would make me feel much more confident in the direction of education in Saskatchewan.

Part 2) After reading pages 1-4 of the Treaty Education document, what connections can you make between the article and the implementation of Treaty Education in Saskatchewan? What tension might you imagine were part of the development of the Treaty Education curriculum?

Perhaps the most glaring tension that I noticed boils down to a quote from Levin, “the more significant the proposed change, the more likely it is to have limited adoption.” Treaty Education was a completely new policy. To my knowledge it had no fore-bearers. According to Levin, the more drastic a change, the more resistance it will receive and the less-likely it is to be implemented. This holds tremendous implications for something as important as Treaty Education. If teachers refuse to implement it, they are not only failing to perform their job as mandated by the government, but they are doing a disservice to their students and perpetuating the current North American world-view that First Nations people and concerns are “less than” or unimportant.

The other issue that I see, as raised by Levine, is that the more specialized a curriculum is, the more difficult it is to implement by teachers who likely do not have the same level of training or education in the field as the experts who shaped the curriculum. The contributors to the Treaty Education document consists primarily of experts in their field and Elders. Admittedly, the Elders serve double duty of acting as both experts in their field and as those having a finger on the pulse of First Nations issues and concerns, but many teachers in Saskatchewan are not of First Nations descent and as such will struggle to present the curriculum. They will not be able to offer the same depth of knowledge in Treaty Education as those who crafted the curriculum. With any luck, teachers will put in the effort to learn about First Nations issues and concerns which will allow them to draw from a greater depth of knowledge as opposed to the shallow puddle of knowledge that many, myself included, are currently drawing from.

Why bother teaching Treaty Education or teaching from Indigenous Peoples’ perspectives?

Why emphasize Treaty Education? What is the point of implementing it and teaching about Indigenous Peoples’ perspectives in classrooms that may not have a single Indigenous student? Does it have any value? Any merit?

Yes. One thousand times, yes.

Treaty Education is not just a topic for Indigenous students. Treaty Education impacts each and every Canadian. Treaty Education speaks to our shared history and allows us to view ourselves in relation to the land we inhabit. Treaty matters.

To quote directly from the Saskatchewan Curriculum’s section on Treaty EducationWe Are All Treaty People. It is important for all students to understand that all people benefit from Treaties 2, 4, 5, 6, 7, 8 and 10, which cover all of what is now Saskatchewan. It is imperative that the British Crown, First Nations and Métis’ history and perspectives are taught in order to respect the Treaty relationship that was envisioned at the time of Treaty-making between First Nations people and the Crown.”

It is important to realize that you cannot simply teach about the impacts of residential schools or the significance of treaty relationships without first having at least a basic grasp of Canada’s history and the part that each people group has played in shaping that shared history. Context matters.

Teaching Treaty Education allows us to better take part in the ongoing conversation about the relationships between Indigenous Peoples’ and Canadians. It gives us a better understanding of that conversation. In his lecture On What Terms Can We Speak, Dwayne Donald states that there’s a disconnect between Indigenous Peoples and Canadians when sitting down at the table to talk. He argues that each group comes to the discussion with their own perspectives and that without understanding each other and our shared history, there will always be a disconnect as a result of the ongoing effects of colonialism.

While it is done with good intentions, you cannot teach Treaty Education or teach about residential schools while bypassing the history of what has happened between Indigenous Peoples’ and Canadians. That shared history is crucial to understanding. As Donald said, “the way you think about the relationship has a distinctive bearing on how you approach it in the classroom.”

And if nothing else, if you still can’t see the merit of understanding our shared history and approaching the conversation well-informed; if you’re still humming and hawing about why you should care about this stuff, remember that it’s mandatory. It’s your job as teachers.

In terms of curriculum, I’ll be honest, I don’t fully understand what it means that “we are all treaty people.” I understand that every Canadian citizen falls under this umbrella and they have rights and responsibilities because of it, but I can’t say with absolute certainty what that looks like. I feel the more that we dig into what it means to be treaty people, the more complicated things will become. It is not a simple topic. As Murray Sinclair points out, there is no easy solution; no quick fix. I think that the important thing is to continue to wrestle with the implications of being a treaty person and fleshing that out in daily life as well as in the classroom. I think that through better understanding our shared past and by sitting down to the table to continue to have these discussions between Canadian and Indigenous Peoples we will, in time, begin to fully grasp what it means to be treaty people.

Kumashiro’s critique of the “good” student.

In the second chapter of his work, Kumashiro makes clear the preconceived notions that so many hold. According to “common sense”, being a “good” student is fitting the mould. A “good” student is one who does not rock the boat by challenging the accepted norms of society. They sit quietly, listen intently, learn the content of the prepared lesson plan, and accept it as canon.  A “good” student is one who does not require any extra care or attention from their teacher.

This notion of a “good” student, and the teaching style that flows naturally from this belief, largely benefits students who do not experience learning difficulties. Students who have trouble focusing in a conventional classroom settings or take issue with the manner in which material is being presented are at a tremendous disadvantage. Conversely, students who fit the socially accepted mould of a “good” student benefit greatly from this definition. In the eyes of society, they do not need to change anything about themselves. They are “good” just the way they are.

This “common sense” approach to what makes a “good” student makes it difficult for teachers to see the needs of students whose learning styles do not fit within the societal norms of education. These ideas lead to not only teachers, but parents and society as a whole to believe that these students are not good at school, that they are unintelligent, or have short attention spans. These attitudes tend to stick with these children as they grow up and they believe that they are not smart, are not good at school, and will never amount to anything academically. 

Out with the old, in with the…old: Wayne Au’s take on Standardization and Curriculum

In his article, Teaching under the new Taylorism: high-stakes testing and the standardization of the 21st century curriculum, Wayne Au discusses the historical implementation of scientific management to the education process, as well as the effects of standardized testing in the public schools of the United States. Scientific management, as made popular by the likes of John Franklin Bobbitt in the early twentieth century, focused on eliminating waste and increasing efficiency in the education process in public schools. This scientific management saw a resurgence in the United States through the “No Child Left Behind” policy which was in affect from 2002 until 2015 (note: this policy was replaced in 2015 by the “Every Student Succeeds Act”). In essence, this policy aimed to create a benchmark with which students, educators, and schools could be more effectively and consistently measured, which in turn allowed the Federal government to reward schools that showed positive results and punish those that were found lacking. This high-stakes form of testing invariably led to standardization in the United States public school system.

Au argues that standardization “[objectifies] students by reducing them into decontextualized numerical objects for comparison”; in other words “by reducing students to numbers, standardized testing creates the capacity to view students as things, as quantities apart from their human qualities” (Au, 2011). The problem with standardization is that humans are inherently complex and learning is not easily quantifiable. While it is crucial for schools and educators to be held accountable for what they are actually teaching students, by reducing students to mere numbers they are being robbed of an education that is tailored to meet their individual needs and contexts. This standardization process caused teachers and schools to focus on results and not on the process of education or student comprehension. By tailoring the curriculum to serve these high-stakes exams, students became little more than products and teachers became mere factory workers focused on results. Educators felt that their hands were tied and they complied with this Federally mandated policy in order that their schools would continue receiving funding and so that they would avoid reprimand or termination. Au argues that this resurgence in scientific management has led to a “New Taylorism” within the educational system and is ultimately detrimental to both educators and students.

My plan moving forward is to search out other authors or articles related to the effects of standardization in curriculum. I believe Au’s article gives important insight into the effects of standardization but I intend to find articles by other authors in order to better flesh out the concept of standardization in curriculum. I am particularly interested in the ways standardization has changed after the implementation of the Every Student Succeeds Act in 2015.

Reflections on Smith’s Four Models of Curriculum Theory and Practice

In their article Curriculum Theory and Practice, Smith discusses four models of curriculum. Each model has its own strengths and weaknesses as well as implications for the classroom. Smith discusses curriculum as transmitted, product, process, and praxis.

1. Curriculum as a Body of Knowledge to be Transmitted

Curriculum as a body of knowledge to be transmitted resembles an outline or textbook approach. The benefits of the transmission model are that the information and objectives are clearly laid out from the beginning. The transmission model is both comprehensive and logical in organization and presentation to the class.

The limitation of the transmission model is that it is simply a collection of material that needs to be covered in the allotted semester or school year with little regard to students’ interest or ability to comprehend said material. It is a wooden approach to presenting information to the class.

2. Curriculum as Product

Curriculum as product is similar to the transmission model in that it has clearly defined objectives and little concern for learning outside of the planned curriculum. The benefit of curriculum as product is that it consists of clearly defined objectives that are easily evaluated.

These clearly defined objectives can also act as limitations to learning. Learning that takes place outside of these objectives is difficult to evaluate and often is not taken into consideration. This clear checklist approach creates learning “blind spots”. In addition to this, there is limited interaction and exchange between student and teacher in the product model.

3. Curriculum as Process

Curriculum as process can be explained as the interaction between student, teacher, and knowledge or what actually takes place in the classroom. The benefit to curriculum as process is that it is tailored to the specific classroom. Educators focus on interaction and the content and means of evaluating their students evolves in relation to the educator/student relationship. The process model invites examination of results and revamping where deemed necessary.

The limitation of curriculum as process is that this tailored education is not uniform and it is therefore difficult to evaluate. With little to no concern for hidden curriculum or preconceived notions of “proper education” held by students and parents, the curriculum as process does not take into account the particular context of the classroom. This model has the potential to be perhaps the most beneficial or the most detrimental to students as the quality of education depends upon the educator’s ability to craft and implement the curriculum.

4. Curriculum as Praxis

Curriculum as praxis can be described as informed or committed action. The focus is not merely on conveying information to students, but opening a dialogue about the broader implications of what they are learning and putting it into action. Curriculum as praxis is about enacting, embodying, and realizing theories, lessons, or skills. The benefits of curriculum as praxis are that it engages a wide range of individuals and groups within the classroom. When implemented effectively, this model undergoes constant peer review among other educators.

The limitation of curriculum as praxis is that such a strong emphasis on discussion and exchange between educator and students could lead to difficulty in covering the required material for the class. The educator acts more as a facilitator to discussion and, similar to curriculum as process, the quality of education received depends largely on the abilities of the educator. It is possible that the biases and personal opinions of the educator would steer discussion and  create a one-sided learning environment.

Author’s Experience

I would say the vast majority of my elementary education was curriculum as a body of knowledge to be transmitted. For example, I distinctly remember social studies classes in elementary school where the teacher placed a page on the overhead projector and we were required to simply write out the information. He read the page to us and gave us time to copy everything down before moving on to the next page (Granted, my note taking skills weren’t exactly anything to write home about in those days, but looking back it seems like a simple handout and some interaction with the material would have been more beneficial). There was very little discussion in the class and we did not have a say in what material was covered or from whose perspective it was presented. For example, we did a unit on the life of a settler coming to the prairies but we did not look at the same topic from the perspective of the Indigenous inhabitants of the prairies or the changes that this mass influx of settlers had on the wildlife or vegetation of the area. The class was very Euro-centric and strictly regimented.

I would say that my secondary education was a combination of curriculum as product and as a body of knowledge to be transmitted. For example, similarly to my elementary social studies classes, my secondary history classes were very rigid in both the order and the way in which the content was presented. We covered material chronologically from a primarily Euro-centric perspective. The classes were slightly more engaging and allowed for limited individuality in note taking, question asking, and assignments. We were expected to memorize dates, names, and facts relating to the material covered in lectures and our grade depended almost entirely on how well we memorized. There was typically one research essay where we were encouraged to pick a topic and engage with what we discovered during our research. This was about the only area in which we were encouraged to dig deep into historical events and, in a sense, converse with the teacher in a sort of dialogue about questions that we had and areas that we found interesting. In my experience curriculum as product was more beneficial than curriculum as transmission because it gave the students at least some form of outlet to ask questions and actively pursue learning on their own terms.

Common sense is not as common sense as one would think.

In the introduction to their book Against Common Sense: Teaching and Learning Toward Social Justice, Kumashiro discusses The Problem of Common Sense. In the simplest of terms, Kumashiro defines “common sense” as that which everyone should know; those thoughts and practices that are unspoken, commonplace, and assumed. “Common sense” is largely implicit although it varies from nation to nation and even region to region. In terms of “common sense” education in North America, Kumashiro argues that, while well-intentioned, it tends to be repressive, narrow-minded, and controlled by the privileged or politically influential.

Kumashiro argues that in order to teach effectively we must look out for that which is deemed “common sense”. These comfortable and restrictive ideologies and practices can be overcome by creating spaces where all students feel safe, are exposed to a broad range of ideas, are encouraged to think differently about “the other” or those different from themselves, and are encouraged to challenge their preconceived notions, biases, and prejudices. Failure to overcome a “common sense” approach to education will ultimately allow a multitude of students to slip through the cracks.