Curriculum as Numeracy

Oppressive aspects of math education

Most students are not comfortable with mathematics so by default mathematics education is oppressive for most students.  I see it in the faces of students during my placement where one or two students clearly enjoy math and the rest are cringing on the inside.

I was one of the students who enjoyed math and the reason I enjoyed it is that I was good at it and the way it is taught fits the way I learn, my intelligence (from Gardner’s Multiple Intelligences theory).  For others who are not like me (most!), it is an ordeal to be taught and expect to learn the “traditional” way.  I remember the kids in my class who did not know the answer to the teacher’s question were considered “dumb” by the whole class even if the rest of the class didn’t know the answer anyway!  The oppressive nature of the math curriculum is changing, and for the better.  Teachers are encouraged to cater to multiple intelligences through guided math that involves different types of math instruction such as games or individual learning.  This goes a long way toward addressing the stress and oppression in mathematics education.

Inuit mathematics as a challenge to other mathematical cultures (including Eurocentric views)

The main ideas that the subject of mathematics deals with are counting, localization, measuring, design, games and explanation.  This is the purpose of mathematics in any culture and therefore a part of mathematics education for the young.  There are at least three ways that Inuit mathematics differ from other mathematical cultures:

  1.  The number system functions on a base of 20, making 20 the basic number just like multiples of 10 are a base in Eurocentric math.  This number system is based on the total number of fingers and toes a person has and is culturally significant in Inuit culture.  Teaching of counting is thus a challenge if one thinks in the Inuit way and is trying to learn a different number system.
  2. The sense of space is different in Inuit culture.  In Eurocentric views, objects are located somewhere on a map or grid and we can describe to others where a place is based on that.  In the Inuit culture, based on the environment where the culture developed i.e. in the ice-covered north with very few landmarks, the description of place may include references to seasons, animals, snow banks or wind direction.  In other words, a location is not just a location, and is put into detailed context by the Inuit.
  3. In measuring, whether it is length or time, the Inuit have a differing view.  For example, the months are not based on lunar or solar phases, but refer to happenings in nature such as “the coldest month” or “where the caribou’s antlers lose their velvet”.  The months are not a specified length of time, but last until the action is completed.

Inuit mathematical ideas differ greatly from the Eurocentric mathematical system they learn in school and also how they learn it.  For example, the traditional way Inuit knowledge is taught to the young is through an elder and many times through riddles.  This is in conflict with the “paper and pencil” approach of Eurocentric mathematics.  Ongoing research is important in bridging the gap and finding ways to effectively teach mathematics to Inuit students.


Curriculum and Treaty Education

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

I think the question should be “Why don’t we teach it?” in a classroom that is predominantly non-Indigenous.  The purpose of teaching Treaty Ed and FNMI Content and Perspectives is to educate and make (especially non-Indigenous) students aware of the rich culture of Indigenous people, the history of treaties and colonization, the initial purpose of the treaties and the violation of these treaties.  It is important to teach about the mistreatments and injustice in order for society to shed racism and prejudice that is directed at Indigenous people.  As Claire eloquently put it, it is not Treaty Ed but more like “Settler Ed” and by default directed at non-Indigenous students!

As a newcomer to Saskatchewan (I’m from the Toronto area) and one who attended school before any Indigenous content was introduced, I am only learning now about Treaty Ed and FNMI content and perspectives.  Before coming to Saskatchewan I never laid eyes on an Indigenous person (remember GTA and urban sprawl!), therefore I have very little prejudice or even information at this point.  Most of it I learned in this class, and it has opened my eyes about the importance of teaching Indigenous content, especially to non-Indigenous students.  It is a shame I never knew any of it and this should not happen to any student in Canada from now on, whether they live in a major city or rural area.

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

For my understanding of the curriculum, the statement “We are all treaty people” means there are two sides to everything.  The very nature of treaties is that they are two-sided: Indigenous and Settler.  Each side has responsibilities and rights under the treaties.  Everything that exists today (cities, houses, roads) is here thanks to the treaties signed long ago with sovereign First Nations people.  Therefore we are all treaty people!  By teaching this truth, important steps toward renewing relationships and reconciliation can be taken.

Teaching students Treaty Ed is crucial in the process of reconciliation and decolonization.  We have all been colonized (both Indigenous and non-Indigenous) and it is hurting us culturally and even environmentally.  As Dwayne Donald said “What kind of education would you have to receive in order to believe you don’t have a culture?”  The kind of education that teaches about Treaty Ed can help students realize they have a culture, and it is tied to the treaties whether they are Indigenous or not.  It can also highlight the tie to the land we all have and how we are dependent on having clean air, water and will all suffer the effects of climate change.  It can help us respect and protect the beautiful land what we depend on as a result of treaties.

As a future teacher, I think it is crucial to meaningfully enact treaty education for all the reasons stated above.  But none of those are as striking as Erica Violet Lee’s statement from Treaty Ed Camp that there is something wrong with the system when Indigenous students are more likely to end up in prison than graduate high school.  Indeed the system is broken and there is no excuse as to why it should be this way.  I would like to be the kind of teacher to help fix this broken system and a large part of it is to teach Indigenous content in a meaningful way to all students.

Curriculum as Place

Learning from Place: A Return to Traditional Mushkegowuk Ways of Knowing

Reinhabitation and decolonization are achieved in a number of ways.  In this article, the authors detail a research study based on some of the activities undertaken by the James Bay Cree community.  The main theme that runs through the article is the connection to the land, the river and the environment that people have.  Intergenerational learning about place is central to the reinhabitation and decolonization process.  In particular, a 10-day river trip with youths, elders and adults was pivotal in the re-connection with the land, sense of community along the river, recognition of burial places (central to re-discovery of ancestors) and re-learning of language.  The trip also highlighted the value land and river have on the social and economic well-being of the people.  The concept of paquataskamik, even as a word itself, brought meaning to the deeply rooted connection between people and land.  The re-mapping of key cultural and historical sites in the original language was also an important part of rehabitation and decolonization.

The concept of place can be adapted to most subject areas as a valuable tool of rehabitation and decolonization.  This is especially true of my subject area, science.  The easiest adaptation is the Indigenous naming of plants and phenomena (for example lightning).  Since language is one of the most powerful tools of decolonization, using original terminology is crucial.  Indigenous spiritual knowledge about nature also brings an important dimension when learning about science.  This can be adapted in outdoor learning situations or even when students are in the class laboratory.  And since science is infused with rich history and colourful individuals, the Indigenous scientific perspective and people should be included in the historical aspect of science.

What influences the curriculum?

Curriculum policy and the politics of what should be learned in schools. by B. Levin (2008)

Before reading: What influences the curriculum?

Curricula are based on the basic knowledge that students need to be successful in life, and at higher levels on the entry requirements of various university programs.

After reading: What influences the curriculum?

It is clear that the government has the most say in what is the curriculum content.  In turn, the government is elected and therefore trying to fulfill the promises that got them elected in the first place.  This is how voters influence the curriculum.  Of course, this is a lengthy process and decades may go by before changes are made.

It is surprising and worrying how little teachers and students influence the curriculum.  After all, teachers are the ones who implement it in the classroom.  They are the ones on the “front lines” and interact with students every day, and they know what works and what doesn’t.  It is the students who have to learn the material and plan their careers.  In a rapidly changing world, especially in terms of future careers, this lag in curriculum updating is negatively impacting students.

The “Good” Student

What does it mean to be a “good” student?  In the commonsense world, it means to go to class, listen, learn, do your homework and pass the tests.  Such a student is expected to show up, ask questions relevant to the lesson, participate, show enthusiasm, not criticize or ask deeper questions.  In other words, the “good” student behaves as is expected of them.  When the “good” student shows up in school they do not challenge social norms and more or less conform to the average.

The type of student who is privileged by the commonsense, is the one who is able to function in the school system as it is set up today.  They may even be genuinely interested in what they are learning and the classroom environment suits them well.  The privileged student in this set up may not exhibit overly questioning or difficult behaviour, and conforms to the majority of expectations of the school, their teachers and their peers.

What may be impossible to realize from the above definition, is that this imposed view of what is a good student goes against what is truly valuable in our society.  The most successful people, or those who make the biggest impact, are usually a little “different”; they question, invent, and think outside of the commonsense.  In school these individuals were probably branded as “troublemakers” by their teachers, and marginalized by their peers.  This definition of the “good” student makes it difficult to believe that all students are good students, and deserve to be on equal standing with their peers.

Thoughts on Education

“There is no way to help a learner to be disciplined, active, and thoroughly engaged unless he perceives a problem to be a problem or whatever is to-be-learned as worth learning, and unless he plays an active role in determining the process of solution” – Neil Postman.

There must be incentive for any action or it will not be performed, no matter how trivial or noble.  Therefore, it is impossible to truly teach a student if they do not want to learn, no matter how great the teacher is or how optimal the curriculum happens to be.  Once the student places value on what taught, it becomes second nature to learn.  There are two complementary components to this:

  1. The subject/topic/problem has to be worth learning or solving, and
  2. The student has to play an active role in the process.

In this scenario, the teacher guides and stimulates the learning process, and the student is ultimately in control of their own learning.  The learning process becomes student-centred, where the learning of a specific subject is guided by the student’s interest, abilities, values and motivations.  It allows for explorations of subjects, not in an equal weighting, but according to the student’s preferences.  The curriculum becomes a programme of “suggested topics”, and puts the teacher in a mentorship role.  In this scenario, it is not possible to have rigid outcomes or indicators for every topic in the curriculum.

Ultimately, it is a matter of quality over quantity in education.  From my own experience, most students do not remember the majority of the subject matter after the class is long over, but they do remember the topics they were interested in, and when they could actively participate in their own learning.

Social Efficiency Ideology

In many ways I am the product of a Tyler rationale style of education.  Most of my early education (elementary school outside of North America) was very much behavioral training including wearing a uniform, standing for the teacher, silence when the teacher speaks, organizing my desk and supplies, responding in unison and so on.  In retrospect, this was in fact an evaluation of “observable skills” and “changing behavior” (Shiro, 2013, p. 58).  The content of the curriculum was less relevant but included poem memorization, cursive writing, and mechanical math exercises that I strove to master just because that was the expectation.  Starting with middle school, I attended North American schools that were very focused on achieving good standardized test scores and it seems we were taught for that purpose.  These schools also instilled a fear that if one does not do well in their classes, university will be out of reach and basically life is over.  These experiences felt like I on an assembly line, as if “the production of an educated person is viewed in much the same way as the production of steel rails” (Shiro, 2013, p. 67).  I was being molded into something I did not want to be and told life is linear and no alternative paths exist.

The major limitations to such an approach to education is that the “assembly line” aims to produce similar results in all that go through it, does not favour individual wants and needs, and does not allow for diversity in any aspect.  The “assembly line” is punitive to those who excel beyond and to those who fall behind.  In many ways, our society relies on those who are different, as they offer a different point of view to allow us to question the way things are, and who are usually the ones who are at the forefront of invention and creativity that drives society forward.

There are potential benefits to the  Social Efficiency Ideology.  For one, it makes it possible to educate nearly the entire population with the limited resources available.  It does promote equality such that no matter what background, the child attends school and is presented with the opportunity to learn and be educated.  What this person does with this opportunity is ultimately in their hands.  Despite its many faults, the intentions of this philosophy are not malevolent, but are a product of their times: the first half of the 20th century.  The influence of the Tyler rationale is still very much part of the current curriculum, partly because of the educational benefits.