Part 1 (Numeracy): Using Gale’s lecture, Poirier’s article, and Bear’s article, identify at least three ways in which Inuit mathematics challenge Eurocentric ideas about the purpose of mathematics and the way we learn it.

At the start of Gale’s lecture, she starts off by stating, “There is no mathematical gene” and that “As infants, we think mathematically before we think linguistically”. She then goes on to talk about how children attended a course and learnt math above their grade level. She then goes on to talk about how many people are able to learn math easily. In Bear’s article, they talk about how in the Western European belief system, there is only “one true answer and one right way”. However, in Poirier’s article, they explain that Inuit communities and peoples believe that there is much more than one right way and one right answer. Another significant way that Inuit mathematics challenges Eurocentric ideas is by who teaches the students. Inuit communities teach children by teachers, but as seen through Bear’s article, children are also taught by Elders and family members. Inuit mathematics education recognizes the importance of intergenerational knowledge transfer and community involvement. Challenging the way Eurocentric ideas have about only being taught by teachers. Furthermore, Inuit teachings in mathematics are taught with “a base-20 numeral system” and “20 and 400 are pivotal numbers”. These numbers challenge Eurocentric ideas. The way Inuit people and communities measure things also challenges Eurocentric ideas. Poirier’s article explains that when Inuit people measure things, they use “measuring tools were parts of the body”; women use “the palm when making atigi (parkas)”. These challenges the norms of Eurocentric ideas because they usually believe the measurements should be by a ruler or a different measuring tool.

Part 2 (Literacy): Which “single stories” were present in your own schooling? Whose truth mattered? What biases and lenses do you bring to the classroom? How might we unlearn / work against these biases?

The ‘single stories’ I encountered in my own schooling were the residential schools. In elementary school, mainly, I was taught that residential schools are bad and that Indigenous people experience a lot of trauma. However, it was not until university that I learnt about the effects of schools and intergenerational trauma. It was not until high school in my later years that I learnt that residential schools did not happen 100 years ago; they were recent. I also learnt about the extent of trauma students experience. Teachers left out information about these schools, showing a part of the story but not the entire truth of it. I also did not learn about treaty rights and Section 35 of the constitution act in 1982, where it was not until 1983 that all Indigenous people were “Indigenous” until I took Indigenous studies in university. If I did not take that class and did not learn about the extent of the trauma Indigenous people and communities had to go through, my viewpoint would be very different. For a while in high school, I wondered why we had to keep learning about residential schools. However, now I realize that we learnt about them, even if it is the half-truth, so we work toward building an understanding and moving toward truth and reconciliation. We learn and work against biases by teaching students the whole truth and teaching students that some ways of thinking are oppressive and cause a lot of damage. By teaching students this way of thinking and getting rid of biases, we teach students and other generations. For example, the student goes home and educates their parents about

• During fall semester several years ago, Dr. Mike Cappello received an email from an intern asking for help. Here’s part of it: “As part of my classes for my three week block I have picked up a Social Studies 30 course. This past week we have been discussing the concept of standard of living and looking at the different standards across Canada . I tried to introduce this concept from the perspective of the First Nations people of Canada and my class was very confused about the topic and in many cases made some racist remarks. I have tried to reintroduce the concept but they continue to treat it as a joke. The teachers at this school are very lax on the topic of Treaty Education as well as First Nations ways of knowing. I have asked my Coop for advice on Treaty Education and she told me that she does not see the purpose of teaching it at this school because there are no First Nations students. I was wondering if you would have any ideas of how to approach this topic with my class or if you would have any resources to recommend.”
• This is a real issue in schools. As you listen to Dwayne’s invitation/challenge, as you listen to Claire’s lecture and as you read Cynthia’s narrative – use these resources and your blog to craft a response to this student’s email, being sure to address the following questions:
  • 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?
  • What does it mean for your understanding of curriculum that “We are all treaty people”.

Email response:

Dear Educator,

I hope this email reaches you well. It upsets me to hear of your situation and the students’ and teachers’ stance on Treaty Education. I am sorry to hear about your struggles in attempting to teach Treaty Education for your Social Studies 30 class. I empathize with your struggles and would like to encourage you to persist in your efforts to teach this important subject matter. It is crucial for both students and teachers to understand the significance of Treaty Education.

The purpose of teaching Treaty Education or First Nations, Metis, and Inuit (FNMI) Content and Perspectives (generally) where there are few or no First Nations, Metis, Inuit peoples is to create an understanding of history and culture that is actively present today and issues from the past. For example, residential schools and the effects of intergenerational trauma. It also promotes classroom diversity and equity, building relationships and creating reconciliation. In Claire’s video, she explains that there are mostly white students in the school where she teaches, with very few Indigenous students. She explains that because of this, it is crucial to teach teary education. She then explains that teaching Treaty Education is about “learning the benefits and responsibilities that come with sharing this land and is about honoring the long history”.       

Recognizing and explaining to students that we are all treaty people and live on treaty land is essential. Chamber states in We Are All Treaty People that “the treaties formalized a shared relationship from which both parties benefit and for which both bear responsibilities”. This quotation highlights how treaties create relationships and how everyone is responsible for knowing about treaties. It also highlights that treaties and Treaty Education are important to teach because it is not just in the past, but in the present and the future, treaties are ongoing. It is also important to teach Treaty Education to recognize the issues of the past and how all people can move toward truth and reconciliation. We Are All Treaty People also points out that we all must respect each other and must work together. 

I encourage you to continue in your commitment to teaching Treaty Education, as it has the power to create awareness, understanding, and positive change among your students. Your efforts contribute to building a more inclusive and informed society.

Thank you,

Rae.

Provide a brief summary of your understanding of the three learning theories introduced in the readings (behaviourism, cognitivism, and constructivism). How can you connect these learning theories with the models of curriculum (product, process, and praxis in particular) that we have discussed?

Behaviourism theory teaching is reflected in how teachers react to students’ behaviour. It is an objectivist learning theory that revolves around human behaviour and observation. However, it is an “unmeasurable states, such as feelings, attitudes, and consciousness”. This theory relies on a system of reward and punishment with an “association between any particular stimulus”. Students who perform well or admirably are rewarded, and those who fail to meet the required criteria face the consequences. By applying this theory, educators aim to shape students’ behaviour and guide them towards desired outcomes. Students are taught to learn a certain way to achieve the desired response and to succeed in the classroom.

I believe that this theory shows the characteristics of curriculum as a product. Students being taught that they must learn a certain way to achieve the correct answer. Students are taught that through reward and punishment to achieve the curriculum’s outcomes. It is also shown in the way teachers manage the students and the classroom. Both curriculum as a product and this theory shows that students must focus on assessments and conform to the teachers ideals.

Cognitivism theory focuses on the ‘thinking’ aspect and internal thoughts, unlike behaviourism. Cognitivism emphasizes the role of mental processes, such as “comprehension, abstraction, analysis, synthesis, generalization, evaluation, decision-making, problem-solving and creative thinking”. This theory highlights the importance of learners’ knowledge and understanding it through their interactions with the environment. It also focuses on teaching “learners how to learn, on developing stronger or new mental processes for future learning”. It gives students different ways of learning and diverse perspectives.  

I believe that this theory is related to curriculum as process. This theory guides students to develop “decision-making, problem-solving and creative thinking”; curriculum as a process also guides students to have the “ability to think critically” by encouraging students to analyze and evaluate their environment. Curriculum as a process and this theory both recognize the need to adapt to student interests by guiding them to become good thinkers.

Constructivism allows students to have “free will and social influences on learning”. This theory emphasizes that “learning is a constantly dynamic process”; this shows that humans are lifelong learners. For example, when people are younger, they may know something about a subject, and as they grow, new information is added. This theory creates a deeper understanding of subjects about school and life while guiding students’ knowledge to constantly evolve. By embracing constructivism, educators foster an environment encouraging engagement and critical thinking while aiding students to make meaningful connections.

Constructivism theory relates to curriculum as praxis. Curriculum as praxis “places an emphasis on judgment and meaning making”. This theory and curriculum as a praxis foster students’ ideas and questions while evolving the knowledge that they already know and adding onto it. And having open and honest conversations about topics and subjects, allowing students to express their ideas.

What learning theories did you see reflected in your own schooling experiences?

Throughout my own schooling experiences, I have seen the constructivism theory. My teachers throughout my life would have honest and open conversations about topics and subjects. This allowed myself and other students to add to the knowledge I had already known. It also gave me an opportunity to ask questions to expand my knowledge. For example, in grade 8, one of my teachers brought in a special guest after we had read a book about residential schools. The guest was an elder who was a survivor of residential schools. Our teacher encouraged us to write down questions we had for her. These questions and her experiences added to my knowledge about residential schools and new knowledge about intergenerational trauma, bringing more awareness to the social issue.

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?

In the book, “Curriculum Policy and the Politics of What Should Be Learned in Schools” according Levin the curriculum is developed and implemented by the government. However, “political leadership will take account of expert opinion but, will inevitably take much interest in public opinion”. This means that the government can be influenced by people around them and by the public when developing the curriculum. When creating a new curriculum or revising a curriculum people from national, provincial, school advocators and sometimes even parents have influence on the curriculum and raise point of issues and add in their thoughts and ideas. When creating or revising the curriculum the ides of what goes into the curriculum, what subjects are in the curriculum, and how many hours/days it should be taught are discussed. However, the government has the over say in what goes into the curriculum.

One thing that surprises me was according to Levin “the latter may focus on the need for high level skills in their own areas, whereas teachers may be more concerned with a curriculum that will work for students with widely varying skills and interests”. To me the first part about this quotation sounds selfish. The second half of this quotation sounds like teachers are wanting the students to explore their interests and expand their skills. However, the part with the latter’s ideas is not ideal. “High level skills” in my opinion should not be included in the curriculum. Yes, schools should be encouraging students to do and explore what they like. But this seems to leave out many students and can possibly lead to being oppressive and harmful. This could leave out many students who do not fix into these ideals. And I believe that the curriculum should focus on the second half of this quotation.

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 tensions might you imagine were part of the development of the Treaty Education curriculum?

While reading “Treaty Education Outcomes and Indicators” I noticed on the first page of who contributed to the curriculum Sub-committee. While reading this I had noticed that like in Levin article he talked about the people who created the curriculum are national, local and school and how the curriculum is talked about in a group of people. In the “Treaty Education Outcomes and Indicators” document are national, local and school for example in the documents it states “The Ministry of Education and the Federation of Saskatchewan Indian Nations”. The curriculum of treaty education is talked about in groups.

What does it mean to be a “good” student according to the common sense?

Kumashiro talks about what it means to be a ‘good student’ in the ideals of common sense. Kumashiro describes a ‘good’ student’ as doing what the student is told. For example, sitting still, listening the teacher, behaving the way the teacher expects them to and being respectful. A ‘good student’ is also supposed to know the knowledge taught in the classroom and demonstrate it while asking questions on the topic explained during the lesson. A ‘good student’ is supposed to do what they are told. For example, when Kumashiro was teaching English classes, the school was strict with their expectations. The school told the teachers what exactly to teach and how to teach, what the students need to know and how they should learn it, write a certain amount of essay and what the write on them. All the information that is taught is on the final exam. Students did exactly what they were supposed to do, they answer questions about things correctly, they had class discussion correctly and wrote about what they need to write about. These students are an example of what characteristics a ‘good’ student is supposed to be like based on the common sense ideals. So, a ‘good student’ based on common sense ideals is a student who does not challenge social norms. A ‘good student’ is supposed to conform to the social norms and expectations of the school and teacher.

Which students are privileged by this definition of the “good” student?

‘Good students’ are privileged students. For example, Kumashiro talked about how he taught a student named M. M disobeyed when doing activities, was loud and acted in a different way then the other students. M did not learn the same way as other students did, she is not a privileged ‘good student’. Instead because of this M was labeled as a ‘bad student’. However, M is not a ‘bad student’, M has a different style of learning, and is punished because she does not fit the common sense ideals of a ‘good student’. Kumashiro described M as a student who wanted to learn and felt bad about not fitting the ‘good student’ characteristics by asking if she was “bad today” and said that she “would be better tomorrow”. M did not fit the ideals and characteristics of a ‘good student’. M is a ‘bad student’ because ‘good student’ leaning in a traditional school environment and do as they are told. M is not a ‘good student’ because she is not acting the way the teacher wants her to act. Students who are disables, have learning disabilities and mental illnesses are excluded from not being ‘good students’ because of the ideas and characteristics common sense demands students to be like. Common sense of a ‘good student’ is oppressive and leave a negative impact of the students who are not include in the category of a ‘good student’.

How is the “good” student shaped by historical factors?

Over time, the perception of an ideal “good student” has evolved, reflecting changes in societal values and educational practices. By studying history, society and individuals gain valuable insights that leads to growth and progress. Observing and experiencing different approaches to schooling and education have played a significant role in shaping these changes. However, some aspects of a ‘good student’ have remained but, evolved from history. For example. In the book “A History of Education” Painter explains describe that the teachers “directing their activity, and giving order” to the students. Historically this has shaped the ideal ‘good student’ from common sense. Listening to teachers, doing what your told, doing what they want they way they want it. These are examples of what it is like to be a ‘good student’ in the ideals of common sense.

Kumashiro’s definition of ‘commonsense’ refers to the shared understanding and knowledge people learn through socialization and education. However, it is worth noting that common sense varies significantly across different regions and cultures. This is particularly evident in Kumashiro’s personal experience, where the common sense she grew up with differs from the one she had to learn in Nepal. For example, the common sense for Kumashiro is to eat three meals a day; in Nepal, they get two meals daily. Both are common sense to those living in that region, but both are not actually common sense. The notion of ‘common’ sense may not be as universal as its name suggests, as cultural customs and values heavily influence it. Therefore, ‘common sense’ is not common at all.

Kumashiro also talks about how paying attention to common sense is essential because it causes more damage than we think. When talking about common sense and experiencing it, people get stuck in the routine of the knowledge that they were taught. Paying attention to common sense is important because it can cause oppression. Teachers and students may go into a school thinking a certain way because it is ‘common sense’; however, this common sense could be causing racism, sexism, classism, heterosexism, colonialism and much more. It causes oppression without realizing that it does. It may be hard to see the effect of common sense that causes oppression. It is easier to see the issue from the outside looking in, so it is essential to take a second and look at what common sense you are contributing to and how it affects others. It is also important to pay attention to common sense because common sense can limit our views. Instead of trying new methods, we fall into patterns of doing the same things repeatedly. For example, when Kumashiro is in Nepal teaching, he experiences a method of teaching that is repetitive and common sense in Nepal. However, Kumashiro tried to change the grading system and used his common sense knowledge of the “American way” but was not examining the issues of that common sense. 

When Kumashiro was in Nepal, and he encouraged a curriculum that consisted of “lectures, rote memorization, textbooks, and tests”. The school in Nepal take a more “Curriculum as a syllabus to be transmitted” model approach to the curriculum. It is more “traditional textbook approach of an ‘order of contents'”. It is very lecture focused; the teacher explains what to do and how to do it and sends out homework that they practice on their own; however, they still need to be graded on their homework. The students are only graded on the midterm and the end-of-year exam. They go through a chapter from the textbook a day to keep on track in order to finish in time for the end-of-year test. The ‘traditional’ model emphasizes the teacher’s knowledge delivery to the student and typically focuses on rote memorization and standardized testing. This approach tends to be teacher-centred and emphasizes the transmission of information rather than the development of critical thinking or student-centred learning. Kumashiro’s experiences in Nepal showed the limitations of this traditional model, as it often failed to meet the needs of diverse learners and failed to engage students in meaningful learning experiences. 

In Canada, students are shown and learn through lectures, but they also learn through field trips for learning experiences. In the Canadian school system they use the praxis model. This allows students to learn outside of the classroom and experience the learning through experience. The schooling is mostly student centered.  It is ‘common sense’ that students are to do homework at home, listen to lectures and pay attention outside the classroom. However, the negative effects are due to students being told what they must do; it can be rigid and inflexible. Depending on the class it can allow for students to explore interests. It also allows students to learn in different ways.