Mathematics

Gale’s presentation on numeracy and curriculum made me think differently about mathematics as a subject. I remember when I was in elementary school we learned the basics to math. Math was just another class that needed to be taken. I was never great at math but I could get the right answer from time to time by following the teacher’s instructions. There was often a textbook the class followed with answers in the back. Often when I didn’t understand I would look in the back of the textbook for the answer because many math teachers would make me feel dumb for not being able to come up with the correct answer. Math would often make me frustrated if I could not get the correct answer. Either I got math or I didn’t there was no in between. I’ve had high school teachers in the past expect us to already know the material s/he was supposed to be teaching us. It is hard to grasp a new concept if the teacher doesn’t explain how to arrive at the answer. Gale’s presentation made me think of math in a different way than I was taught it. Gale gave me hope for future mathematics educators.

Inuit mathematics challenged Eurocentric ideas about the purpose of mathematics and the way we learn it on so many levels. For instance, the base-ten system is an Eurocentric idea but Inuit mathematics uses the base-twenty system. Gale explained to us that the reason behind this is inside the igloo it is often very warm; therefore, the Inuit people remove their clothing to cool off. The Inuit peoples would sit in a circle inside the igloo, therefore, their feet and hands would be in front of them. Thus, it made more sense to use all ten toes and all ten fingers to count creating the base-twenty system instead of the base-ten system based on only fingers. Another way Inuit mathematics challenged the Eurocentric ideas about the purpose of mathematics and the way we learn it is through the way Inuit people used oral language rather than pen and paper. Indigenous people often told stories that were passed down through generations, which passed knowledge from person to person. In the math classes I was in we had textbooks, whereas Inuit mathematics would not have. Another way Inuit mathematics challenged Eurocentric ideas about the purpose of mathematics and the way we learn was through the multiple worlds for each number. In different Indigenous languages, there are several words for numbers or words that mean a number and a little bit. In Eurocentric ideas, there are specific words for each number and no word is a number and a little bit. Eurocentric ideas are spot on where other languages are approximations. There are several ways that Inuit mathematics challenges Eurocentric ideas about the purpose of mathematics and the way we learn it, which I did not know before the readings and lecture.

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“We Are All Treaty People”

Treaty Ed is very important not only because it gives another perspective but because we live in Canada and every Canadian is a Treaty person. Growing up there were a few Indigenous Peoples that were in our school and community but they were definitely the minority. Treaty Ed and FNMI content were put into my English Language Arts lessons through the literary texts we read throughout the course. Another place where I recognized Treaty Ed was in my Social Studies courses, we often talked about how treaties were formed and what collaborations took place in the making of the treaties. In my Social Studies courses, we also discussed the effect the treaties had on Indigenous Peoples and Settlers. Although there were not a lot of FNMI students in my community and school my teachers still felt the need to implement Treaty Ed into my classes. I think that it is important to have Treaty Ed implemented into each subject area because we live on Treaty Four land. I like how Claire Kreuger started implementing Treaty Ed into the curriculum at such a young age. People often believe that eight and nine-year-olds are not old enough to absorb such heavy information but they most certainly are. Kreuger is dedicated to the teaching of Treaty Ed and all teachers should use her as an example to see how important Treaty Ed is.

In the email Mike received from an intern is a perfect example of why Treaty Ed is so important. The students have been uninformed on the topic of First Nations and probably have a lot of knowledge that is not valid. I think the intern is doing a fantastic job trying to find a way to inform the students on proper knowledge. Once this intern is able to break through to these students the knowledge that these children will obtain will be substantial.

The term “We are all treaty people” according to my understanding of the curriculum means that everyone should be properly informed about Treaty Ed. As a Canadian that lives in Southern Saskatchewan, I am on Treaty Four land. I think that it is important to inform students on how the treaties were collaborated and formed, what the effects of the treaties are, and why we still have treaties today. It is important to have more than one perspective in each lesson. Wherever Treaty Ed can be implemented it should be so we can educate our future generations about what happened in the past so they can appreciate the past. In the English Language Arts and Social Studies curriculum it states that students need to learn how to learn from the past and appreciate the present and respect the future, Treaty Ed does this. We are all treaty people and we need to recognize this.

Curriculum as Place – Reinhabitation & Decolonization

The Mushkegowuk found ways to utilize the land, which is known as reinhabitation. On page 80 of the reading, the river was the way of life for the Mushkegowuk for thousands of years. The river has several different uses and meanings. The river was important to the Mushkegowuk because runners would travel up the river to give information. A community youth stated that they used the river for fishing, hunting, and camping. The Mushkegowuk bound diverse communities together through social, cultural, and economic activities. But decolonization in the article was mostly shown when it speaks about the old ways being taught again, bringing in a new perspective on the culture and language.

I am a pre-service English teacher, for the English Language Arts A10 curriculum identity is a huge topic. Being cautious and being able to adapt to these ideas and considering place in my own teaching will present its own challenges. The best way to represent the First Nations community is with someone more educated on the topic (ex., elder). I think that First Nations and Treaty education is very important. I would adapt these ideas by bringing First Nations culture, traditions, and languages into the classroom. I will do my best to make sure students are well educated about First Nations as best as I can.

Autonomous vs Ideological Curriculum Examination

For my curriculum critique, I examined the English Language Arts A10 curriculum. When looking at the curriculum I noticed that there was a balance of the two literacy models. In the Broad Areas of Learning, both literacy models are seen and in each section of the Cross-curricular Competencies. For example, in the Developing Literacies section, it states, “To achieve this competency requires developing skills, strategies, and understandings related to various literacies in order to explore and interpret the world and communicate meaning” (Saskatchewan Ministry of Education, 2011). This shows how the skills need to be developed first (autonomous) to be able to relate to literacies in order to explore the world (ideological). Both of the literacy models are also prevalent in all three sections of the Aims and Goals. In each section of the Aims and Goals, there are skills that need to be taught first before they are able to be applied to different cultural understandings. Whee autonomous is presented in the curriculum, ideological is usually applied after the skills are taught.

Citizenship Education – Curricular Problem?

Citizenship education is a curricular problem because in many curriculums not all three citizens are represented. A “good” citizen can be one of the three types. A student can be a “good” citizen if they are a participatory citizen, personally-responsible citizen, and justice-oriented citizen. If a teacher is teaching the student to be a participatory citizen they are teaching a student to know how to properly protest and make decisions/problem solve based on politics. A personally-responsible citizen is a citizen that does their civic duties. And a justice-oriented citizen is a citizen that takes social change. All three of these citizens are “good” citizens but depending on the location of the school, student, and teacher the student may not be given the opportunity to learn all types of citizens, which is a fault of citizenship education in the curriculum.

Citizenship education is implied throughout the curriculum there is not a specific place where citizenship education is specific. In the Broad Areas of the curriculum, citizenship education is usually most prominent. It is the teacher’s responsibility to put it into each lesson to teach the students how to become a “good” citizen. The curriculum just skims citizenship education.

What Makes a “Good” Student

According to common sense, a “good” student is a student that comes to school with the knowledge they learned from the media, parents, family members, etc. Students do not come to school as blank slates but slates that are able to be molded. Teachers want students that they can fill their “glasses” like in the diagram shown on page 24 (Kumashiro, K. 2004). Often teachers believe that students come in with no knowledge and as the semester goes on their glass becomes filled.

Particular students are privileged by this definition of the “good” student. Students that come in with less knowledge and are able to learn and be molded through the lessons they are being taught are the students that are privileged. The students that are able to be modeled by the teacher are going to get more attention, therefore, learn more. Whereas, the students that are seen as “good” students won’t get as much attention and time spent on teaching them.  

Since the idea of a “good” students is seen as common sense students that do not learn in this way are left out to dry. Since the idea that students come into the classroom as empty glasses that need to be filled shows a misunderstanding of how students learn. The idea that students are empty vessels that need to be filled was set back in the past therefore, people believe this to be true, which is troubling.

“Education is not a preparation for life; education is life itself.” – John Dewey

The quote which I resonated most with is: “Education is a social process. Education is growth. Education is not a preparation for life; education is life itself.” – John Dewey

In ECS 210 we have been discussing what is meant by curriculum being a process. What happens in the classroom beyond the curriculum is curriculum as a process. This quote further expresses this by saying, “Education is a social process.” I agree with this part of the quote because what happens in the classroom is very important. The curriculum is not the only part that is important within the classroom but also what happens beyond the curriculum.

Children are constantly growing. Dewey states, “Education is growth.” As a teacher we are constantly learning, as students, they are constantly learning too. No one ever knows everything. Therefore, the fact that Dewey goes to say that education is growth, he is expressing that the more knowledge the more they are able to grow, which I strongly believe. As children grow they are able to better themselves education does this for them.

As a future educator, I believe that everyone needs education to better themselves. Heart surgeons at one point in time went to school to become where they are now. If they did not have the education that they have now they would not be who they are today. Dewey states, “Education is not a preparation for life; education is life itself,” I strongly agree with this because I think people are constantly learning. Children do not have to go to school to learn knowledge. People are learning with everything around them, which goes back to the beginning of the quote where Dewey states, “Education is a social process.” Children are learning from the world around them, which is beyond the curriculum.

Curriculum Development From a Traditionalist Perspective: Tyler’s Rationale

Tyler’s rationale is summed up into four different questions. Tyler’s rationale is attempting to teach children the essential skills they need to live day to day life. As a traditionalist perspective of curriculum development, I have witnessed this in my own schooling experiences. For example, in many subject areas in the past, my fellow classmates and I were taught essential skills that we would need to better ourselves in our future. For instance, in English Language Arts, as a high school student, you are taught how to present yourself in a professional manner (ie., writing emails, resumes, cover letters, etc.). By being taught these professional manners you are taught how to obey and hold yourself within society, creating a “good citizen”.

Tyler’s rationale created a lot of discussions because many people found major limitations in his rationale. The biggest limitation in Tyler’s rationale I think is the idea that Education is a very complex system and hard to manage as a system but Tyler was able to find a rationale which is comprised of only four questions. Also in the article, “Curriculum Theory and Practice”, the author states that his rationale can end up giving the learners little or no voice. When children are the ones that are being taught it is difficult if they are taken out of the situation and given no voice. Also, the author states, “It can lead to an approach to education and assessment which resembles a shopping list. When all the items are ticked, the person has passed the course or has learned something.” When education and assessment begin to be a checklist that is just checked off, children begin to not learn anything. Children begin to take the back burner. These are just a few of the major limitations that Tyler’s rationale has.

Although there are several major limitations to Tyler’s rationale there are also potential benefits to his rationale also. For instance, Tyler’s rationale gives teachers certain skill that needs to be taught within their lessons. Therefore, teachers are given something to look forward to in means of having a final destination for their lessons. In other words, Tyler’s rationale provides direction.