Exit Slip # 10: Inquiry Project Update

 Amrit and I have found our sources now and have several different possible real-world connections that we will incorporate depending on what we receive from those conversations. We have started our slides and are starting to get more specific in our plan of starting with an introduction, detailing the research, and going into the activity. Narrowing down the scope of our project has been a little difficult because there are so many aspects to Indigenous Perspectives, but we are trying to stick with knowledge that directly impacts our study, while leaving helpful links for our classmates who might be interested in exploring those other aspects.

Annotated Bibliography for on Indigenous Perspectives in the classrooms

Annotated Bibliography for on Indigenous Perspectives in the classrooms

Karishma and Amrit are working on the inquiry project on Indigenous perspectives in the classrooms. We plan to start with the introduction of Indigenous culture and after that we will discuss the academic impact and SEL impact on the students. The articles and videos that we are using in our research are as below:

· Barta, J, & Shockey, T. (2016). Finding the ‘Space Between’ in Developing Mathematical Curriculum and Pedagogy across Cultures: The Mathematical Ways of the Northern Ute. The Journal of Mathematics and Culture. 10(3). Retrieved from: https://journalofmathematicsandculture.files.wordpress.com/2016/12/barta-shockey-final-august.pdf

These articles include information on how Indigenous peoples of Ute used or continue to use math in their lives. It provides explicit connections to curriculum-required content, as well as different perspectives, such as spatial awareness.

· Cherinda, M. (2015). Integrating Indigenous Knowledge into Mathematics School Curriculum: What is the Story so far? Ethomathematics Studies. doi: 10.13140/RG.2.1.2598.1282

In this article, a research was done on shifting traditional teaching practices into hands-on activities. It also tells about how this shift helps students socially and emotionally by developing their cognitive skills. It also explains how to create connections between cultural knowledge and mathematical knowledge.

· Chrona, J. (2015). Learning recognizes the role of Indigenous Knowledge. Retrieved from: https://firstpeoplesprinciplesoflearning.wordpress.com/learning-recognizes-the-role-of-indigenous-knowledge/

This blog page describes what Indigenous Knowledge is and how it connects to various subject areas, including math.

· First Nations Education Steering Committee. (2020). Math first peoples: Teacher resource guide, elementary & secondary. Retrieved from: http://www.fnesc.ca/wp/wp-content/uploads/2020/09/PUBLICATION-Math-FP-TRG-2020-09-04.pdf

This textbook includes good descriptions of what constitutes Indigenous practices/perspectives but since it’s a fairly new textbook, not much is mentioned about previous successes in implementing these ideas. There are also various activities listed that are designed to help teachers tie Indigenous Perspectives and curriculum goals together.

· Galindo, Ed. (2009). Compassion: A Hearts-on Paradigm for Transiting Native American Students into a STEM University Environment. The Journal of Mathematics and Culture. 4(1). Retrieved from: https://journalofmathematicsandculture.files.wordpress.com/2016/05/compassion-a-hearts-on-paradigm-v4-1.pdf

This article details the efforts of a collaboration project between a high school and university in Idaho called “Indian Summer,” which aimed to increase Indigenous student enrollment into STEM fields by working with students on locally relevant issues. Although specific to Indigenous students, this article illustrates the Indigenous Perspective of “hands-on-hearts-on” learning and how this benefits students on a social and emotional level.

- Goeson, D., Nicolidakis, M., Gamble, K., & Houghland, M. (2017).Weaving Math Aboriginal Mathematics Inquiry Team. Burnaby Schools Website. (https://burnabyschools.ca/indigenouseducation/wp-content/uploads/sites/4/2017/11/weaving-math.compressed.pdf

This PDF details the lesson plan and successful outcomes of a weaving activity done in a Grade 10 math classroom. We plan on conducting a similar activity with our class using paper instead of yarn so that our classmates get a sense of what incorporating Indigenous Perspectives in a classroom actually looks and feels like.

· Meaney, T., McMurchy-Pilkington, C., & Trinick, T. Indigenous students and the learning of mathematics. (pp. 67-87). Rotterdam: Sense Publishers. doi: 10.1007/978-94-6091-970-1_5

This article discusses the reasons why Indigenous students struggle in Western-centred math classrooms in Australasia. The article also includes suggestions of good ways to incorporate Indigenous perspectives in a meaningful way (e.g. group work is an Indigenous perspective so long as it is framed that way because it includes oral passing of knowledge and collaboration).

· Nolan, K., & Weston, J. H. (2015). Aboriginal perspectives and/in mathematics: A case study of three grade 6 teachers. In Education, 21(1), 12. Retrieved from: https://ineducation.ca/ineducation/article/view/195/788

In this study, three teachers are given a kit that includes various math activities involving Indigenous perspectives. The article discusses the results each teacher found in their classroom, which ranged from no perceived gain in mathematical knowledge to a seamless incorporation of both Indigenous knowledge and curriculum-required mathematics.

· Peterson, S. S., Jang, S. Y., San Miguel, J., Styres, S., & Madsen, A. (2018). Infusing indigenous knowledge and epistemologies: Learning from teachers in northern aboriginal head start classrooms. McGill Journal of Education, 53(1), 26-46. Doi: 10.7202/1056281ar

This article talks about SEL and Academic impact of indigenous knowledge. It also reflects the impact of residential schools on the students' social emotional learning and how they lose their language and get disconnected from their land and ancestors. This article is full of real examples presented by the students, how they share their cultural knowledge and land acknowledgement and feel connected with other students in the classroom.

· Toulouse, P. R. (2016). What matters in indigenous education: Implementing a vision committed to holism, diversity and engagement. Measuring What Matters. Retrieved from: https://peopleforeducation.ca/wp-content/uploads/2017/07/MWM-What-Matters-in-Indigenous-Education.pdf

This article talks about building interpersonal relationships among students in the classroom by allowing students to present their cultural knowledge thoughts in an authentic way. It also explains the impacts of connecting students with the real world by acknowledging the student’s prior knowledge and skills.

· Troutman, J. & McCoy, L. (2008). Re-membering Mathematics: The Effect of Culturally Relevant Lessons in Math History on Student’s Attitudes. The Journal of Mathematics and Culture. 3(1). Retrieved from: https://journalofmathematicsandculture.files.wordpress.com/2016/05/re-membering-mathematics.pdf

This article describes the importance of teaching culturally and historically relevant mathematics to students by showing the attitudes of different students towards math that lacks this connection. That is, this article shows that including diverse backgrounds, including Indigenous perspectives, increases all student motivation and SEL.

· Stavros Stavrou. (Nov 22, 2015). Aboriginal math education: Collaborative learning [Video]. Youtube. https://www.youtube.com/watch?v=eHyvlrbCiAY

This video provides some examples of how to incorporate land into the math classrooms. It also presents how aboriginal language acknowledgement helps aboriginal students to build confidence and feel connected with other students.

Exit Slip #9: Inquiry Project Progress Report

 We are currently still going through our sources to determine which are the most relevant. We briefly contemplated looking exclusively at Indigenous Perspectives in a Canadian context, but found that there aren't enough articles detailing the effects of Indigenous Perspectives in a math classroom on students; resources are more focused on introducing activities to use in the classroom or explaining what Indigenous Perspectives are and the key aspects that should be incorporated in a math classroom without necessarily listing results. However, we have quite a few sources in North America in general, as well as a few from Australia and Africa, which share similar issues of having a Eurocentric curriculum.

In preparation for our real-world connection, I have reached out to four different people of Indigenous background from Prince Rupert, one of whom has been tutoring students in the community for over ten years, and another who has already been working on introducing math to her two-year-old. In addition to this, I have notes from a talk I had with the Indigenous Education teacher from my practicum school. Amrit will also be looking to hear from students that are not of Indigenous background to see how they would feel about learning Indigenous Perspectives in the classroom. I may reach out to students in my hometown and my practicum school, depending on how many responses we receive from the others. I am hesitant to contact elders at this stage because I don't wish to rush the process. I would like to do that in the future if possible; however, I don't know the best approach to organizing an interview and what we should be prepared with beforehand.

Our proposed outline for our presentation is 

1) Introduction to what Indigenous Perspectives are and how they relate to a math classroom 

2) Discussing our findings on the effects introducing these perspectives has on students 

3) Interactive activity (we are thinking a weaving exercise that our classmates can use recycled (or other) paper for)

Inquiry Potential Links for Annotated Bibliography

Amrit and I are still reading through our selected links to make notes and change articles/videos that may be less relevant but here is a link to our google doc for the time being:

https://docs.google.com/document/d/1LVYqUvWxDa52QCz-uqi5z2uUkLEbXVE5oWjvv37efNI/edit?usp=sharing

Exit Slip # 8: The Inquiry/Research Process

 There were some interesting perspectives brought up in today's discussions. There seemed to be a range of opinions when it came to facilitating creativity in terms of what should be allowed and what should be discouraged. I personally believe it's about definition. For example, if I say "all angles in a triangle add up to 180 degrees," I am taking for granted some assumptions about what plane I am in. Of course, it would be tedious to mention all the stipulations to a concept when speaking about it but that's why laying ground rules and mentioning that there are other options out there is a good idea. If we show our students that most of what they know (reading, writing, math etc.) are through chosen conventions, this can broaden their perspectives and show them that there are more possibilities in the world besides the ones they are used to. That's why assigning inquiry or research projects would be a good idea - that way students could explore these less conventional ideas or learn more about aspects of math that they are interested in. Letting them play around with mathematical ideas will not only allow them deeper understanding, but hopefully more investment in the content because they are developing a stronger background and asking questions they want answers to.

Entrance Slip # 7: Permitting Creativity in Science

Image source:https://sfworkblog.files.wordpress.com/2013/09/janet.jpg

I thought it was interesting that Bavelas mentioned how the ones who discover an idea may not be the first to have noticed it. It just shows how taking a chance and pursuing something that contradicts the norm is how we move forward. It struck me as not only a good illustration of how technology and ideas develop, but that it was also a mirror of activism as well; often problems are overlooked because "that's just the way things are," but certain people are able to break past that and insist on a better way or a new perspective. This program brings to light a lot of issues that I had either never heard of or turned a blind eye to in the past, but that is no longer an option when we realize that what we teach in a classroom is going to effect our students. Similar to an idea from a previous reading, what we exclude is as important as what we include. Insisting things are a certain way and enforcing that on students will absolutely kill their creativity; even if we know they are wrong, it is sometimes useful to allow them to reason their way to the correct path because there is value in the struggle as well (although a nudge in the right direction is probably a good idea if they are too far off).

The idea of not trying to find a preexisting category for our observations is one I had to learn through researching for our Inquiry project. When I initially spoke to an Indigenous Education teacher at my practicum school, I was struggling with what Indigenizing the curriculum looked like and asked him how we could avoid tokenism, because up until this program, I thought that was an acceptable way to bring Indigenous perspectives into a classroom. However, I have realized since then that I was trying to place knowledge and perspectives that were new to me into a system I already knew and how that was problematic. The Indigenous Education teacher told me one of the best ways to bring Indigenous perspectives into a math class specifically was to look at incorporating cross-disciplinary ideas. As he explained it to me, Indigenous people don't have a concept of separating subjects the way schools traditionally have done and so creating projects that don't focus solely on math is a way to achieve this Indigenization (along with recognizing the Indigenous aspects of said project). 

The idea of being opposed to multiple tests for fear of contradictory results is an interesting one. Although I agree "Fear stalks us from the beginning and continues throughout, until the results are in and checked"(p.321), I don't know that I think this way about multiple testing. On the contrary, I find myself holding back expectations until the test is complete, and keeping that same attitude for future tests. It may be a self-defense method (a, "Oh well I didn't think it was going to go well anyway so I was right," sort of thing), and generally celebrations are belated. In terms of exploring inquiry with my students, I want to try different activities and be okay if they fail. It's likely not the same thing in terms of multiple "testing" of an activity or inquiry subject because each class will respond differently so one success doesn't necessarily mean it will continue to be successful in the future, but then the opposite can also be said - failure doesn't mean the activity should be discarded completely. However, if a pattern does arise, it would be interesting to investigate why that is the case - is the subject something that seems to interest a large number of students? Or is the topic out of the students' range of abilities at the current level and should something else be tried?

Women, the Nobel Prize and physics (accidentally wrote about this but I'm just going to leave it up)

Image source: https://www.cbc.ca/news/canada/saskatchewan/canadian-nobel-physics-prize-winner-girls-women-stem-1.4847839

One of the major things I believe we can do is bring up representations of the successes achieved by different genders and other underrepresented groups of people in the field we teach. Along with the representations and explanations of those prominent people, we need to be meaningful in the way we present this information. For example, if we simply stated "Donna Strickland is the third women ever to have received a Nobel prize in Physics out of over 200 recipients of the prize in that field," we may be trying to highlight how impressive Strickland's achievement is, but might unintentionally send a message to our female students that success in physics isn't easily attainable for women. As Shohini​ Ghose says,"This is not a problem that can be fixed by women. It's more of a structural, systemic problem, and unless we get everybody involved we're not going to be able to deal with it" (https://www.cbc.ca/news/technology/nobel-prizes-women-gender-1.4847608). I think stereotypical portrayals of physicists/mathematicians at an early age contribute to this systemic problem which continues on as children grow older and doesn't change unless they are exposed to the wide range of people who are contributing to a field. If this continues, those children become the adults who eventually end in positions of authority or decision-making and if they don't check their implicit biases, they allow those biases to affect their decisions on who is more qualified for a job or who should be accepted into a program etc. As teachers, we have a responsibility to be those role models who are aware of their biases, are continuously trying to break that cycle, and empower all of our students to choose which path they would like to take. Some of the suggestions Donna Strickland made for teaching physics included examples that are catered towards traditionally feminine or culturally diverse ideas such as the use of dance, spinning wool, cooking, and involving nature when introducing physics concepts. These examples are less explicit and don't necessarily show women in physics or culturally diverse physicists, but they help make the subject more accessible and relatable to different groups of people. In this way, I see the importance of introducing implicit as well as explicit representations to better engage all of our students in the subject we are teaching.