Symbolic Worlds in Time/Spaces of Practice Reflection

 

Local Matters Reflection

 One of the points that resonated with me was the "promising girls" idea. I had never really felt any explicit distinction between any gender in high school, however, during one of my on-call E.A. days last month, someone said to me, "You will enjoy that class - it's a bunch of girls." The implication here was that boys are harder to handle and girls are generally well-behaved. I actually noticed that at the elementary level in the city that I am in, there was a greater reference to/use of gender stereotypes in comparison to the high school. Phrases like, "boys and girls," splitting the class into boys and girls, and talking about student behaviour in terms of "The boys in this class are...." and "The girls in the class are..." were much more frequent. Part of the reason may have been the generation of the teachers who were teaching. For example, "Hey guys" is a phrase that was common when I was growing up and so I say it a lot. I've been trying to switch out "guys" with "folks" "class" "crew" (during hybrid lessons it was "online crew" and "in-person crew") but it is hard to break out of language that was deemed appropriate for the entirety of my life (I of course understand why it is necessary in terms of creating an environment where everyone feels included). Another part of it may have been because the high school has an active GLOW (Gay, Lesbian or Whatever) group, so the school environment as a whole may be more aware of these issues as a whole. I think these points, which may seem subtle to some, tie in well with the point "[we need to]... move beyond the moderinst habit of assuming that self/identity is separate from knowledge/learning" because there are non-binary students and students that don't fall under the stereotype of their gender that are being underrepresented or completely neglected in the environment in which they are meant to learn. If they are not seeing themselves reflected in the content or when they are excluded this way (e.g. "Boys and girls"), they aren't connecting with the content to the same degree and therefore their learning is negatively impacted. 

Although it is mentioned that race may or may not have been a contributing factor to these generalizations of "unpromising boys/promising girls," I was also reminded of biases in my own community and how this negatively impacts students - more specifically, the idea of "unpromising Indigenous students." Growing up, we did learn about Indigenous culture, but did not focus on Indigenous history or Truth and Reconciliation and I frequently heard racist or stereotypical descriptions of Indigenous peoples being said in everyday conversations. One of these stereotypes was that Indigenous children all came from unstable homes, apart from a few exceptions, and therefore they wouldn't be able to achieve academic success. Of course, this is a terrible outlook and negative stereotype which would have negatively impacted the self-image and self-esteem of Indigenous students and had a direct impact on student learning. This is why it is so important to be aware of these biases and to actively empower these students as well. Of course, the history of residential schools and Indigenous Peoples' relationship to school is an additional factor at play. However, even allowing the space for students to be themselves without predetermined assumptions being placed upon them based on something they can't control, such as gender and ethnicity, is a huge part of our jobs to ensure these negative stereotypes are not perpetuated and so that students aren't inhibited by what society/teachers view them to be.

Mathematics for Human Flourishing

1. One of the points that stood out to me was the idea of math typically being attributed to mathematicians or only a select few. I've found it unfortunate how, at least in my experience, there seems to be a fixed mindset assigned to math - as though someone either "has a math brain" or does not. Not only does it undermine the effort someone made to learn the material, but it also makes it seem like math is this exclusive club "math people" are born into and no one else stands a chance of entering. It's both lonely for those who love math and discouraging for those who have trouble problem-solving in the typically accepted way. However, I think it is important to frame problem-solving as a human activity, and therefore linking math to an everyday activity that everyone does, which there are strategies for that we can explore. 

The other point that made me stop was math as human flourishing. Francis Su claims "mathematics cultivates virtues that help people flourish" (p. 10), and while I appreciate and agree that math needs to be humanized and placed in real-life contexts to assist in framing math as something everyone can access and can improve their skills in, I find this description slightly unhelpful. In my opinion, every subject can arguably be framed as something that cultivates virtues that help people flourish. For example, art is interconnected with creativity, cooking (apart from directly helping our basic need to eat) requires patience, science can teach responsibility etc. So if everything feeds human flourishing, why would someone choose to focus on math, especially if they have had negative experiences with it, heard negative attitudes surrounding the subject, or been discouraged from pursuing it? I still agree with the solution lying within providing context for math so that it becomes in-reach, however, I personally don't see the point of linking math to virtues.

2. I think the phrase "Every being silently cries out to be read differently" means students don't want to be placed in the stereotypes that are attributed with them based on race, gender, reputation or something else beyond their control. I think students ultimately want to be seen. Parker J. Palmer says, "The human soul doesn’t want to be advised or fixed or saved. It simply wants to be witnessed — to be seen, heard and companioned exactly as it is," (https://onbeing.org/blog/the-gift-of-presence-the-perils-of-advice/). I believe this is what students want - to be able to explore freely without someone swooping in to impose their advice and judgements based on their own experiences and ideas of reality. Students want access to experiences that will help them achieve goals that speaks to their souls and for others to witness their success in doing so. 

I know that I have personally felt or directly been discouraged by university professors when trying to learn higher level math. I feel that there were other problems at play here - limited time to learn (3 months for an excess of knowledge covered in one course), problems with standardized testing/grading etc., and lack of formative feedback, but instructors were also at fault. There was this feeling that the professors were these experts way above us, which was true in terms of the knowledge they held; however, some acted as though the amount of knowledge they held entitled them to be gatekeepers to the subject. Even though office hours were there so we could go to professors for help, some would be very condescending or act as though our level of understanding was so low that it was a waste of time to even try to explain the concepts to us. Because of this atmosphere, I constantly felt scared to admit I didn't understand or acted like an explanation made sense when it really didn't. I have sensed that same feeling in my students based on their past experiences with math and I would always try to make it really clear that I was there to answer any question they had, and that the type of questions they asked had no bearing on how "smart" I thought they were.

Entrance Slip for July 12th - Inquiry Map

 

July 5th Blog Reflection Post

1. Name: Karishma Sharma

2. Teaching Specialization: Mathematics

3. Practicum Reflection:

a) One of the moments that made me smile was working with students who were initially struggling and watching their progress and eventual success. One student in particular hesitated with their questions in the beginning but slowly became unafraid to ask me to repeat explanations and try questions similar to those we went over and have me check them over. By the end, the student's questions became more specific and they were better at articulating exactly what they understood and where they were still confused. I think that was an amazing realization for me because that's exactly what I want students to be able to transfer outside the classroom as well.

b) One of the major challenges I found was attendance. Our school had a remote week -  in-person week rotation and students often skipped the remote lessons. When students skipped class, it became nearly impossible to catch them up and have them understand the content they were meant to cover on the current day. I quickly realized I needed to hold them accountable during the off-weeks as well so I began implementing "Homework checks" with feedback given back, which were solely formative assessment check-points (and I was transparent about this as well). I found that a higher number of students participated and were at least less behind than they would have otherwise been. I also found that this method benefited the students who were already on-track because they were able to receive feedback at more regular intervals.

c) I have two things in terms of what I would like to learn. First is my on-going journey of learning about Indigenous Perspectives and how to bring those to my classroom in a respectful and meaningful way. I was able to work with the Indigenous Education Department here in Prince Rupert and I feel like the deeper I get into this inquiry, the more I realize I really don't know much at all. I also realize it is not a subject where I can "study up and become an expert in" and that it is vitally important to listen to Indigenous voices and collaborate with Indigenous people in my community to properly represent Indigenous Perspectives.

The other thing I would like to learn more about is how to effectively keep parents/guardians in the loop with their child's progress - both problem-areas and successes. During the pandemic, we lost out on this outer community aspect and I anticipate having to put in some work while navigating this area of teaching (not because I think parents are against me, but more so being organized enough to keep parents updated/involved to an appropriate extent). 

4. I think the most important thing I would write to my future self would be to stay humble and to continue to learn from those around me. I find that most of the role models I have in my life are in love with learning and that in turn inspired me to be motivated and try new things myself, which I would argue fueled my creativity and passions. I would want to tell my future self to keep that energy going and to lead by example for the next generation of students in the same way my role models did for me. 

5. I have a (tentative - provided I complete the program!) TTOC job in School District 52 starting this fall.

Informal Interviews Summary

 Here are a list of suggestions/tips we obtained from our informal interviews:

General suggestions:

- Link learning targets with First Peoples Principles of Learning objectives

- Remember to slow down and teach at a speed that allows students to learn rather than rushing through content goals (in line with the FPP "Learning takes time and patience"). Emphasize content that is important and spend less time on content that would be nice to cover but won't effect the students' ability to succeed in the future.

- Build relationships with students (FPP and also SEL)

- Create an atmosphere where students are able to express and explore their identity (FPP and SEL)

- Show students tangible examples of roles in their community and tie those into class lessons (e.g. talking about astronauts feels far away but maybe a local job where they can actually see it’s doable would work better)

- Find the math in the Indigenous culture/history, avoid tokenism

- Don’t generalize
    - not all Indigenous students are comfortable sharing their culture or info about themselves  

- Bring in/attention to people in STEM who happen to be Indigenous.
    - we don’t refer to people as “the White biologist” so don’t do the same thing for Indigenous people

- Challenge 1D story of Indigenous people by introducing more contemporary and positive viewpoints
- Professional development - don’t be afraid to learn alongside the students

- This is an ongoing process so it's a good idea to keep learning about Indigenous culture and continue to build/maintain relationships with your Indigenous Education department (and Indigenous communities if possible)

Activity Examples:

- Talking circle activity: explain the significance of this Indigenous custom and implement it into your class as a regular/reoccurring element.

- Basket story example: Disclaimer: We do not own or have permission to use this story - we are simply using it to illustrate a point for the purposes of this class: One of the storytelling application problems we were told was about a cannibal woman who lived on a hill. In this story, they talk about this cannibal woman and how parents would warn their children that if they were bad (or maybe were out after dark? I can’t quite remember), that they would be taken by this woman. Sure enough, some children in this story ignore the warnings and are taken by the cannibal woman, who carries them up the hill in a cedar basket. There are say, six children of various ages who are placed in this basket and taken. The question is, how big would that basket have to be to carry all six children? This is a non-numeric question that requires students to research and figure out what they need to solve this problem.

- 3D/360˚ totem pole - classes came in and asked questions about the process and the artist was able to talk about his technique, which included a lot of mathematical concepts

    - be on a look out for local projects where you may be able to do this  

- patterns in weaving

- storybooks of local Indigenous stories with teaching guide (available at your local Indigenous Education Department)

Guest Speaker/Co-teachers:

- It's better to build up to Indigenous guest speaker co-teacher (i.e. mention Indigenous Perspectives in the classroom regularly and also prepare students by letting them know a guest speaker might be able to tell us more about whatever topic it is we're talking about)
    - check with speaker first if it’s okay to put your hand up for a teachable moment/making connections to previous class
    - etiquette is huge:
        - invite them like a guest to your house
        - prep students to be respectful
        - make sure students thank the guest afterwards
        - send a thank you gift - often a reflective card about what you learned
        - possibly invite them to your class again
    - kind of like meeting the mayor - give them the proper respect they deserve
- don’t isolate the Indigenous aspect

- Indigenous guest speakers and videos etc. not just for content goals, but also for representation for students

More Resources:

- Abbotsford website: curriculum.abbyschools.ca
- Suggested books: Dr. Martin Brokenleg Reclaiming Youth At Risk
- Dr. Joann Archibald Indigenous Storywork
- Encyclopedia of American Indian Contributions to the World: https://mexikaresistance.files.wordpress.com/2013/09/american-indian-contributions-to-the-world.pdf
- When looking for resources, it’s often helpful to look at things that are not necessarily targeted at math because you might be able to identify the math within those resources yourself (we were recommended the general FNESC website because it has a lot of content)

Course Reflection Post

Image source: https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2Fkrisztibunica.files.wordpress.com%2F2013%2F01%2Finquiry-cycle.gif&f=1&nofb=1

 A big theme of this class for me was moving away from the traditional "teacher lectures and students do homework" format of a math classroom to a more holistic approach and gaining strategies to do so. One of the pieces we looked at that was highly influential for me was the Jo Boaler video. It seemed like such an obvious concept - that our focus in math needs to switch from computational to real-world/meaningful problems - but she just presented all the information and research in such a clear way that it is still with me. Another very influential reading/presentation we watched was Dr. Robin Kimmerer's work. As I am still navigating and learning more about Indigenous Perspectives, I find myself referring back to her braid metaphor for ways of knowing quite frequently. Sustainability in math is still a little overwhelming for me, however, I have been able to gain some insights during other courses and also by tying it back to Indigenous Perspectives. Specifically, I found the idea of teaching math as a part of a whole, as opposed to an isolated subject helpful in finding a way to introduce sustainability, at least a little bit at a time, as I myself explore the topic. Other helpful methods of teaching we talked about were embodying math, the effects of marking, which we talked about in other classes as well so it was nice to have complementary material and gain a deeper understanding of these topics as well.

In terms of suggestions for next month, I'm not sure if this is really a topic or not, but I would be interested in finding out more about assigning less traditional assignments/projects to students. For example, we talked about Mike Naylor's math novel, and my SA had me read The Curious Case of the Dog at Nighttime in which the main character often described his thinking or events using mathematical puzzles or concepts. It would be interesting to hear from teachers who have assigned novels as readings, creative writing math pieces, or other things not typically assigned in math classrooms and how they explicitly tied that to the course or emphasized the mathematical importance along the way.

Inquiry Project Reflection Post

Image source: https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Totem_poles_in_Prince_Rupert_2.jpg/220px-Totem_poles_in_Prince_Rupert_2.jpg

 Here are the slides for Amrit's and my inquiry project:

https://docs.google.com/presentation/d/1-reZ5v1zqvOBf-ijZqi2-QvIw1j9RFKeBb3mE_-J62w/edit#slide=id.p

Through the course of researching this topic, I was met with quite a few surprises. First of all, I hadn't realized how many teachers were using the FNESC textbook. Because it has been a short amount of time since the book was published, I anticipated not being able to collect a lot of information on the effectiveness of its usage. However,  I hadn't thought about looking into Indigenous knowledge implementation from around the world until we started doing our research. 

We discovered that a lot of similarities between the struggles Indigenous students faced here and in places like Australia and Africa. Through reading on the strategies used in other parts of the world, we were able to find methods that would help us in our own classrooms. In addition to this, we did find some instances of successful integration of Indigenous Perspectives in Canadian classrooms as well as what we should avoid (or what is less effective). I am glad that we were able to find a lot of resources and starting places for integrating Indigenous Perspectives into our classrooms and I hope to delve deeper into them through the continuation of our Inquiry project.

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.

Exit Slip # 7: Culture and Gender Stereotypes

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 I took a look at the Math Guru videos and website, as well as the University of Nottingham women in mathematics video. It seemed that a lot of the women spoke about how there was a turning point when they realized that math was accessible to them until they discovered otherwise or discovered that they really connected with the field. Therefore there was this default in place that they had to overcome to realize they were fully capable to succeed in math. That default is what we need to move away from and I think introducing voices from people of different background and genders is the first step in doing so. This made me think about the importance of presenting these voices. In math history class, we speak about ways we can diversify concepts by introducing their non-Western origins, which I wholeheartedly agree with. I think the key here is to introduce these ideas organically instead of having a day where we just talk about, for instance, "Women in math" but quickly move on to "standard" curriculum content in all its Western, male-dominated context. I can't count the amount of times I've cringed at the blatant "feminist" message in a show (e.g. on an episode of The Flash, the women ended up on a mission together, which was going really well until they went around in a circle saying "#feminism" in a very inorganic way). We need to show students that women, people of colour, people who belong to the 2SLGBTQ+ community etc. are all out there participating in, succeeding in, and expanding the world of math without coming across as inauthentic because otherwise they won't believe us. My thoughts right now are to try and incorporate as many different prominent mathematicians with different backgrounds as possible to help normalize this reality with my students. Also, like Vanessa Vakharia stated, we need to get away from the idea that someone is or is not a "math person" (and I'd say the same about any discipline) in general. Showing that math is accessible to everyone and that it's never too late to start the learning process is another notion we need to convey to our students.

Inquiry Topic

 

Amrit and I wish to explore Indigenous practices in relation to math and the effect that it has on students' social-emotional learning as well as academic understanding and performance. I personally connect to the topic of Indigenizing my classroom because I'm from a town where approximately 40% (or more, if you count surrounding villages) of the population is Indigenous. We grew up learning pieces of Indigenous culture and history in school or community events and I learned a little more while working in our local museum as a summer student for a few years; however, I hadn't encountered the applications and connections of Indigenous practices with math until I entered this program. I would especially like to learn more on the subject, not only to aid in fulfilling the "Incorporate First Peoples worldviews, perspectives, knowledge, and practices to make connections with mathematical concepts" requirement of the BC math curriculum, but also because I will be returning to my hometown or surrounding villages to teach. Therefore, incorporating Indigenous perspectives of math would double as a way to bring representation of many of my future students' own culture into the classroom as well as respecting and honouring  Indigenous ways of knowing.

Entrance Slip # 6: Tact of Teaching

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1. "Good teachers are intuitively aware that the daily activities of teaching and learning are conditioned by such subtle factors as the atmosphere of the school and classroom, by the relational qualities that pertain amongst students and teachers, and by the corporeal skills or embodied knowledge that teachers enact." (p.5)

These qualities are requirements stated for teachers to effectively act with pedagogical tact. As discussed later in the article, these are examples that require awareness apart from oneself and recognizing that one's actions in combination with things such as the current atmosphere, relationships etc. could have various (possibly unwanted) results. That's why tactful teaching requires such frequent improvisation. I believe developing these skills comes from experience, but also making sure we are present when we are teaching. If a teacher teaches for five years but isn't making an active effort to reflect on what went wrong or what worked well during their lessons and interactions with students, they aren't building this tact and are doing a disservice to their students. Another part of this is building relationships with our students. If we can learn more about each individual, we can have a better idea of their background and what kind of learner they are which can help inform us of the best way to interact with them.

2. "Indeed, the substance of pedagogical acting takes place at this level of temporal immediacy
that does not permit a reflective stepping back from or out of the situation in order to consider the various alternatives and consequences of those possible alternatives in concrete everchanging situations." (p. 12)

Pedagogical tact is also therefore the ability to reflect on spot and deal with a situation in the best possible way with confidence and speed. Here, it is essential for a teacher to have practical wisdom so that they don't react in a way that is detrimental to the students and/or their learning. Again, experience and actively trying to better our teaching is what I believe will help develop these skills. Another point might be to stay up to date with the latest research in education to help us develop strategies to deal with certain situations we might not be equipped to handle or that are new to us.

3. "Rather, when we are involved as teachers with our students then we are part of this classroom, this world, in which we practice what we know as teachers. In other words, our pedagogical practice expresses itself as an active understanding of how we find ourselves here as teachers with certain intentions, feelings, passions, inclinations, attitudes, and preoccupations." (p. 18)

Even though a teacher  teaching with pedagogical tact may separate from themselves while being absorbed in the observing and engaging with different happenings around the classroom, their identity still plays a factor in their style. I would say this also ties into practical wisdom because if we are aware of where we come from and what's important to us, we are more grounded in our decisions and can therefore interact with our class with more confidence and understanding. In other words, I believe we need to have an understanding of ourselves and a strong sense of what our teaching philosophy is before we can gain the wisdom and ability to do the right thing at the right time within our classrooms. I believe this also requires maintenance because we will likely change as people as we grow older or are exposed to new ideas/strategies over the years so it would be a good idea to check back on our philosophies from time to time to make the appropriate alterations. 

With regards to the effect on students, teachers, and parents, I would think that the initial years of our teaching would be slightly turbulent for everyone because we as teachers will still be developing a lot of the skills we need to cope with certain situations over top of trying to teach the course content effectively. However, if we actively reflect, make an effort to build relationships with our students, stay up-to-date with research in education, check-in with ourselves, and have a strong sense of what we believe is important in teaching, I believe we will eventually reach a point where we have the confidence, pedagogical tact, and practical wisdom to interact successfully with students and parents, and effectively teach. Of course, there will still be problems/new situations to encounter after these initial years, but these will just add to our list of experiences to learn from and hopefully better deal with in the future.

Exit Slip # 6: Effects of Marking & Ranking

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My hope is that my students become autonomous, critical thinkers, that are able to function in society as well as work to make it a better place. I think traditional marking systems in which the teacher is viewed as the holder of knowledge that students are comparing their own answers to doesn't make for a classroom environment that generates those types of students and thinkers. Additionally, the highly competitive and often merciless nature of our percentage-based grading system shifts the focus more from learning and self-development to a battle of survival that comes with its share of anxiety and unfairness. Overall, I understand ranking systems are likely favoured for efficiency and "practicality" reasons, but I also believe they strip away our opportunity to move forward as a society if we are working against each other and forced to look out for ourselves over collective humanity. When students are so focused on scoring well in courses and less focused on their individual journey as learners, they might feel less inclined to voice and explore their own thinking and instead conform to what they believe the teacher expects. I hope that I can move away from that objective in my classroom and create a space for students to make mistakes and learn from them without feeling that their future is threatened in the process.

Entrance Slip # 5: Marks, grades and their effects in schooling

Image source: https://blog.yorksj.ac.uk/moodle/files/2015/10/marking_feedback.jpg

As the students in the article pointed out, letter or percentage grades put a lot of pressure on a person and don't necessarily reflect their learning. I have been on both ends as a student. I once had a class in which I scored 24% on the first midterm and 50% on the second midterms, didn't really know what was going on, and still ended up with a B- in the end, without having improved by the final. I remember coming out of that class feeling like it was an utter joke but it likely had less to do with the instructor's teaching and more to do with the ways grades were calculated there. On the flip side, I have also been in situations where, even though I've improved by the end of the course and have gained proficiency in the course, I still have an overall lower mark because that's the way the grade averaged out. Therefore, from my own experiences, I understand that letter/percentage grades aren't the best indicators of knowledge or understanding so if I could take that into consideration with my students, I would like to. 

I have read about assessment methods including formative assessment throughout classwork and homework, providing feedback like it said in the article, and involving students in building criteria which was also mentioned. Even though giving letter/percentage grades the traditional way fits the system better and feels more organized or "fair" because they're just based off of right and wrong answers on a test/homework, these strategies would benefit a student more as the intention with them is to facilitate learning, create autonomy in students as opposed to trying to control them, and decrease unnecessary anxiety from fear of failing rigid tests. Letter grades and percentages can often be unforgiving and very much set in the mindset that the teacher holds the answers and the student must memorize the correct way to come about those answers, while these alternative methods show care and hope for success for the individual behind the score.

All that being said, I do understand that the current system requires percentage grades from students and does still rank students based on these grades, even if only in part. I think another reason why they haven't been done away with is because people like to organize others into boxes, which, to an extent, I understand. I may know my students, how they've improved, the different skill sets they have and the backgrounds they come from; however, if a university or employer was looking to take in one of my students, there is only so much they could learn from me, and only so much time they could spend per applicant. Over top of this, they don't know me either so they have to be cautious while taking in my input. Therefore, I think grades have this illusion of objectivity attached to them - if the student performed well on standardized tests, that must mean they are hard-working or worthy of the mark. I'll admit I'm not sure how this particular problem would be solved but I would be interested to see what alternative methods of accepting/hiring there are out there that I may not have experienced.