Entrance Slip #3: Mathematics education for sustainability

To be perfectly honest, this article was a little overwhelming for me to read. At first, I was intrigued by the usage of real-life examples that might compel students to think about their choices, such as the food production example on page 21. I began thinking about all the different areas I could explore by creating word problems that had more meaning than the traditional real-life examples that tended to deal with currency or very specific scientific ideas. 

However, when I began reading about chaos and encouraging students to search for the mathematics required to solve a problem, I began to worry. I do believe in expanding my students' minds and allowing them to explore and research within math, but the sheer amount of research and background knowledge that I feel I would need to be a good leader within these activities was what overwhelmed me. I need to have an idea of the field that I want my students to explore before assigning them projects within it but I feel under qualified to teach about areas such as sustainability, technology, and other sciences so I'm not sure what the best course of action is.

My thoughts on bringing climate change and mass extinction into the classroom is that it is a choice individual teachers have to make. I think to a certain extent, we incorporate our interests into our classes because teaching about things we are passionate about helps to inspire our students. I personally believe that sustainability is a topic that is important for me to bring to my classroom and so I would be able to inspire or at least bring awareness of it to my students. On the other hand, I don't believe it should be required of all teachers. For example, if a teacher personally didn't believe in the importance of sustainability or took a more pessimistic approach to the subject, it could be detrimental to the students. 

Coming back to my lack of knowledge about sustainability, I believe I could better handle students’ and adults’ knowledge and emotions if I had a stronger background to draw from when answering questions. I am genuinely thinking of taking time off after completing this teaching program to research sustainability (and other fields that I feel are important) and determine how to bring that to my classroom in a productive way so that I'm prepared beforehand and not figuring it out as I go. Not only are students and their parents views important to think about, but also fellow staff members. If I can't stand behind introducing sustainability with confidence and a plan, I'm not going to be able to answer any skepticism that comes my way or provide good advice for those looking for how they can take action.

Exit Slip # 3: Webinar with Dr. Robin Wall Kimmerer et al.

Image source: https://warriorpublications.files.wordpress.com/2015/08/sweetgrass-braid.jpg

Today's webinar as well as the reading from Braiding Sweetgrass were very inspirational. Dr. Kimmerer is very poetic in her delivery of her ideas - I found myself moved with the way she so effortlessly expressed herself and the strong imagery brought forth with all her metaphors. As I mentioned in our class discussion, I am still trying to understand what I can do to fully bring Indigenous knowledge into my math classroom; but I think the first step is to actively seek out new perspectives and research Indigenous culture. Another idea I resonated with strongly was "What do I love too much to lose?" It is certainly a strong guiding point for when we feel there are just too many problems to deal with. To me, this is a good reminder to focus on what is important - even if it's just a few issues important to us personally - so that we can make productive changes. I really admire how Dr. Kimmerer talked about turning her grief into love and using that love to act. It is such a wise outlook on life.

This webinar also brought back some memories for me. I remember being an EA in a socials studies 9 class where a student was struggling to find resources for their research project on a certain Indigenous tool. One of the other students in the classroom who was of Indigenous background said, "You're not going to find your answers in a book. Go talk to an elder."  Then, a few days later an Indigenous speaker came to another class and he said something similar. Actually, what he said was, "Go out, buy some donuts, bring them to an elder, and just listen. The snacks are for the both of you because you're going to be there a LONG time." What he was trying to convey to us was that there is a lot of important knowledge among the elders that isn't going to get passed down unless someone is there to take it in. Although I don't think it's my place to be one of the carriers of that knowledge, I think it's still important for non-Indigenous people to listen to the Indigenous perspective for our own understanding so that we are not shying away from it due to ignorance or fear that we will make a mistake.

Entrance slip # 2: Robin Wall Kimmerer on scientific language and the language of animacy

Image source: http://dorothystewart.net/2010/11/26/pipelines-through-paradise/

 I personally have never been a strong enforcer of learning the proper terminology for mathematical ideas. If a student wants to call it "flipping" instead of "reciprocating," I won't fight it because they're explaining the idea to me in a way that makes sense to them and I feel that terminology just bogs down this thinking process. That being said, terminology has benefits such as saving time and frustration. For example, a student might search, "The little number beside the big number," and spend a fair bit of time locating the word "exponent" before locating the answer to their question about the concept. Terminology is also more useful when we teach the rationale behind it or why a certain convention is used. For example, x ∈ ℝhas a significance if you understand set notation but is a confusing idea out of context. The problem is that the origins to all terms are not always short stories. Instead, I think it's more useful to focus on usage rather than names. For example, it's great if someone knows the words "percentage" and  "fraction" but more useful if they are able to apply those concepts in the real world, such as calculating sales tax or dividing a recipe in half. This is a simplistic case but I think it applies more broadly to teaching math as a whole. 

I appreciate what Dr. Robin Wall Kimmerer says about the difference in language structure between English and Indigenous languages. As she states in her article, she is not advocating that everyone learn a new language, but instead to shift our focus to respect things in nature instead of taking an arrogant, human-centred view on everything. I think just introducing that idea of considering the animacy of "beings" within our world and speaking in terms of "someone" instead of "something" is a good start in Indigenizing my classroom. This of course would only speak to some students and each person would likely make a personal choice one way or the other, but just by introducing that idea, it opens the students' minds to that perspective. Although I spoke above to how I personally don't emphasize names and focus on ideas in math, Dr. Kimmerer's experiences and the Indigenous perspective of speaking about "beings that are imbued with spirit"(p. 55) using vocabulary for animated beings resonated with me because it reminded me of my culture. For example, my grandmother would be angry with us if we handled books in a rough manner. Books, particularly those that contain some form of instruction, are seen as objects worthy of our respect so while we don't view them as alive, we still acknowledge their importance and are careful when handling them. Therefore, if I actively try to acknowledge of the animacy of beings in my classroom, I believe there will be some students who will resonate with the idea as well or at least understand it, even if they don't fully agree with it.

Exit Slip # 2: Jo Boaler's Video and Breakout Room Discussion

Image source: https://ed.stanford.edu/faculty/joboaler

Jo Boaler's video on student inquiry included many key ideas that I think will be the foundations for our teaching methods. This idea of multi-dimensional learning being our goal is something I think many classrooms have adopted or are beginning to shift towards already. My biggest concern, which was shared by members in my breakout room, is that, coming from a one-dimensional educational background myself, I may not be able to keep up with all the ideas and methods that my students will come up with. The way I'm thinking about it now, I will constantly be needing to read up on math, not just to increase my knowledge for myself, but so that I can be better at my job. I would absolutely love to do that, but I'm concerned it's not a sustainable thing to do. 

This thinking led me to wonder if it's better to introduce a topic in class briefly before jumping into class activities, or, like Jo Boaler suggested, should we be letting the students explore the topic themselves first by giving them activities that encourage thinking about the topic and reconvene at the end to discuss the various approaches? Giving the introduction at the beginning narrows their scope, which would help me focus on questions that may arise but limits the students to approaches that make sense to me and may not line up with their thinking. On the other hand, letting them think it through without my influence would certainly allow them freedom, but would then make it difficult for me to address every single path that arose. Other concerns raised by my colleagues in the breakout room were related to student participation. The group we saw in the video example of multi-dimensional learning was eager and ready to participate. What happens when there are students who are too shy or lack the self-confidence to participate? How do we encourage them to take part without singling them out?

Entrance Slip #1: Grant & Zeichner: On becoming a reflective teacher

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Grant & Zeichner's article, though written in the 1980s in America, is still applicable in Vancouver in 2020. Many of the questions being asked such as what knowledge should be taught to children and to what extent should a teacher control a student's learning and behaviour are still relevant to consider as a teacher candidate in this day and age. One of the ideas that stood out to me was how the way a teacher teaches in their classroom could reach out and affect a student's approach to life - specifically, the idea that teaching a student to conform instead of teaching a student to think critically could have a bigger impact on the student's approach to life in general. Of course, a number of external factors also play a role in what approach a person takes in life. However, by defining conforming as the opposite of critical thinking, I believe this article has clarified my need to actively strive to have my students ask questions instead of accepting everything I say as fact for fear that they will continue this habit in the real world.

There wasn't a lot in this article that struck me as dated or irrelevant but I did notice a few times that questions posed were either loaded or provided a simplistic version of the opposing viewpoint. For example, when discussing the consequences of our beliefs, one of the questions posed was, "... which of your current beliefs are the result of outside forces over which you have no control, and which beliefs are merely rationalizations masking an unwillingness to risk the difficulties and/or the possible displeasure of others that would result from their implementation?"(p.111). This struck me because I interpreted this as implying teachers who are more routine as opposed to reflective are doing so to avoid consequences or are lying to themselves. I believe this is a overly simplistic view and that some teachers who have developed a structure and choose to teach this way are doing so because they believe it's what's best for the students, possibly because that was the way they were taught. I don't agree with remaining rigid when it comes to my teaching method and I definitely would like to strive to become a reflective teacher. However, I also believe there is a danger in misrepresenting the opposing side and that arrogance isn't going to help change the view of those who believe in their rigid method.

Some useful reminders and pieces of advice in Grant & Zeichner's article include having a clear idea of what our priorities as individual teacher candidates are, focusing on information within the program that is applicable to those priorities, and to actively participate in our practicum by asking questions. I think all of these points are connected because having a clear idea of what is important to us will help us ask the right questions and avoid becoming overwhelmed with the abundance of information we will be exposed to throughout the program. Another interesting point they made was to consider that there are always alternatives to whatever we are being told. The idea that we should be aware that there are things being omitted, although obvious, is a good reminder that we have that choice to explore alternative routes should we disagree with a certain methodology we are being taught, or if we encounter trouble when we enter the workforce.

Exit Slip #1: Frank McCourt Teacher Inquiry

It was really interesting to learn about Frank McCourt in today's class. One of the ideas he mentioned that really resonated with me was to not put on an act with the students because they can easily tell. This is something I've struggled with during tutoring or working as an E.A. Students definitely don't respond well when they think they are being fooled or tricked so I understand and have experienced how attempting to put on a "mask" is a losing battle. I'm still trying to find the balance between discipline and going with the flow while teaching so I think this will be an ongoing process for me.

Another thought that stemmed out of our discussion of Frank McCourt was exploring different ways of teaching. I was reminded of a teacher I worked with who said she often has to gauge the class before deciding how to teach them. For example, some students are more hands on learners in groups while others prefer to work quietly by themselves. Of course this is true in any classroom on an individual basis, but looking at the majority really helped this teacher shape her lessons. In this way, I don't think teachers have to choose one way of teaching and stick to it for their entire career or over all of their classes; it's more of a back and forth between the class and the teacher, much like how Frank McCourt would join in his class's resistance to a book.

Hello!

 I'm looking forward to diving into our Inquiry class.