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.

Exit Slip #5: Response to Embodying Math/Science Discussion

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One of the things that struck me from the discussion posts was how one group pointed to the scale of an octave being logarithmic. We had actually used logarithms as an example of an area of math that would be hard to connect to crafts/activities because of its abstract nature but it was awesome to see that another group had that answer for us! 

I also liked that a group mentioned that reflection is an important factor of implementing activities and making them meaningful. I think the same can be said about abstract learning. It would be useful to have students reflect on their learning to help them have a real sense of how much it is that they actually know and what parts they need to work on or ask for help with. I've noticed that a lot of students immediately panic and say things like, "I don't know what's going on! I just suck at math," when in reality, I've seen their work and they're almost there. Adding moments of reflection would help students from getting overwhelmed and also maybe notice some patterns in their learning (e.g. the days they're not understanding the concept may be attributed to the fact they were up until 3 a.m. the night before).

Entrance Slip # 4: Birch Bark Biting

Image source: http://www.isuma.tv/aboriginal-perspectives/rosella-carney-birch-bark-biting-photos

I think involving the body/other senses in teaching math is a wonderful idea. While reading about birch bark biting, I tried to compare it to my experience with learning symmetry, transformations, and proportions. While I mostly dealt with graphs, colouring in boxes, or cutting out shapes and moving them around, they were all actions done on something separate from me. Birch bark biting would require creating patterns through a different medium. That in itself would likely make a larger impression on students, which is then amplified by using different senses. While you do touch the paper and move shapes if they're cut out, holding the bark and folding it would be a stronger use of touch because bark feels more tangible and has a different texture than paper. Additionally, using teeth to bite into the bark makes use of taste senses and has an additional variable in terms of how hard you bite into the bark. Birch bark biting is also an Indigenous activity which is tied to the culture and practices, so the activity itself is more meaningful in general (not to mention beautiful). 

I thought it was interesting that through working on this activity, students started by creating shapes without a clear goal in mind but slowly began developing their own ideas about what kind of shapes they wanted to create. This in turn meant they started developing their skills in symmetry, transformations, and proportions through hypotheses, experimentation, and logical thought based on their findings. I believe this is proof that sensory activities like these connect students with the concepts in a stronger and more meaningful way. I recall a lesson on waves in physics where we had to physically move and imitate the motion of a wave in order to complete an experiment. In this way, we were embodying and experiencing the subject instead of learning about it outside of ourselves. Another activity in which we used different senses was in Hindi class. We were learning how to pronounce a certain line of letters and it required us to move our tongues further back and make them touch the tops of our mouths. To ensure we did this correctly, our professor made us wash/sanitize our hands, and then physically push our tongues with our fingers to the proper spot. Because of this activity, I am much more aware of the way I pronounce words requiring those letters and pronounce them with a higher rate of accuracy. This made me wonder about muscle memory. Do sensory activities stay with us more because our bodies are remembering the feeling of going through that motion? Or is it more to do with the fact that activities break classroom routine and are therefore more memorable?

Exit Slip #4: Discussion questions for Renert article

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I think there were a lot of useful and thought-provoking discussions in our class today. It was interesting to see how there seem to be differences of opinions emerging from the topic of sustainability and how it relates to the classroom. Some thought it was vital to make that a major focus, or at least that bringing deeper real life examples should be a priority. Others believed it was an important topic but maybe not necessarily a huge focus for a math classroom and should maybe be introduced as a mini lesson, for example. One comment I found particularly compelling was that someone in the group chat said there is a place for escapist art and also a place for social commentary art and that they believe it's the same case for math. I thought that was an interesting thought - that we don't have to pick one or the other.

Another idea that I would like to remember emerged from our breakout group's discussion of learning with students. While I was reading the article, that thought scared me because I thought I would be too inexperienced to handle it (which will probably be true for the initial years). However, as we discussed potential strategies to handle this, the idea of exit slips or a question box was one I really liked. Engaging the students by covering material they want to know about as well as showing them how they can get their answers through research and resources they might not have encountered would likely help their learning in general. It would also help the transition to future math activities with more open-ended answers that required them to search harder if they were continuously exposed to that research process throughout the course.