Final 450 Course Reflection

Chronologically, this blog post was written last. If you would like to read the previous two, they are found through these links:

• EDCP 342 reflection
• EDCP 442 reflection

In any case, let's get started! Bullet points, one last time. I'd be lying for sure if I said I wasn't feeling sentimental, considering that these were some of the most densely packed 13 weeks of being with the same group of amazing people.

• I found this very funny, considering that 1) I ended up having a LOT to say, and 2) this was something I said at the beginning of each of my blogs. Little did I know I would be the biggest rambler on this side of the math cohort, possibly within the history of UBC math cohorts who have had to make reflective posts on blogger.com.
  
  
  
  
  Sometimes I look at the Earnings page of my Blogger dashboard and wonder if I could legitimately make a living as a blogger. That I can't really say for sure, but I think I've been particularly reflective enough such that I could do something about it (haha).
  
  
• After having just read the reflective teacher paper response from September, I have to say this regarding all 3 of the courses: there's a cuteness that I'm gazing at in this mirror to the past. I distinctly remember the head swirling sensation that I felt during the beginning of the semester, and even now it's sort of coming back. This program has been a series of internal transformations, all catalyzed by my inherent tendency to reflect. I'd go as far to say that the reflections are automatic; during the early weeks of this program, I reflected so so much. (Evidently; it does make my job a bit harder right now having to reread everything... but I feel like I was a pretty interesting writer. Patting myself on the back here.) Especially in this course called Inquiry, there were countless reflections that, while required for the course, were a way to navigate the various activities and other contents we were engaging with in class.
  
  
• On the note of engaging with activities and contents through reflective posts, I did find that to be an interesting bookend to this whole reflective teacher thing that I personally felt attuned to. One of my "criticisms" for this course for the longest time has been that the class felt aimless up until the inquiry project. Perhaps it was because I didn't exactly know how to define inquiry-based learning despite probably being told at some point in September, but perhaps there's a cute design of this course at play here where inquisitive thinking would allow one to reach a point where they understand the point of inquiry. Quite circular, but even circles are beautiful mathematical objects. Wow! I did not think I'd get that poetic here, but this course and others have been all about poetry. The clever design continues to persist, so that's why I put quotes around the word "criticisms". But I digress. Despite my tangent just now, it would be nice to have a bit more clarity on the grand-scheme-of-things purposes of the activities we were doing; looking back, we did a lot of garden-based learning for the first several weeks, we weaved with plants that we snipped up, pulled thistles, learned about the arts being integrated with mathematics and so on. Each of them felt like they had a localized purpose -- blog posts such as the one where I snipped around at home with strings and threads read off as interested and almost flow-like, but didn't really go into the overarching theme of this course. I did find myself being confused and asking the age-old question that every teenager asks at some point in a mathematics class: "Why are we doing this?" At least that's how I felt, but the design of the course with all its reflections was an interesting way to get all of us to navigate this confusion, which in itself manifests as questioning and realization -- inquiry. So after writing this bullet point, I don't know what an optimal plan would be. But given the type of people entering this program, I'm sure they would benefit from the structure of 450 that I went through as is.
  
  
• Minor tack-on to this already long point: re-reading my past blog posts, I think it would be worthwhile to make clear how everything fits into the fabric of this course. For me, there was a hesitance for a lot of these class activities simply because I didn't know why things were happening, so some scaffolding would have gone a long way to put not just myself but also future students in the right mindset. (I remember around the middle of the semester explaining all the courses I was doing to my high school friends, and this course was the only one I couldn't really give a clear cut, summative description for.)
  
  
• In contrast the long bullet point about this course feeling hard to identify its aim, I did like some of the conceptual tools we were given. Mathematical terminology and false dichotomies were great in particular, given how often they came up in my conversations with people later in the program. While I don't have much to comment on specifically, I did like the little activity I drew out with the prhombuses as well as my whole spiel about false dichotomies, dichotomies in general, scales between values, spectra, and extending it to entire intersectionalities. Those were certainly some of my stronger blog posts, at least in terms of how interesting I found them to be.
  
  
• Very short bullet point, but I do appreciate having this record of reflections. I was originally hesitant on the whole blog format, but it nice to have everything just laid out bare for future reference; one of my blog posts goes into possible ideas for mathematics in the garden that I pushed into the back of my mind. Stay strong with the blog format -- it's easy to learn, decently intuitive, and a creative way to reflect.
  
  
• Let's spend this last bullet point talking about the inquiry project.
• Going back to the long bullet point, I did feel *slightly* underprepared for this project. While the conceptualizations of this project happened just before the short-term practicum, I felt that the whole "locally I know the purpose of what we're doing, but globally I can't quite pinpoint what the point of this is in the grand scheme of EDUC 450" sentiment lingered in the back of my mind. While there were certainly valuable experiences in the artistic activities we did and the topics we thought about, it all felt very disconnected from the all-important inquiry project we did at the end.
  
  
• I did appreciate the timeline given for the inquiry project though, and found that the process was generally very supportive and well laid-out. Despite feeling disconnected from the rest of the course, I knew what I was supposed to be doing the entire way, from conceptualization to fruition. I also appreciated that we were prompted to have a topic idea before the short-term practicum; it was very clever design. On one hand, we could start thinking about our topics while observing and teaching in our classes. On the other hand, we could also change our minds completely (as I had, to my benefit) and have the freedom to reconsider. Definitely keep this timing aspect of the project for next time.
  
  
• As for my project, my thoughts are already on that reflective blog post and so I don't have much to add here. It's recent enough for everything to line up with what I currently think.
  
  

Once again, and one last time: thank you all for being such wonderful companions on this part of my journey to become a teacher. I'd like to thank my cohort for being one where I could confidently and eagerly brag to my friends and classmates from other cohorts about how great we have it, Susan for being a supportive professor who showed enthusiasm but also care for her students, and the guest speakers that imparted their wisdom in different domains. Although the course felt disconnected from itself at times, there were certainly hints of a global purpose behind it all. If I remember anything else, I'll add it to this blog post. Otherwise, I'll be signing off. See you all later!

Inquiry Project: Slides Link and Reflection

The link to the slides can be found here:

https://docs.google.com/presentation/d/1-CsogKJXyBRLs4MG0cZSvNfP0tNw1O5K1rr0gW_wv0c/edit?usp=sharing

The reflection will come after I present.

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(I will be typing this out in bullet points; I feel that after I've done it the past few times, it's just easier to get into the flow of things. Internally, there's a constraint that I place on myself where I need all the ideas to flow together, but bullet points alleviate that mental block.)

• In terms of the research of this project, I found it surprisingly difficult! I think that if I didn't email Peter Liljedahl as Susan recommended, I wouldn't have even had a starting point for my research. A lot of these initial confusions and lostness stemmed from the fact that I had no terminology to settle on; when describing what I wanted to look into, my school advisor used the phrase "individual helping". I came up with a bunch of different things, like "assistance", "one-on-one" and eventually settled on just my own definition of "small assistance" after much thought. The motivation for switching to "small" assistance instead of "one-on-one" or "individual" is because it's not always going to be one-on-one; with how rampant Thinking Classrooms and group work are (heck, even most of the articles I read had a group work lens), it is important to include them in a more encompassing term while maintaining the time-pressure environment that I wanted to focus on. Regardless, it was still my own terminology, which made finding articles surprisingly difficult. Most of my articles were found because of the word "intervention" that Peter Liljedahl identified, but I didn't want to just call it that because it ignores situations with explicit calls for help (while interventions mainly concern unprompted teacher insertion into students/groups working).
  
  
• The whole time I wanted to capture the whole "helping students during free work time" interaction, but honestly? I didn't think that it would be expandable to so much. I showed in the beginning and ending of my slides the cycle of these interactions: 1) task setting, 2) monitoring, 3) initiating, 4) during, 5) leaving, and it loops back to 2) until the work window ends. For the next inquiry class I want to explore further in the stages I did NOT cover, namely task setting and during. I'm not sure if this is strange or contrived, but during my research I actually found quite a bit of information on those phases, but I brushed them aside because I wanted to keep my scope as succinct as possible. Even with the phases I chose to cover, I found that my coverage ended up going for 30 minutes! If the presentation count on my day was any higher, I'm not sure if I could've gone through it all. On one hand, this is such a rich, analyzable topic despite being centered on such a small interaction. However, it does show that I need to work on my time management skills a bit more. (Though I will confess, I did not have enough time to condense what was on my slides. Mark Twain strikes again.)
  
  
• Speaking of the topic and including less information, the content on the slides was only about 60% of what I actually wrote down on my notes! I conducted extensive interviews with several teachers at my practicum school, wrote articulate notes when reading the literature, and even synthesized a few of my own conclusions. When I got home after my presentation, I thought that while it was nice to flesh out the purpose of small assistance, I missed a lot in terms of fleshing out the real-world of teaching. Yes, many of these purpose-related things were shown in the real world of teaching; for example, not giving the answer right away, body positioning and classroom setup, and additions to small assistance were very real-world sided, but I should've gone more into the practical aspects that play off the whole time-pressured environment that initially sparked this topic. Many of my points were things to make assistances richer and more productive for mathematical thinking and self-sufficiency, but not much of my presentation (aside from the additions section) went into alleviating the time issue. There were things that I observed in my practicum school for sure, but it felt like beyond the additions there were no clear-cut ways to juggle the time-pressure assistance-demanding environment.
  
  
• In terms of ways that I've seen other teachers dealing with the time issue, I've seen: putting up answers on the projector after a halfway point (according the teacher, it's because it still allows a process to happen, it just shifts the mathematical thinking process to a different focus), abruptly leaving after getting students to a certain point where the teacher thinks they are able to work autonomously, and... well, most of what I was going to say for this bullet point really pertains to the "additions". On that note though, the "additions" section was originally called "alternatives". However, I thought about it and realized that we still need to have these small assistances; they are a key part in formative assessment and supporting students as I had stated in my presentation, and they can exist IN ADDITION TO all the other strategies I listed near the end. So after writing this bullet point of my reflection, I have to say I feel better about the presentation that I offered to my classmates.
  
  
• Also, speaking of my classmates, I think that the presentation itself was quite successful! I got positive responses from some classmates and even some requests for my slides (which can be found at the top of this blog post), which gave me a warm fuzzy feeling inside. It made me feel like this topic was as helpful and rich as I had initially believed it to be. For some context, I was originally going to cover either one of the following topics: 1) addressing math phobia with progressive mathematics, and 2) how much teacher-like responsibilities and powers we can give to students. During my short 2-week practicum, I found myself reminded of a very frequent interaction, i.e. what I called "small assistance". In many points of my educational life, I've been on the teacher side of these interactions and felt like I was pretty good at it, but certainly not a master who figured out the art. Whether it was on a Discord server where students pinged helpers for assistance, classroom volunteering experiences, or circulating the classroom when I give students a problem to solve, these interactions were all over the place but no one has truly mastered the art -- in fact, it seemed like it was far from it! For complete beginners, their temptation is to just hand-hold the entire process. After some coaching, assisters don't do that much, but may still succumb to sticking to a student for too long and not juggling as well as they could. Et cetera.
  
  
• Then there was the activity. Ever since I had picked out this inquiry topic and was told that we needed an interactive activity, the activity I ended up doing was in the back of my mind the whole time. I needed a problem where I could differentiate teachers and students despite all of being in the same class... then it hit me: the STUCK problems from Chapter 11 of the Thinking Mathematically textbook that we all worked on in EDCP 342 were right there! Each of us could be teachers of our specific problems which we conquered before, but everyone else didn't. The best part: each of these problems presented a challenge to even our mathematical brains. Typing up the activity slides, I was very excited... though unfortunately, not all of my classmates were there (I think there were about 3 - 4 missing by the time I had to present, so I had to enlist the help of the very helpful Marina -- can't wait to work with her, she gave off a great first impression). Originally, I had four groups which would've given more material to work with during the slide deck presentation, but three ended up working out just fine. The three groups were particularly interesting because they all ended up being very unique situations:
  
  
• Saiya's problem was allegedly the easiest, and despite having 3 "students", they were all able to solve the task at hand. There were fun observations that made me smile knowingly during this! It turns out that the problem was on the easier side, because I did not expect the outcome. However, there is important value from this that I didn't even plan for: even when your students are done doing the task at hand, you should still give them a chance to explain what they did and their thought process... which didn't really happen. To Saiya's defense, the setup was more of a completion challenge than a genuine small assistance situation, but the scenery was still very plausible and so I feel these comments could be made during my presentation. From my observations, I saw high fives and simple checks to see if they got the right answers, but it would've been nice to see more ;)
  
  
• Jacob's problem looked like it was on the tougher side, but his group members cheated a little bit; they gathered together to solve the problem together despite the instructions saying to stay seated. I guess there was the loophole of the chairs being wheeled. Darn. In any case, Jacob was working hard to describe the situation, but even then it still seemed to my POV that there was a bit of a struggle going on. To Jacob's defense, there was a timer element that affected everyone's psyche a bit for this activity, since we couldn't necessarily defer to something like a FIT time tutorial or some other additional measure. That being said, this was another happy accident: the group work factor! The other groups were separated as I had intended, but because of this group, I was able to make a point by asking Jacob on his thoughts if his group was split up and he was unable to help both at the same time, which he admitted would've been harder. This is in line with what I observed in a Grade 8 class on my school visits; I noticed the teacher assisting two students sitting next to each other, and she was able to juggle between the two. The physical proximity makes it a lot easier to navigate the time-pressure while helping both students, as they were working on the same types of questions.
  
  
• Mark's problem was to be solved by Marina and Madison, who were both sitting on opposite sides of the room. It was interesting to see the points in my slides being set up through this group as well; Mark ended up spending more time helping Madison with a body orientation that resulted in Marina working on her own for a majority of the time. Since I found the body orientation point to be one of the most interesting results of my research, I felt vindicated by witnessing this. Jacob had an excuse because all his students were working next to each other, but I feel that if he had to juggle another student sitting far away it would be easy to give into an autopiloted body orientation, especially if the student was sitting in a spot such that Jacob would be facing the wall (whereas his other students were on the window-side of the room).
  
  
• To wrap this reflection up, I think the inquiry process was something that I could see myself getting into. However, I have to admit that it is quite a time-consuming process; not just because of the research and presentation preparation aspects, but also because if one gets REALLY into the research and topic like I did, they would end up wanting to use a lot of time to polish their work as much as possible. Hearing about what will be coming up in the next inquiry course made me feel at ease, but also curious. Considering how my inquiry topic is connected to something highly practical, and my possible extensions on the topic line up with the whole practical aspect that Marina was previewing us about, I could see myself learning a lot more about how to be a better assister in the classroom. Not only that, but the papers I looked at already covered some strategies regarding the During phase of these assistances; I plan to look deeper into some of the articles that I read (in addition to any new helpful literature) for my next inquiry stage. Saiya also reminded me of a book that's called "The Formative Five", which I will have to check out. 

This was quite a ramble, but I think I got all my thoughts out regarding this project. If I have anymore I will put them in a bullet list below, but expect the points to be shorter than the ones above. thank you besties.