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.