---
- To start this blog post off, I would say that the key underlying thing that this course taught me was less so what to teach, and more so how to describe what is being taught with terminology. Many of the concepts discussed in class for the "first" time are things that I've thought about and even discussed to some degree of depth before, but I lacked the linguistic abstractions to go any deeper. Some examples of these linguistic abstractions include: flow states and ability/challenge, relational vs. instrumental mathematics and understanding, Lockhart vs. non-Lockhart mathematics, conservative vs. progressive, and everything in between mathematics, the types of curricula, and arbitrary vs. necessary mathematics. For instance, of course I always had thoughts about things like what is being taught explicitly versus implicitly -- but having the language introduced to us to make sense of things and communicate our stances has proved to be very helpful, even in discussions with teachers in the real world. I remember bringing up the 3 curricula article during a chat about how much group work should be in a mathematics classroom (because one sub-discussion was how much should we concern ourselves with exposing students to group work when their other classes likely have it). The interesting thing is that with many of these teachers, they've read the same articles, so it puts me on the same discussion playing field as them.
- The next thing I want to talk about is the few puzzles that we were assigned to attempt and make blog posts for. Thinking Mathematically and being STUCK be thy name. Whether it was the locker problem, soup can problem, or the many problems in Chapter 11 of the Thinking Mathematically textbook, I appreciated the low-floor-high-ceiling aspects of these problems. If I could make one suggestion right here for future iterations of the course, it would be great to have a neatly identified list of these types of problems somewhere on the class blog or on a separate document file, etc. I find that question types like these are great to pose to students as a way to get them thinking mathematically in general without too much arbitrary knowledge required. While I admit if there's a catalogue it would be easy for our cohort and other teachers to just home into them and homogenize, the questions would still be great to have as a resource. After all, it's nice to step away from the regular explicit curriculum while still exercising those math muscles.
- As for the assignment balance, I feel like I'm not completely content with it. Sure, there was certainly value with having the mathematics art assignment in there -- however, because there was also a similar art assignment in the mathematics history course (admittedly, there were a few people in 342 but not 442), it felt like there was slightly too much time allocated towards the artistic side of the assignment balance overall when there could've been more practical aspects of the course baked in. By this, I mean that I preferred the assignments where we had to lesson and unit plan considering their practicality, and would've preferred them to be slightly earlier so that we could receive feedback sooner. The unit plan "in-class peer review" process could also be given more time; considering how much my group wanted to spend on their individual unit plans and their corresponding lesson plans, there was not enough time to get thorough feedback (most of the feedback done was of a general, structural and quick-fix nature; there wasn't enough time to go in-depth unless one asked their classmates outside of class time). I also feel that is important because while we've spent so much time peer-reviewing our non and curricular microteaching lessons (which is how I feel should be), the final unit-scope assignment missed out on this. Again, not to say that the artistic assignments were a waste of time -- far from it. If the assignment structure remained the same, I don't think it would be much of an issue. But it did strike me a bit strangely when I saw two courses with similar assignments.
- That being said, I felt that this course, 442, and 450 had something going right with the blog structure. While I was originally a Canvas believer (and I still kind of am, mainly because it's a bit easier to dive into the past without pressing "older posts" 3 times in a row), there is a bit of a simplicity with Blogger that makes it feel less formal and therefore easier to just get thoughts out on the board. As my reputation as a long blog post generator continues to establish itself (I can see it happening as I type this blog post out...), I have to say a large part of it came from just being allowed to ramble as long as possible. I wouldn't change the wording just because it's more scalable for grading purposes, but I found myself ignoring the whole "write 1-2 paragraphs" instruction relatively quickly. I appreciated having the guiding questions to narrow down my thoughts for many of the reflective blog posts, so that's something I would want to continue for future offerings of this course. On another hand, I think my classmates appreciated the generous minimum blog post requirements. It was nice to have expectations be oriented towards what things should be included in the posts.
- I will comment more on the garden in my EDUC 450 final course reflection, but very quickly: I have a relatively middling stance on having the garden be a key setting. It certainly has value for learning as another access point for students who may not benefit from a traditional classroom setting as much and I appreciated having a model to work off of should I teach in an outdoor garden, but I still think it should be incorporated in moderation. How I see it is that while the traditional classroom is like a basic carbs-veggies-proteins meal that you can always fall back on every day, the garden is more of a fancier restaurant meal that you'd treat yourself to once in a while. It is a richer experience, but I don't think it could be done every day especially for a diverse range of students, some of which may be strongly against the garden. Though I would say being in the garden every day had highlighted that disadvantage of constant garden visiting, ironically enough. (Though this is much harder to control, I think the sheer distance away from the rest of the campus also made it more difficult for a lot of my peers.)
This is only the first of my three end-of-course blog posts, so I won't say too much more here. I am feeling a bit sentimental though because I've made many strides in teaching through this course, and I feel that it has prepared me within the short 1-term timeframe for things like lesson and unit planning, alternative approaches to teaching mathematics and providing me the language to talk about mathematics education. The class tone was also a warm one that I feel allowed us to be the best cohort we could be; a large part of the successes and enjoyment of these courses is because of how comfortable I could be around my cohort; the social aspect was one that I would encourage fostering organically in future offerings of the course. Really promoting that we are all in this together and allowing us to have discussions about what we are learning are a few things that made it easier for my cohort to connect, and as a result I feel like I've learned so much.
