Month: October 2022

A fairly simple representation of my learning network. To elaborate on some things: since the whiteboard I chose to work on was not very big, I grouped all my lectures, labs, assignments, textbooks & readings, etc together. I think the thing that maybe doesn’t show through on this map is the degree to which Youtube acts as an educational resource for me. Not only is Youtube my go-to for tutorials for how to solve specific questions in math or computer science that I cannot figure out, but I watch videos about cool applications of math when I’m cooking, or interesting algorithms in coding when I’m doing my laundry, or film analysis when I exercise, or political video essays when I’m unwinding and getting ready for bed. As a rule of thumb, if I have any downtime in a day, I spend it on Youtube learning new things about the subjects that I’m passionate about, and discovering new subjects for me to learn about later. I can then watch more videos about on Youtube to expand my understanding of these new subjects, or I can take to my Professor’s office hours to learn about, or read the Wikipedia article(s) to find other related fields that may interest me, as well as more formal in-depth resources, like scientific papers. 

Another observation of the map is that all roads seem to lead to the “practice” node at some point. This makes sense; I’m studying computer science and math, and the only way to get better at those things once you’ve grasped the concepts is to just practice applying them until you’ve got the hang of it. Something that surprised me is how little I talk to my peers about my classes; once I really thought about it I realized I talk with a peer about once a week per class. This is because I have some pre-existing friends in all the in-person classes I’m taking, so more often than not when I talk to them we tend to drift from discussing academics towards a more casual, “just-hanging-out” type of conversation, which I chose not to really count. When we do feel the need or the want to discuss the class seriously, we do that, but it’s not very often. My connections are relatively in ratio to how high the class is on my priority list, although its hard to see that in this format. I spend the most time in office hours with my CS prof, and very little with my health class prof, mostly just an email from time to time. Similarly, while I draw on the same resources (Youtube, the recommended textbook, lecture, office hours, etc) for most classes, I simply spend more time on certain classes, and thus the strength of the connection is stronger.

I chose to give this learning activity a shot because I wanted to explore how I have set up my learning network; since most of the nodes I have listed I am either a (mostly) inactive participant, like watching a video on Youtube or a lecture, or I am working (mostly) on my own, like in a lab, or doing an assignment, or practicing, I had an initial impression that my network was rather small. However, while I think that while the number of different overall nodes might be small, the value of the learning that I can glean from a well crafted lecture, or video, or textbook is quite high. This also attests to how valuable open learning is. I have Youtube as my primary learning resource for a reason, and that is because all the educational content that I view on Youtube is designed in a way that it is meant to be accessible and open, and focuses on the learning for the sake of the learning, with these new concepts or expanded knowledge bases meant to fit right in to the understanding of any given viewer. I don’t think I learned as much as I could have about my learning network, mostly on account of the limited size of my medium disallowing for an exceptionally expansive or detailed map, but I did gain some insight, as discussed above. If I were to do it again, I think I would try to zero in on the nitty gritty details, since I already have the “big picture” map here.

While I am currently trying to make my way into the computer science program, along the way I have had to and will have to take a plethora of mathematics classes. Math is a subject that I have very mixed feelings about, and the way in which math is taught and my experiences in learning math throughout my life will be the basis of this reflection.

I went to a charter school from grades four through nine, which for the unfamiliar reader is a school that has been given permission by the provincial government to deviate from the standard curriculum in a specific way, designated by that school’s charter (hence the name). The school I was lucky enough to spend my early education in was chartered by the concept of “inquisition based learning;” the students were encouraged to cover the learning outcomes described by the curriculum, but were offered vast arrays of different pathways that they could choose to reach the destination that is the understanding of the content. If a student wanted to construct a space shuttle in Kerbal Space Program, (a space flight simulator game in which players construct their own shuttles and program flight paths into them,) to demonstrate their understanding of both elementary physics like acceleration, gravity, mass, parabolic and rotational motion, etc they could. Students were able to practice argumentative writing by selecting a current event they felt passionate about and argue something relating to it. One of my friends once proved a probability model by writing code that modeled the event, letting the simulation run for a few million iterations, and showing that the resulting data fit the algebraic theory; this was submitted for grades as a final project for the probability unit of our math class.

Beyond the choices for the ways in which they were able to model their understanding, students were also given incredibly free reign over how to build that understanding. There was, of course, the standard lectures and lessons given to the students by the wonderful staff of the school, but beyond that, once the students were turned free to work in whatever method they chose, they were allowed and even encouraged to do everything that they could or wanted to do to build their understanding. Naturally, this resulted in a lot of students taking interest in others’ work, and so a highly collaborative space of learning emerged. I helped debug the code for the probability modeling I spoke of before, and that friend of mine helped to give my further insight to what the algebra that I had chosen to work with actually meant in reference to the real world. I got a deeper understanding of parabolic motion as it relates to rotational/periodic motion when my classmate explained what their space shuttle simulation was doing mathematically when it broke through escape velocity and made the change from parabolic motion of “rocket goes up, rocket falls down,” and into the periodic motion of orbit around the earth. It was not uncommon to see students teaching other students mini lessons, in which they might go over what the teacher had said in lecture 30 minutes earlier from another viewpoint, for a small collection of other students that hadn’t quite grasped the concept from the handful of examples and explanations from the structured content. If a teacher saw or overheard a particularly potent example or way of phrasing the material that we were supposed to be covering, they might briefly interrupt to class to have the student elaborate for the whole group, or might come interact with the smaller group to further build on what the students were discussing, and incorporate that method of explaining the concept into future material.

Furthermore, the teachers were also very keen on fostering that sense of inquiry in the students; I have had conversations with my math teacher about generalizing pythagorean theorem beyond the third dimension, into the fourth, fifth, nth, concepts that I am just starting to work with more formally now, in a 200 level math course; I have had conversations with my physics teacher about how electrical circuits can form logic gates; my english teacher personally lent me half a dozen books on philosophy ranging from aesthetics to existentialism to morality to logic; the list goes on. The teachers were always approachable about topics of interest for the students even if they were only remotely related to the material that the course covered.

As I’m sure the astute reader has now realized, this educational experience that I am describing is one that, whether intentionally or not, has an exceptionally contectivist coloured tint to it. Participants were encouraged to aggregate from all resources that they could find relevant, with the staff, books, online resources, other students, even video games as approachable avenues of knowledge to be considered. By giving students the ability to express their understanding in whatever way they most wish to, students are inherently incentivised to relate the material to their own understanding of the world and their previous experiences in it. In turn, students go on to create real, tangible artifacts of learning, ones that are far more personal and meaningful for them than any worksheet. And finally, the culture of collaboration had learners sharing their work at all stages of its development with the other students in the classes as well as the educators that were in charge of those classes, i.e. the entire spectrum of the network. Most importantly for the purposes of this post/essay/reflection/whatever you want to call it, let it be known that this method worked and worked WELL for both math and the sciences, subjects which in my later experience I have found people do not think that connectivist or other similar educational methods, are optimum for teaching.

However, once I left that school, things took a turn. In higher education, there is a problem with education for STEM. Most classes seem to be set up in a way that minimizes both real understanding, the building of that understanding, and most importantly, collaboration. They focus on weekly worksheets, highly weighted and stressful standardized tests, brief covering of the concepts to make room for exhaustive covering of poorly selected examples, in order to drill into students the methods that are applied to these concepts, but leave vague the concepts themselves. In university math in particular, it feels like the entire course is set up in a way where it is you, the student, versus the content, and there is no-one around to help you, and no second chances. This is disastrous for so many reasons. Firstly, and most importantly from a perspective of student understanding, this method does not actually grant any meaningful understanding to the students. Students are taught only to do math. They are taught how to recognize when the method that they have been drilled on in their weekly worksheets and copious examples in lecture is the correct method to apply from this standardized question, and then apply it unthinkingly. Any understanding of what the math is actually doing and why this method works, what  all the terms are referencing in the algebraic expansion that the student autopilots through is all coincidental at best. 

But unfortunately, with the way that the courses are currently planned out, and how assessment is done, this is really the best way to have the maximum number of people do the best in the course. Since the outcome of whether a student is said to have done well in a course or note is handled mostly by standardized tests, midterms and finals, and students only get one shot at these, then it makes sense that instructors do their best to teach students to pass these tests, rather than teach them the material. If the assessment were different, like midterms or finals were 2 day long take-homes, where students could have time to think about the questions, apply their understanding, and get feedback, (even if that feedback is just “yes, that’s right” or “no, try again”), then this method of teaching is no longer required, as the summative assessment wouldn’t be a question of if a student is able to rotely apply a method for solving a question that fits the pattern of other questions with which to apply this method, and doing that thirty times in an hour, but rather if they have the actual understanding to take a look at a problem, and apply the concepts to solve the problem, and do so iteratively until it works, more like how these things work in the real world. Worksheets could be done away with and replaced with collaborative assignments mean to actually build understanding of the concepts that the courses currently merely feign to teach, and instead of every single lecture and tutorial being about going through as many examples as can fit into the timeslot, we could have lectures that actually work to truly teach the concepts and build understanding in the students. Beyond that, a more project based approach, as implemented in my earlier schooling discussed above, could also be put to great use in terms of allowing for students to iterate on their knowledge and learn mastery in both understanding and applying the concepts.

I think that mathematics gets a bad rap among students not because it is truly a difficult or grueling subject, but rather that the chosen assessment dictates that its instruction makes it so. As my own personal experience attests, a collectivist style of education for mathematics and other STEM fields is certainly possible, and I would argue preferable to what we have now. In the real world, scientists often work as a team over an iterative process to design and implement a solution to a problem, or to gather and analyze data in meaningful ways. They are not on a 50-minute timer with their career relying on them being able to answer questions about calculations; nowadays, computers handle most of that. They are being tasked to apply the concepts, to know how to collect the data, which programs to apply to that data on the computer, and if they forget something like a formula, they can look it up in the blink of an eye on the internet. But what they cannot simply google or hand off to a piece of software is how to actually apply the concepts in new, innovative, or novel ways. While both are certainly important, in the modern world the ability to apply concepts outweighs the ability to do calculations. However, our current system teaches primarily the latter. With some changes to make the education more accurately reflect the needs of people living in a digitally connected world, with connectivist learning being an excellent model to lean on, I think that education in math could be overhauled into one that fits the modern era and gives students the conceptual tools and understanding that they need. 

Why I chose this reflection:

If it wasn’t obvious from my post already, I have strong feelings on the way that math is taught in higher ed, stemming from how wonderful I found it when I was experiencing it in a more connectivist model. In doing this learning activity, I developed my understanding of how connectivist models can work in more formalized, in person environments, as I hadn’t really considered that portion of my education as it relates to connectivism until writing this piece. As my learning profile mentions, I am an advocate of open learning, and I think that the current method of teaching mathematics is one that goes against the principles of education being collaborative and open for all students to engage in, since the current method of teaching mathematics can be quite painful, especially for students who may be neurodivergent and don’t do well in standardized test environments.