Sep. 23, 2026: Battleground Schools

Battleground Schools was extremely thought-provoking as I stopped to consider my positionality for Mathematics. In terms of learning, I would advocate for a progressive approach. In doing so, students become more connected to the material, thereby enriching their education. However, upon considerable introspection, I believe my teaching style reflects more conservative methodologies. This stems from my instructors showcasing Mathematics as purely procedural, so I mirrored these algorithms when teaching as well. I began to consider how to become progressive in teaching, because I now see my overreliance for my students to shift to relational learning themselves, depriving them of deeper education. I do harbour a genuine passion for Mathematics, thus, I hope that by sincerely conveying these sentiments to my classroom, I can begin to diverge from conservative ways of teaching and instead focus on what makes it captivating.

By demonstrating my enthusiasm for Mathematics, I hope to change others’ disdain towards it. Battleground Schools mentions how the discontent centered around Mathematics required a reform of its teachings, and this intrigued me. I was always aware of the resentment held for Mathematics, so this made me question how I can enlighten my students, and destigmatize the study. It begins with showing copious amounts of fascination. To get others to care, one must show why they care to begin with. Otherwise, if students see that a teacher is disinterested, there is no motivation from both parties, and the course content loses relevance. For students to enjoy Mathematics, a teacher must love Mathematics, and only then will they start to question it.

Another compelling stance from Battleground Schools was its references to the skill level of the teachers themselves. During the three Mathematical revolutions, some of the teachers were not extremely versed in their practices, and I thoroughly empathized with this. This revelation caused me to question what constitutes a good teacher. Veritably, a well-informed teacher does not equate to an effective educator, as it does not translate to how they successfully guide their students. Most definitely, a certain level of fluency is required, or else this results in students lacking confidence in their mentor. Nonetheless, perfection should never be the primary objective, because flawlessness is not why students are here to learn. If students solely wanted excellence, AI would be their outlet. Therefore, as I also become a teacher with flaws, I want to demonstrate for my students why they should care for Mathematics instead.

EDCP 342 Group Project

Group members: Pla Sey, Leo Lee, Jarrad Fjelstad. The art piece is Little Wire Quadrics by Amanda Taylor Lipnicki.

 We first needed to figure out what materials we needed. Rebuilding the pieces using a wire base felt obvious, but instead of copper wire, we used aluminum wire as we thought it would be easier to manipulate and solidify. To connect pieces together, we used magnets and silicon tape. It still took some time to get used to the materials:

Pla thought of interesting ways to spin and form the wire:

Leo eventually managed to create a hyperboloid:

Then we quickly followed that with a paraboloid and cone:

We had to pay close attention to the orientation and position of the magnets:

Though small, the magnets were powerful, and it was a challenge keeping them separated for use:

Taping tiny magnets to wire was tedious and often ineffective, so we abandoned them and decided to try just using the tape:

The tape was sticky enough for the pieces to hang together.

At this point, we also discovered that none of us knew how to knit or crochet, so we decided for a more minimalist presentation, with the pieces’ frames visible.

The pieces starting taking recognizable form: 

The paraboloid-in-pieces takes its final form:

As does the saddle:

For the interactive part of a project, we are planning on presenting the pure-wire replicas and asking students to see if they can identify the functions that create the particular 3D graphs, either as one-variable functions (for cross-sections) or two-variables.

Then, we will present the 2D tape/magnet/wire pieces in a pile and see if students can rebuild the figures and identify the functions. 

Sep. 21, 2026: What is meant by 'curriculum'?

Elliot Eisner’s article “The Three Curricula That All Schools Teach,” points to a thought-provoking argument about what is simply taught out of habit in academia. I have learned in my LLED 366 class that many schools repeat lessons and reuse books over the years because of financial budgeting. Until reading Eisener’s article, I never stopped to realize how this is reflected in STEM. He highlights how STEM is valued more over arts, and this was a perspective I agreed with as I experienced how STEM was expectationally harsher. However, when further reflecting on my biases, I began to realize how disproportionate the focus on STEM really is compared to arts. In truth, STEM is habitually seen as more difficult due to there being no other academic contenders. This is not to argue that arts have the potential to be more challenging, but it reinforces the idea that education neglects creativity in comparison to metrics. As schools prioritize numerical results, it takes away from the thinking that goes into the arts, and this is alarming as it actively prevents students from being nurtured multimodally.

Eisener also alludes to the concept of focusing on not just what schools are teaching, but also what they are not teaching. More precisely, educational systems implicitly lead students to conform to external expectations. With academic achievement being a focal point in schooling, there is a strong inclination for students to chase after metrics instead of looking towards their own passions. This stood out to me too, as I find it peculiar that there are views that certain institutions provide more valuable education than others, when they all inherently provide similar content. While I do think it is beneficial that students get the most out of their learning, and have an active goal to strive for, I also see how misleading and harmful these convictions can be if not accomplished. Instead, I believe there should be an increased attention on multimodal learning, such as through indigenous ways of teaching. 

When connecting Eisner’s ideas to the mandated BC Provincial Curriculum, he presents an idea that course subjects were menu items of sorts. This metaphor interested me, as much like a menu there are limited options. The student is presented with what seems like free will in their education, but they are really only being allowed to choose from what is available. By extending this notion, it follows that students are not truly products of teachers, but are instead the projected expectations put on teachers. This observation is striking, as it elucidates to the possibility that students are not truly being shaped by the content they learn. In essence, while students are still learning, due to the mandated BC Provincial Curriculum, Eisener demonstrates that this process is more akin to senseless replication.

Sep 16, 2026: Least/Favourite Mathematics Teacher

My least favourite Mathematics teacher was strictly a textbook teacher. The school’s textbook was the only taught modality for course material, and it was taught verbatim. There was no connection between the students and the teacher, and it felt as if the same lessons would have been learnt if read independently. Nevertheless, the tests’ questions remained unpredictable. While it covered the same units, the questions extended to concepts that were never before seen in class. This was extremely stressful as a student, as it felt as though the expectation was to possess a relational understanding of the material, despite only being presented with it in an instrumental manner. This made me realize that when becoming a teacher, I never want my students to be surprised during exams. While I may not be able to fully control if they are able to extend their instrumental understandings to relational, I want to present as much variance in content as possible so that they can always be prepared. Overall, in my experience with my least favourite Mathematics teacher, there was a general disconnect felt between the students, the lessons, and coursework, resulting in a strenuous academic experience. 

My favourite Mathematics teacher was a teacher assistant, so we shall call them TA. As a student, I am particularly appreciative towards the structure and connective efforts put forth by my teachers. TA followed a consistent routine for every tutorial. They first reminded us of the class material, followed by emphasizing which aspects should be focused on, and even curated relevant examples for our homework. Moreover, TA was extremely respectful and direct with us. One particular lesson, TA’s asked “What’s the most important part of a question?” Trying to exemplify the attitude of a model student, I replied “Understanding what exactly it’s asking of us?” Unfortunately, I was incorrect and the proper response was “The answer.” Though this was very blunt, I appreciated how simple TA broke everything down for us. “The answer” did not imply that the process was irrelevant. It was a reminder that there is an end goal to each question, and that one should actively work towards it. This mindset reconceptualized how I continued to solve Mathematic problems. Although it was something I intrinsically knew, actually hearing it was an imperative piece of advice that helped me experiment with what was being taught, and I felt reassured in doing so.

As I become a teacher, I want to learn how to create meaningful connections through constant encouragement, and show my students that their journey through academia will not be linear. As I grow into becoming a teacher, I would like them to understand that I too was a student, and am empathetic towards their growth as learners. I want to demonstrate compassion and take the focus off formulaic replication, fostering inquisition instead. In doing so, I hope they can truly connect with the material instead, and not be encumbered with exceeding academic expectations. In essence, if done correctly, I would have been a teacher who was able to impart lessons that my students can carry with them past a single semester, and maybe these lessons could even extend beyond academia.

Sep 16, 2026: Locker Problem

Hello Everyone,

First I started with drawing out the problem to see if I noticed any patterns.

Figure 1

Figure 2

The first thing I noticed is that locker #1 will forever remain closed because no other students will touch it. I then applied this same logic to recognize that lockers 2, 3, 4, and 5 will never have their state changed moving forward with the other students.

After I realized that lockers do not have a change in state after they have been passed, I considered prime numbers. Prime numbered lockers will only be touched by Student 1 and itself. Hence, each locker is first closed by Student #1, and is then reopened by their respective numbered student.

Therefore, I was able to conclude that thus far, locker 1 will be closed, and all prime numbered lockers will be open.

The next objective I wanted to consider was how odd and even numbers were affected.

Figure 3

I considered 6 because I already saw that 4 finished closed, so I believed perhaps even numbers finished closed. Unfortunately, this did not yield any helpful results. Moreover, I was able to further infer that odd numbers would not particularly yield much of a different outcome as well.

However, it was this conjecture that brought my attention to a number’s factors.

Figure 4

I noticed that numbers that had an even number of factors finished open. This led me to my next theory: lockers with an even numbers of factors will finish open, and lockers with an odd number of factors will finish closed.

To test this, I arbitrarily chose numbers 8, 12, and 16.

By listing their factors, I indeed did confirm that lockers with an even numbers of factors finished open, and lockers with an odd number of factors finished closed.

Furthermore, as each locker will only be touched by its factors, it logically follows that if touched an even number of times, it will retain its starting state, (open,) and the opposite if touched an odd number of times, (closed.)

Therefore,  I conclude that my answer for the Locker Problem is: all lockers with an even numbers of factors will be open, and all lockers with an odd number of factors will be closed. As the question does not ask for a specific amount of lockers which are opened or closed, we are done.

Sep 14, 2026: Richard R. Skemp

Richard R. Skemp’s Relational Understanding and Instrumental Understanding argument for relational understanding over instrumental understanding is extremely compelling, and is a focus I intend to implement in my own classroom. There is a common misconception that exceptional grades are equivalent to understanding, and that memorization is identical to learning (Skemp 4). For as long as I have worked within a classroom, this has been a recurring issue I longed to resolve. However, as instrumental understanding is heavily ingrained into BC schools’ curriculums, it is nearly impossible to pivot towards a relational approach (Skemp 11). To combat this, as a future Mathematics teacher, I plan to create pre-lesson packages for my students, which will include logical explanations to example questions. The packages will serve as a soft introduction to course material, which could spark sincere curiosity. Additionally, should my students have further questions, they may bring them to the lesson as well, thereby leading to relational understanding.

As excelling in grades is seen as the overarching standard, many students find instrumental understanding easier for their learning, and feel compelled towards it for both an easy and reliable strategy (Skemp 8). Though I do not agree that the ends justify the means, I would not want to go against my students’ ways of learning. Everyone learns at a different pace and by different means, and my goal would be to find a middle ground to support them. To lead them towards relational understanding, I would ask my students to participate in answering classroom example questions. When trying to explain concepts, one finds oneself having to organize their thoughts in such a way that becomes most comprehensive to others. In doing so, this organically leads to relational understanding. In essence, my goal is to make my students confident in their learning, and by implementing these strategies, relational understanding becomes the catalyst that enriches their education.

Hello World

 Hello Friends !

Happy first day of class ^ - ^

I am forward to working with everyone. Thank you all for your support throughout the semester.

Nailong from the Richmond Night Market