Math Art Project (Check-in)

 Topic: Women in computer science or a woman in computer science (Lovelace, Hopper, or Hamilton)  

Artistic Form: Interactive 3D display  

Reference List: 

• https://dl.acm.org/doi/abs/10.1145/543812.543853

• https://www.proquest.com/openview/698bc6cc298c3e4918e0f9de3ad2f461/1?pq-origsite=gscholar&cbl=37905

• https://ieeexplore.ieee.org/abstract/document/1702333?casa_token=Uj1sBm7PiQAAAAAA:TXoTNoCakL_UvDySV8qL9d4Jz2eE_GID4leOkT945mlkBH_I4nNBE629Q30rrQX25E5_UfjS

• https://dl.acm.org/doi/abs/10.1145/609784.609818

• https://dl.acm.org/doi/pdf/10.1145/129852.214846

• https://ieeexplore.ieee.org/abstract/document/4051189?casa_token=UQ-orSzi9DIAAAAA:IRE1Rgln3I4mxby5tUTaRqEizA3ws8-TswYnl7NuCOeJAlXUKss29E7CRrzr9rXsYVk5bFYY

Education in Medieval Europe

    The first quote that made me stop and think was “The very word ‘liberal’ implies that these arts belonged to the education of free men, not to the technological training of slaves” (Schrader, p.264). I was reminded of my privilege in receiving an education. I had assumed that liberal referred to free thought and not to people who are free. This is an interesting take to me because that kind of access to education is prevalent, to a lesser degree, in most countries around the world. Liberal arts education is available to you if you can afford it and are not overburdened by other responsibilities. I think it speaks to the inequity in our societies are continue to make higher education inaccessible. 

    The second quote that made me stop and think was “Those who did go on into law or medicine did so for profit” (Schrader, p.271). I find this quote rather amusing since growing up in a Chinese community, this was definitely a pervasive belief, to the point where parents only viewed school and education as a means for future profit. I have a lot of respect for people in law and medicine, but when I hear about dentists performing procedures that their patients don’t require, and billing the insurance companies, I can’t help but think that they’re grifters. Existing in a capitalist society makes it difficult for any to pursue education purely for the sake of education and knowledge and I wish that were not the case.  

    The third quote that made me stop and think was “There were no examinations in the modern sense of the term. The student had simply to swear that he had read the books prescribed and attended the lectures. To qualify for a degree, he was required to participate in public disputations, either defending a proposition or opposing one defended by another student” (Schrader, p.272). This brings up important questions regarding assessment. At some point, possibly when schooling became compulsory, the purpose of exams became weaponized as an accountability tool in addition to determining students’ understanding. What’s interesting is that the alternative to the exam seems like what could be considered a thesis defence. One of the benefits of a system like this includes allowing adequate time for students to think about ideas and synthesize something meaningful, showing a higher level of understanding according to Bloom’s Taxonomy. What I also find interesting is how this also adheres to the modern idea of authentic assessment, in particular the need to defend your stance. 

Schrader, D. V. (1967). THE ARITHMETIC OF THE MEDIEVAL UNIVERSITIES. The Mathematics Teacher, 60(3), 264–278. http://www.jstor.org/stable/27957550

Here's Looking at Euclid

    I believe that Edna St. Vincent Millay’s poem describes Euclid as an unparalleled genius who transcended the mediocrity of the general population to create something original; a new way of seeing the math world. The allegorical poem seems to compare Euclid to Jesus in that sense. In regards to Beauty, I think Millay is referring to it as something with great importance since she chooses to capitalize the B, making it a proper noun. She suggests that it’s subjective for everyone except for Euclid who is able to anatomize Beauty and see her bare. Euclid is able to see objective truth and does the world a service by showing Beauty to others. 

    I think Euclidean geometry has been so popular over the centuries partly due to how well 

organized and visual the math is in Euclid’s Elements and partly due to the mystery and intrigue behind Euclid. Euclidean geometry’s foundational building blocks only rely on five postulates, none of which are incredibly complicated. It starts with a point, line, and circle which makes it incredibly accessible for students starting out in math. The way that the book progresses, it becomes increasingly obvious how similar math is to art. It’s the construction of patterns and structures using basic building blocks. Euclid’s Elements is an exemplar of good mathematics that continues to inspire students. 

    My experience of learning Euclidean geometry has unfortunately not been as inspiring as my description above. I learned it mostly through lecture-style delivery. There was no discovery or creation. It focussed mostly on exercises that prepared us for a test. I was luckier than some of my peers because I had better short-term memory, at the time than others so I did well on tests, however, I would say that geometry was and still is one of my weaker areas in mathematics. The current BC curriculum gives teachers a lot more flexibility in how they teach, and I believe building a strong foundation of Euclidean geometry through exploration, discovery, and synthesis would be beneficial to students.

Embodying Mathematics

The first thing that made me stop and think was the concept of embodying mathematical proofs. My worldview is highly influenced by mathematics, but it has been more passive and focused on observations so it’s quite inspiring to see a more active approach to seeing people, math, and their connection to the world. Related to the first thing, the second thing that made me stop and think was the idea of human agents becoming the mathematics we do. I find the idea of instrumentalizing our bodies for the pursuit of math to be quite provocative. One does not simply do math, but they become math and become part of the canon of the development of mathematics. 

The dancing Euclidean proofs activity in class was quite interesting. Since we needed to choreograph the proof, there was additional care in deciding the sequence in which we would perform each step. This was evident when watching the other groups rehearse and perform. Our group decided to perform a rap, which similarly required careful sequencing. However, where other groups felt the math with their bodies, we engaged with the proof using another sense, hearing. 

This kind of activity may be helpful for mathematics learning and understanding mathematics history in a secondary school context such that it contextualizes the mathematics students are learning. Math is no longer decontextualized numbers on a page and becomes something that you experience or something you become. As one is doing and thinking about such an activity, it also provides students with some reprieve from worksheets and gives them an opportunity to bridge the empathy gap between themselves and the many contributors to mathematics. Regarding constraints and challenges, the biggest one that comes to mind is the cultural hegemony and the pervasive idea that mathematics is answering carefully designed questions. There will be pushback from parents and students who claim that we’re not teaching math or that it’s not rigorous enough. Another concern will be from your colleagues who question your practices and worry that you won’t cover enough content to adequately prepare students for further math courses.