Trivium and Quadrivium

 “Of the seven liberal arts, the quadrivium comprised what we might call the scientific studies of the day” (p.265-266). This quote made me stop simply because quadrivium was grouped as one of the liberal arts. Given that the quadrivium is made up of hard science based subject areas, I found it very surprising that it was grouped as a liberal art. However, putting into perspective the time the quadrivium was defined, I can see how it would have been considered a liberal art as that field was definitely more prevalent during that time, and the support for ‘hard sciences’ was not as great as it is now. 

“As for the quadrivium, as the sciences are called, since they have little to attract in themselves and produce only a meager profit, most of the students neglect or omit them entirely” (p.270). This quote made me stop due to the reasoning behind students choosing to not continue their education in the sciences. I found this quote quite relatable as a science student myself. While I was completing my science degree, there was often talk amongst students and students not in the science faculty that would comment on the lack of profit that could come from the completion of a science degree, without at least one extra degree after your undergrad. However, I found that the students who truly loved science were not worried about profit at the end of their schooling! Again I have to put this quote in the context of the times, where science was just starting to make a rise.

A general view of the medieval universities would seem to indicate that at any given time, whatever arithmetic was known was taught”(p.273-274). Finally, this quote surprised me in making me realize that there was a time where whatever arithmetic was known it was taught. While the amount of mathematical advancements and new fields created since that time is very large, it is still incredible to think that all known math was taught and available for students to learn. Now we are learning all different fields of math, but I can’t imagine learning about all of the arithmetic that was ever known, during my university education. 

Numbers with Personality

In terms of Major’s paper, I would say that Ramanujan had a personal connection to numbers. Given what he said about positive integers, and Major’s paper I would assume Ramanujan has OLP as he is attributing personal characteristics to numbers.

I think the points Major brings up in her paper regarding number personality and the ways in which different people interpret numbers could be very interesting to introduce to high school students. I definitely think I would introduce aspects of this concept in the classroom when I thought it would add to the material being taught. For instance, when teaching the Pythagorean Theorem, I talk about how Pythagoras and his followers believed every number had a symbolic identity. I do think this topic of numbers with personality could be used as a good way to get students engaged and potentially help make connections to the way they think of and interpret numbers. Another way I may use these ideas in the classroom is creating an activity where students are asked to pick a number and describe or draw it to represent the personality they feel the number has. Additionally, I would most definitely introduce the idea of synaesthesia and OLP. One of my friends who is also a math teacher has synaesthesia, however she wasn’t aware she had it until someone brought it up one day as an adult, so I think it is an interesting note to make especially in a math class where students could be assigning personalities or colours to numbers.

I don't think numbers particularly have different personalities for me. However I do kind of think of odd numbers as harsher more set in stone numbers for some reason. That being said I have a very black and white thinking mind, so a number to me is a number and I have not typically thought of a number, month, letter or days of the week as anything other than what they are and what they are used for. However, I would say certain summer months vs winter months have different personalities for me just due to the weather and the activities I do during those months. I have always thought of the summer months as loud happy months, whereas the winter months I think of as quite quiet. Although, I have always had certain subjects associated with colours and I don’t have a reason for it that I am aware of. For instance I think of math as a very blue subject and I think of science as a green subject, and psychology as a red subject.

Assignment #1 - Personal Blog Reflection

Something I learned from the project was using imagery to explain math and especially a math formula that is quite foreign to students the first time they see it. As well, throughout the process of researching for this project I learned just how complex math history can be and how I should always examine the history of math past that of the person given credit for making the discovery. Finally, I learned how providing a brief history of a mathematical topic can help get students engaged in the lesson and provide context to the material they are learning as it often seems quite abstract to some students. 

After completing this project a takeaway I have is ensuring when I explain math history to my class that I take into account all potential contributors to the mathematical theorem or advancement. As well, always looking to see if others potentially from less recognized areas may have actually proved a theorem but not received credit. Additionally, I will use our classroom extension in my classroom when introducing the Pythagorean Theorem, to help students gain a deeper understanding of the formula and be able to see its use in more complex situations.

Dancing Euclidean Proofs

One stop that I had while reading this article was the discussion around learning involving perspective. I connected to the idea that as readers of mathematical proofs, we are completely responsible for understanding the proof, while being detached from the representation of the proof in words or pictures on the page. However, by dancing through the proof, they felt as if they were active agents making sense of the mathematical representation. I found this really interesting and something to think about as a future teacher, making it possible for students to make sense of the math they are learning in an active way. 

Another stop that I had was realizing the cross disciplinary opportunities that come with math if we as teachers can think outside of the box. As was demonstrated by dancing, there are plenty of other cross disciplinary ideas such as art, sports and so on that could be used in a classroom setting to demonstrate different math concepts, allowing students to form their own connections to it and actively partake in their learning. 

Finally, by reading this article I was reminded of the importance of learning from the land regardless of the subject area. In math I think we can often forget of ways to extend our mathematical learning out of the classroom. But going outside and being active or observing our surroundings is a great way to make real life connections to math and allows students to make connections to their surroundings through math and also apply what they learn to situations and things they see during their everyday life.