Course Reflection

Overall, when looking back at all of my blogposts and the content we learned throughout this course, my main two takeaways revolve around the euro-centric view of mathematics we are taught in schools, as well as the reality of "humanity" behind mathematics. 

I really appreciated that this course was very holistic and took a less-euro centric approach of studying the history of mathematics. From our reading to if Pythagoras was Chinese to Islamic mathematicians, I really enjoyed learning about other cultures and how they have shaped our understanding of mathematics today. This theme was especially prevalent in my assignment 3 topic since I chose to look into an Indian mathematician, but nonetheless I thought this was an extremely important takeaway about this course. I am glad that we were given the opportunity to explore these perspectives, as this really helped shape my learning of math history in a more accurate way. I wish other history courses were taught this way, especially in high school, because I think this would foster a more inclusive environment of all cultures!

My second main takeaway is the important of mathematics to our heritage, and how studying the history of mathematics really brings out the humanity of math. From my experiences in BC public school, I had never really learned about mathematicians or any sort of mathematics history, so all of these topics were quite new to me. Throughout this course, I really understood the value of learning math history because it changed my perspective on mathematics and allowed me to view it in a much more dynamic way. Rather than seeing math as simply numbers, rules, and proofs, I now view it as an integral foundation to our progression as a society! I especially enjoyed our readings such as the "Numbers with Personality" of the Mayan numbers, and the Eye of Horus + Unit Fractions, because these pieces really made me think of how numbers can have such strong meanings on both a personal and cultural level. My ideas regarding the importance of math to different societies and civilizations has strongly progressed throughout this course, and I am very happy to have explored these topics. 

Overall, as a non-mathematics student, I thought this course was a really interesting way to view mathematics in a lively, intriguing way. I think this course is especially helpful for teacher candidates, and my only suggestion would be to continue including interactive and creative opportunities for teachers to strategize how they can make math more digestible and interesting for young students to learn. I really enjoyed assignment 3, so I think the addition of using more creative outlets in assignments 1 and 2 may make this course more impactful. Other than that, I really liked the structure of the course and would definitely recommend to future teacher candidates, as well as students in other faculties. Thanks for a great semester Susan and Amanda! 

Assignment 3 Reflection

 I am really glad Margot and I chose the history of Brahmagupta for our assignment 3 topic because it allowed us to explore a mathematician who is not commonly talked about! As I've mentioned numerous times throughout my blog posts, I really appreciate the fact that we get to explore mathematicians from different cultures and backgrounds, and trace the history of these ideas and how they came to where they are today. 

One of the most interesting things I found about Brahmagupta was that he had significant contributions in both astronomy and mathematics. This is something I discussed in my post about Islamic mathematicians as well, as many of them had made great achievements in astronomy as well and other fields such as geography and poetry. I had never realized how dynamic these individuals were, and I think it is really cool and important to give recognition to all of these accomplishments. 

Ancient India in general has significantly shaped our understanding of mathematics today, such as the hindu-arabic number system, the concept of zero and solutions for quadratic equations. These are such important foundations to mathematics therefore it was really fascinating to research Brahmagupta's participation in these findings. 

Overall, I really enjoyed assignment 3 as it gave us the opportunity to explore an interesting topic in a really creative way. I also really enjoyed seeing the other group's presentations, and I was really impressed by their art mediums! My peers in this class emulate my takeaways from the Indian/Islamic mathematicians - versatile individuals who are talented in drawing, poetry, and dancing, on top of mathematics! This project was a really fun way for everyone to engage in the culture and humanity behind mathematics, and served as great inspiration for future teachers to incorporate a similar activity in their own classroom. 

Mathematics of the Golden Age of Medieval Islam

 I found this reading very interesting because it shed light on a different perspective of mathematics that is not commonly talked about. I really appreciated that we were assigned this reading on Islamic mathematicians since they have made such remarkable contributions in a number of fields. 

One of the first things that really surprised me was Al-Khwarizmi's contribution to "...assist in the construction of a map of the known world...". We have talked about Al-Khwarizmi in class, but reading about how he achieved this using 3 different problems that combined both theory and practice was quite interesting. This map that showed the distribution of cities, islands and seas on the earth's surface is a significant achievement and an incredible legacy for Islamic society, so I found this fact really fascinating!

Another thing that really stood out to me was Al-Biruni's work on Indian society and culture. I found it really interesting that he did work in comparative religion between Islam and Hinduism, and had apparently reported these comparisons with a sense of honesty that isn't commonly found. I think this work especially intrigues me because I personally have ancestry tied to India, and was raised muslim, so the idea of this early work really fascinates me and I would love to read more into Al Biruni's findings in his work India.

The last thing that surprised me was that Umar al-Khayyami was mainly known as a poet outside of the Islamic world, despite his significant contributions to mathematics and astronomy. He had written great works on algebra, and conducted extensive work in astronomy which allowed him to propose and revise the calendar in use at the time (which in my opinion is a very significant contribution!)

It was really fascinating to read about all of these Islamic mathematicians, and one of my main takeaways is that these individuals were all very talented and well-versed in a number of disciplines. Not only were all of these individuals mathematicians, but they all had significant achievements in other fields such as geography, astronomy, and poetry. I think this would be enlightening for students to learn about so that they could get more exposure to different cultures achievements, and have a less euro-centric education. I think another interesting takeaway for students would be that the mathematicians were not "boring" individuals "obsessed with numbers" which may be a common misconception among students, but they actually interested in a number of captivating fields! These takeaways may add more humanity to mathematics from a student's perspective, and may make the subject appear less daunting! 

Assignment 3: History of Brahmagupta

 

For our project, Margot and I made a painting/drawing to convey Brahmagumpta's achievements and contributions to mathematics and science. Something we found particularly interesting was that Brahmagupta has made significant contributions to both astronomy and mathematics, therefore we wanted to creatively portray this in our chosen artwork. Thus, we decided to draw a portrait of Brahmagupta, and depict the background as the galaxy with stars and planets around it to incorporate his achievements related to astronomy. While we plan to briefly touch on this in our presentation, we find it fascinating that he contributed findings about the solar/lunar eclipse, the longitudes of the planets, and the conjunctions of the planets with each other as well as with fixed stars. The focus of our presentation will be on Brahmagupta's contributions to mathematics, and we will be highlighting the general linear equation, the general quadratic equation, the concept of the number zero, and his estimate of the length of the year (our fun fact about his astronomy work!). While Brahmagupta has made other significant contributions to mathematics, we will be focusing on the stated concepts for the purpose of our presentation, which is why we chose to only put those on our drawing. Here is a link to our prepared slides to view all of our content for our presentation!

link:  https://docs.google.com/presentation/d/1qZt8XmiocP6gPTl9JIvMU40ckoujaadoECoVCsESiRE/edit?usp=sharing

Assignment 3: History of Brahmagupta

 For our final project, Margot and I will be discussing the famous Indian mathematician Brahmagupta, and exploring his contributions to mathematics as well as science and astronomy. Our chosen artistic medium will be a painting. 

References:

Brahmagupta - Biography. (n.d.). Retrieved from https://mathshistory.st-andrews.ac.uk/Biographies/Brahmagupta/

Puttaswamy, T. K. (2012). Mathematical achievements of pre-modern Indian mathematicians. Chennai: Elsevier. doi: https://www.sciencedirect.com/book/9780123979131/mathematical-achievements-of-pre-modern-indian-mathematicians

Rare Book Society of India. (n.d.). Algebra with Arithmetic and Mensuration, with the Sanscrit. Retrieved from https://www.rarebooksocietyofindia.org/book_archive/196174216674_10152952839976675.pdf

Selin, H. (n.d.). Encyclopaedia of the history of science, technology, and medicine in non-western cultures. Retrieved from https://books.google.ca/books?id=raKRY3KQspsC&pg=PA162&redir_esc=y#v=onepage&q&f=false

10, N., Nachiket, 22, F. M., Author, F. M., 15, S., Swapnil, . . . Ranka, A. (2012, August 13). Brahmagupta. Retrieved from https://famous-mathematicians.com/brahmagupta/

Trivium and Quadtrivium

 This reading was very eye-opening and stimulating. One of the first things that jumped out at me was this idea of the liberal arts, "the very word 'liberal' implies that these arts belonged to the education of free men, not to the technological training of slaves." The Greeks wanted to ensure that free men would be contributing future members of society, and associated 6-8 different types of learning as essential to to their learning. One thing that is really stands out to me is how did these ancient scholars distinguish what is worthy of a free man? Why were technical skills, like medicine and architecture, looked down upon in those societies? I think this is especially interesting because I do think our society is quite the opposite now. For example, the BC high school curriculum was really focused on STEM careers, and primarily only had a variety of grade 12 class options for those in the math/science stream. I remember the whole curriculum changing in 2017 right after I graduated, where many arts and humanities classes were just introduced for grade 12 students, such as philosophy and genocide studies. Now, we can see this shift of accepting arts classes as "important", however this was not the common perception when I was in high school. 

Another thing I found interesting was that "the seven liberal arts were denounced by such Christian writers" due to the opposition of paganism, however this changed once Christianity became recognized on a more widespread basis than paganism. Once Christians did not view paganism as a danger anymore, they were then accepting of the pagan education system. I found this interesting because growing up in a western society, there is no intersectionality between religion and education, therefore I had forgotten how a difference in religion between two groups could have an impact on standardized education like this. 

One more thing that stuck out to me was that the "essential" nature of arithmetic was due to an "emphasis on the art of computation, especially the method of establishing the date of Easter." Again, it is really interesting to see this influence of religion on education. At the time, Christianity was dominant in European society, and therefore being able to compute the date of Easter was "essential" and "important". It appears that society will place emphasis on certain disciplines based on their needs at the time. Today, technology is arguably the focus of our society, and we can see this not only in our increasing use of technology, but also the increase of students choosing to study computer science in post-secondary to adapt to our society's changing needs. 

Overall, I do think education is strongly correlated with society's perceptions at the time, and this was a common theme in the article as the author discussed the different periods of mathematical development. 

Numbers with Personality

I found this reading to be very thought-provoking, and really made me think about my personification with numbers. For example, I really liked the poem at the end of the reading on the number eight, as octagons are the shape of a stop sign, which has many different connotations accompanying it. It was really interesting to read this personification of the power that eight can hold, and how everyone will automatically obey her rules because of this authority that she has. 

The quote "each of the positive integers was one of his personal friends" really connected with Major's paper on Mayan numbers, as she describes the personalities and visual representations associated with the Mayan numbers. These "head variants" were described in the article as an "unnecessary tool for writing numbers", and while this may be true, I do think that this connects back to previously discussed themes of  humanity and culture in mathematics. I really like this idea of looking at numbers as more than just a numerical notation, but associating values, traits, or an identity with it. I think this approach would be specifically useful in schools, especially at the primary age, where children can associate numbers with meaning, rather than an abstract digit. I can imagine that a 6 year old child would much rather associate the number 5 as a "motherly figure" and be able to use their imagination to illustrate different connotations, rather than just thinking of it as 5. This could be very useful for learning mathematics, as the concept may seem less daunting and abstract, and may even seem "fun" for students, as they can be creative with it! For example, students could create a story with the different numbers representing different characters, and therefore will have more positivity associated with numbers when using them in more difficult applications like algebra. 

I personally have never thought about associating numbers with personality, however this prompt does remind of anniversaries and special memories being associated with dates, which I previously discussed on my blog! In terms of days of the week, I definitely think I associate personality traits with different days. For example, Mondays are personified as hard-working and organized for me, since Mondays are the first day of my week where I usually tackle a lot of school work. Fridays are personified as fun, optimistic, and happy because of the saying "TGIF" as well as it being the end of the week. Sundays are characterized as relaxing and stress free. It's interesting because I have never thought about this before, but I do make these unconscious associations with the days of the week!