Course Reflection

 

I didn't know what to expect when I first entered this course, I had reservations about 'math history' and honestly thought it would be a boring class. I think mainly because the portrayal of history throughout my education career has been one of boring facts and learning about when a historical figure was born - I really thought this class would just be looking into the life of famous mathematicians. Boy howdy was I wrong about that! From the very first reading 'Why teach math history?' my ideology changed. To me, math history was just 'when was Rene Descartes born? Where was he born? What did he do? Ok moving on...". That first reading made me realize there's more to math history than just the historical figures. There's layers of representation, inclusion, exclusion, inaccuracies, and techniques that deserve deeper dives into. It also really set the tone of the entire course and gave purpose to all the readings and assignments we were to complete throughout the course. I think my favourite reading was the one on if Pythagoras was Chinese and the Eye of Horus. The first paper opened my eyes about how representation can be important for young students, and also how Eurocentric our education system is on the west. The Eye of Horus was exciting because it allowed me to explore; I absolutely love myths and stories about ancient gods - tying it in with math was extremely fun and I think can be used in the classroom. 

I think I've also learnt that history can be used to build on current ideas. How can we use our ideas of fractions to solve ancient Egyptian problems? How did they solve them? How were they able to build such fantastical structures or have functioning societies? They needed math! 

In terms of potential changes to the course, I wonder if changing the name of the course could be an option -- perhaps it's a pessimistic viewpoint, but some students may be unenthusiastic when initially thinking about 'history of mathematics'. Having a different name like 'Exploration of ancient math puzzles' sounds interesting. I'm not really sure if that's a good suggestion or not though (lol)! I think another potential change would be more doing. I think there were obvious constraints with COVID this year and everything being online, but I felt very disconnected (no pun intended) at times. Even if there were more mini assignments like creating our method of false position, or making our own 3x3 magic square in place of longer readings could be more engaging for students.

Overall, I had a blast with this course. I learned a lot about the history of math, but even more about myself and how this course can effectively enhance my pedagogy moving forward. I'm excited to take my knowledge in the classroom and I'm thankful to both Susan and Amanda for putting on such an enjoyable course. It was an absolutely crazy semester, but it was also one that filled me with optimism for the future. Have a wonderful holiday! 

Assignment 3 Reflection

 

One of the biggest takeaways from this assignment for myself was how important documentation has been for our exploration of different cultures and historical figures. Throughout this course we've learnt about historical mathematical inaccuracies that we've been told are true -- yet through dated documentation we're able to find the inaccuracies and debunk them. With the case of Polynesian star navigation, there is so much information, but very little exploration due to the wayfinding methods being passed down orally through generations. The techniques themselves though are extremely impressive; I have always been a fan of astronomy, and have been able to find star constellations to tell direction, but the ocean is a completely different ballpark. With the unpredictability of currents and waves, it's amazing how these explorers were able to navigate the sea with such precision and accuracy. It was also interesting to see the historical accuracies used in media today.

The movie Moana has a lot of cool moments that use star and wave navigation, both methods that were used by Polynesian islanders a thousand years ago. I think correct representation in mainstream media is extremely important for all audiences as it can allow people to connect or relate to the material in a stronger way.

In terms of the art piece -- I enjoyed collaborating with both Jacob and Zach. We had a few meetings about what they would write about in their poem and how I could incorporate it all into a single art piece. The collaboration aspect, as always, was enjoyable (although a lot of it was individualized work), but the art piece itself was fun. Growing up I never associated math with art, they always seemed like 2 separate classes that never crossed into one another. However, this class, as well as 342 have helped me understand that there are options, and they should be explored! Like the Polynesian islanders exploring the Pacific, I should explore the depths of math and art :)

Assignment 3 - Link to Drive

Drive

This drive should contain our poem, art piece, and a time lapse of making the art piece.

Mathematics of Medieval Islam

 "His book was the first Arabic arithmetic to be translated into Latin, and its influence on Western mathematics is illustrated by the derivation of the word algorithm." -- What I found very interesting about this point is in relation to what this class has been structured around: the dismantling of Euro-centric culture, and acknowledgement of others' accomplishments that are often looked over. This quote (and really this entire book) highlights the importance and impact that Hindu mathematics had not only on the eastern side of the world, but the western too. It is often passed over how a word like 'algorithm' or how decimal place value systems were created, and since we really only learn about ancient Greek mathematicians and philosophers (in western schools), it's easy for us to make the inference that ancient Greeks invented everything with mathematics. Instead, this quote shows us that the east was in some ways, much more influential and played a bigger hand in aiding the ancient Greeks. Hindu mathematics in some cases, was so advanced that we still use some of their systems to this day. It's unfortunate that we do not highlight these important findings in school. I think creating a way to teach about proper history of mathematics would open more doors for students to feel connected to the material.

"Another important work of 'Umar's was his Explanation of the Difficulties in the Postulates of Euclid, a work composed in 1077, two years before he presented his calendar reform...'Umar treats two extremely important questions in the foundations of geometry" -- The interesting thing about this is the idea of collaboration. Often times when we think about ancient times, we geo-lock philosophers and mathematicians to their born region. In my head at least, I just imagined the Greeks collaborating with other Greeks, the Chinese with the Chinese and so forth. I don't know why I never conceptualized the ideas of collaboration across borders, perhaps it's because it's hardly mentioned in school. Nonetheless, this quote invites collaboration, challenging one another, and working together to make sense of something that may be difficult to understand. In a classroom, tis could be like giving proofs and having students explain them as a group to me; collaborating and working together to explain the intricacies and difficulties. Collaboration is a key foundation of math (and in life), and should be encouraged for all students

My final point isn't an excerpt from the reading, but a general and overall thought I had that could be implemented in my mathematics classroom. Similar for our assignment 2, where each student looked up the history of a mathematical concept, I think a cool idea would be to have students look up the history of a famous mathematician. I think this would be eye-opening because most students would immediately think Greek mathematicians; there are only so many though, and they will be forced to discover new ones, such as the famous Hindu or Chinese mathematicians. This is a good way for them to see the world and how influential the east was. I think it would be a good inquiry project for a younger group, like grade 8's or 9's to have this as an introductory project. It invites them to think critically as well as keeping their minds open at the start of the year.

Assignment 3 - bibliography

 Jacob, Zach, and I will be doing a project on how Polynesian Islanders used the stars for navigation. We will be doing a poetry piece accompanied with a visual aid. Our draft reference list can be found below.

Akerblom, K. (1968). Astronomy and navigation in Polynesia and Micronesia. Stockholm: 

Ethnogratiska Museet. 

Bruce, L. 1976. Preliminary Study of Three Polynesian Sources for Celestial Navigation. In 

Micronesian and Polynesian Voyaging: Three Readings, 1-23. Miscellaneous Work Papers, 1976:1. Honolulu, Hawaii: Pacific Islands Studies Program, University of Hawaii. 

Coopersays, David. “Astro Navigation Demystified.” Astro Navigation Demystified. Accessed 

December 8, 2020. https://astronavigationdemystified.com/. 

Guedes, Carla Bento, and Duane W. Hamacher. “How Far They’ll Go: Moana Shows the Power of 

Polynesian Celestial Navigation.” The Conversation. Accessed December 8, 2020. http://theconversation.com/how-far-theyll-go-moana-shows-the-power-of-polynesian-celestial-navigation-72375 

TED-Ed. How Did Polynesian Wayfinders Navigate the Pacific Ocean? - Alan Tamayose and Shantell 

De Silva, 2017. https://www.youtube.com/watch?v=m8bDCaPhOek

Trivium & Quadrivium

"Logistic was practical and utilitarian, a study for children and slaves; logic was a liberal art, a study for free men" I stopped at this point it really showed the progression we've made in terms of who we allow education for. Let alone the prejudice against women and people of color in recent times, going back even further we education was even more exclusive and elitist, not allowing others to learn and having slaves. I know that the educational system isn't perfect, but we have made some good steps forwards in being more empathetic and inclusive. Even with post-secondary education, I think Canada has the right idea with subsidizing for their citizens, I compare it to the US where some students can't afford post-secondary school and cannot afford to get a degree. I hope that we can move into a world where education isn't discouraged because of pricing, but everyone can have an equitable shot of success, no matter their socio-economic background. We shouldn't discourage smart people from succeeding because of money.

 "towards the end of this period, the Hindu-Arabic number system was beginning to be known in Europe"  This caught my attention because it reminded me of my assignment I just recently completed. I hadn't learnt about the impact that Hindu-Arabic math had, especially on our decimal place-value system. It originated in the east and moved over to the west, yet in school we aren't taught that. We are just told what it is, and because so much of the curricula is taught from the perspective of ancient Greek philosophers and mathematicians, I just assumed it originated from there. This highlights the importance of teaching mathematical history as having an accurate account of history could inspire people of different race/ethnicities to feel properly represented.

"The arithmetic of the schools did not receive the wholehearted approbation of all the people" This quote made me stop because we were talking about medieval mathematics and yet this problem still persists today. Mathematics to some is seen just as computation, and doesn't have much depth to be explored into. I believe this starts from a place of math anxiety in common days, where people are turned away from mathematics at a young age and do not come back around to appreciate its beauty. This could also be because students haven't been properly taught math in a way that inspires creativity or inquiry. As we move forward with developing how we teach, we can hopefully inspire young math students to see how interesting and applicable it can be.

Numbers with Personality

 

 

To think that each of the 'positive integers was one of his personal friends' seems a little outlandish to me. My first thought was then 'are the negative numbers his enemies then?', which could lay into the personification of numbers moreover, but was strange to me nonetheless. I believe that the quote is seen as playful and more of a connection that the speaker has to the world, connecting him through various means such as numbers. The world is often surrounded by numbers and as we walk through the world we encounter numbers every day, to have them as your friend would be to see the beauty and positivity of numbers, having a positive relationship with them and appreciating them for all they do. 

I think that it would be a cool idea to bring into the classroom, perhaps towards a concept with exponents and large numbers or scales, as they're often hard to conceptualize. As someone with a wild and colorful imagination, perhaps we could use the sheer scale of a large number like a monster or golem and show creativity through that lens. For scale factors students can draw themselves and a monster overlain on them, and find the scale that would proportionally make their monster correct. For representing large numbers, we could perhaps give a large number a name or represent it by a drawing, and refer to it as that in future classes. I'm not entirely sure how I would bring in personifying numbers strictly as I don't completely know the benefit in it.

Personally I don't think numbers have personalities, although like the article mentioned, I have seen instances where people see numbers as lucky or unlucky. Specifically in Chinese culture the numbers 4 and 8 have significant meaning. In sports I've also seen people thinking numbers are lucky, or associating a trait to a certain number. In hockey a famous defenceman named Bobby Orr wore the #4, so naturally many young kids would wear that number to imitate him. In terms of months of the year, I think we could associate weather to personalities, with Winter being cold and a little dreary, but Summer being light, happy, and excited. There are also ties to astrological signs that many people believe in.