Course Reflection

 We looked at Babylonian, Ancient Egyptian, Russian, Greek, Maya, Islamic and Indian Mathematics. One key takeaway for me in this course was recognizing the importance of integrating Math history into my classes because it shows students how Math is part of human history and people all around the word have made math discoveries - sometimes coming to similar discoveries without ever communicating. I think learning concepts in the context of how they were developed could be a great activity for students because it helps them see the inquiry process of math. Another key takeaway was that Math has been taught from a very euro-centric perspective and this means our disciplinary language can be racist in the sense that it highlights only the discoveries from white people. I didn't know about many of the mathematicians we learned about and how many concepts were developed before Greek mathematicians arrived at the ideas, yet we know them by the Greek names. I want to highlight a variety of mathematicians in my classroom. I had a lot of fun with my final project. I think I would have enjoyed spending more time looking at specific high school content and how we could incorporate math history into various lessons.

Final Project slides and reflection

 Slides

I really enjoyed making this project. My family is very musical and I actually got this idea from my dad, who recently wrote an article on tempered tuning and we talked about the harmonic series and how saying something is "harmonious" is connected to how harmonics sound good to us because they are in nature! I enjoyed researching the history and thought it was really cool how the name came from the musical connection. I think the Harmonic Series is such a great example of the beauty of Math and how it is all around us. I chose to make the art project the way I did because I thought watercolour would show the layering of the harmonics well. I was really happy with how it turned out and I really enjoyed painting again and trying to make colours that were just slightly different from the last. There is so much more Math that could be explored that is related to music.

Final Project proposal

 

Your topic: Harmonic Series 

Artistic format: painting and musical examples

Draft reference list: 

pg 271 Math through the Ages William P. Berlinghoff and Fernando Q. Gouvêa

https://math.libretexts.org/Bookshelves/Applied_Mathematics/The_Essence_of_Mathematics_Through_Elementary_Problems_(Borovik_and_Gardiner)/06%3A_Infinity_-_Recursion_Induction_Infinite_Descent/6.06%3A_The_harmonic_series

Kullman, D. E. (2001). What’s Harmonic about the Harmonic Series? The College Mathematics Journal, 32(3), 201–203. https://doi.org/10.2307/2687471

https://www.youtube.com/watch?v=Wx_kugSemfY

https://www.earmaster.com/music-theory-online/ch04/chapter-4-6.html

Bain, R. (2003). The harmonic series. The Harmonic Series (Overtone Series).

Islamic Mathematics

 I thought it was interesting to read about how Muhammad ibn Musa alKhwarizmi introduced the concept of decimal positioning notation. I wonder what led him to use a base 10 system.

I was also interested to read about how Islamic art played a big role in the development of geometry. I think this shows how creative math can be. Math can be both beautiful and practical as these designs at applications in creating borders and infinite designs.

Once again, I am led to reflect on how mathematics is a shared human history and a beautiful example of people building off of other ideas and furthering the field based from their personal and cultural knowledge. More concise geometrical constructions and proofs were developed by Ibn Sinān and Muslim mathematicians with inspiration from the Greeks. 

Maya numerals article response

I think the Taxicab Numbers story and Major's paper show that numbers can have various associations for different people. I thought it was interesting that her paper explained the frequency of those associations through linguistics and the reality that we use words to identify those numbers so different parts of a brain form connections. It is interesting to me the history of how different cultures "named" the numbers. This topic also made me think about the book Flatland and how shapes are given personality which is similar to this. In that book, the culture of the day is reflected in how women are only lines and seen as having not very much dimension of variance. I think everyone has some associations with certain numbers even if it is through math, it is still connecting different parts of our brain. 

I'm not sure I would introduce the idea of numbers having personalities to my class but I may introduce the history of how numbers were named depending on the context. I see the value in students making associations with different numbers and maybe in younger grades, drawing numbers with different personalities might be a great way to build some associations, but I don't think this would be a high school-level activity. 

I wouldn't say numbers have personalities for me but I do have associations with certain numbers or mental images for them. Similarly with the alphabet, days of the week or months, I don't have personalities connected to those but I do have mental images. For example, I always picture the months of the year laid out in a backwards C with sharp corners. January at the top left, May at the top right, August at the bottom right and December at the bottom left. Our brains are fascinating!

Trivium & Quadrivium

I found it interesting to read about the history of Christianity interacting with the liberal arts education. I think there is still a debate present in faith communities about what knowledge is important to learn and where it conflicts with the goals of different religious groups. Can faith and math go together? 

It seems that theoretical mathematics was an important study. The article mentions philosophical approaches to mathematical thinking. I think this is less of a value in our culture today and I wonder why. Perhaps society right now is more interested in making sure students have the practical skills they will need in a future profession than in developing that theoretical type of thinking.

So interesting to read about how there was a theology of numbers and numbers being gendered. I think that people today sometimes have special numbers or lucky numbers. I sometimes think there are "nice" numbers that have a kind of symmetry or pattern to them.

This article reminded me how in history we can see patterns of pendulum swinging. At one time theoretical knowledge, rhetoric and mystery might be valued and then there is a shift to very scientific knowledge or instrumental skill perhaps. I think this shows why historical understanding is important, even in mathematics. It shows us the different environments where mathematics was developed and how it was valued. 

Dancing Euclidean Proofs

I appreciated the creator's comment on how dancing through the proofs helps the participant understand the process step-by-step as opposed to looking at a completed proof. I think that doing something physically makes it easier to remember and I was reflecting on how I had to memorize so many proofs for my geometry class but if I had worked through them in an embodied way, it would have been easier to remember them. 

"As we embody mathematical entities, the dance becomes symbolic of mathematics as humanity and humanity as mathematics." This quote stood out to me in the article because I like the idea of mathematics being connected to human history and something that every person can participate in. In the other video we watched about Labyrinths there were testimonies from a couple participants who said they had a lot of fear around Math but doing something embodied opening their mind to the idea that Math could be accessible and enjoyable. 

I think including embodied practice is a fantastic idea in a Math classroom. I was thinking that even counting on our fingers is an embodied tool many students use - but there's actually some prejudice against it sometimes! I think with high school students it would take a little bit of work to get their buy-in as they may be concerned about what their peers think or about looking silly. Another obstacle is that it takes time/money - especially if you want to take a class on a trip to the beach for example. Also, it would be important to make sure it was accessible to all students.