Course Reflection Post

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What I've learned:/How my ideas have developed:

I found this course extremely valuable to me. I learned about several different civilizations and their contributions to math. Additionally, my idea of where math came from has been altered and I have a better idea of how certain mathematical concepts changed over the years - I definitely have a greater appreciation for our modern-day format of algebra! 

At the beginning of the course, I was opposed to giving error questions to students. As I have progressed, I am beginning to see the value in them. Often, even if there is no answer or the question doesn't make any sense, it is important for students to be able to identify this and have enough confidence to state that in class. This is a part of real life as well because these things happen and we can link error questions to examples in history where prominent mathematicians were either wrong or spent a long time trying to prove something, only to realize there question wasn't clearly defined or had a flaw in it. This shows students that the path in problem solving isn't always a straightforward one and can help them develop connections with mathematicians instead of viewing mathematicians as these untouchable geniuses that don't speak to modern-day students and their own struggles.  

Additionally, this course has also been an integral part to my own personal learning journey in the sense that it is a point of convergence of many of my interests. I have learned how I could make use of my own hobbies/interests in my future classroom in a way that will help my students' learning.

Ways to improve the course:

I know we were meant to cover more than we were able to in this course but I honestly felt that focusing on a few areas of math history and briefly talking about others was a beneficial way to take in that information. I think if we had tried to cover more, we may not have had a strong understanding of any civilization's math, whereas now I feel that I have enough information about Egyptian and Babylonian math so that if I was to read more about them, I would know what was happening. The places where we received good previews/overviews of the other types of math and important people in mathematics that we didn't talk about in class came about in the assignments, which I think were really useful. It was always great to hear about a topic from classmates who we spent the term building connections with through class discussions; if they were really passionate about their topic, the rest of us then naturally became interested in that topic and were effectively given a gateway option to dive deeper into that topic if we wish to. 

Overall I am very thankful to have been taken this course with such wonderful instructors and classmates as well!

Assignment 3 Reflection

Oops! Guess I was too excited about dancing to pay attention to the graph

 Through this project, I learned a lot about Aryabhata's sine table, some of his sine/geometric relationships, and more about Indian dancing. One of the points I messed up on (and I will add a note to the slides) was that I actually misrepresented the dance. If I was to go back and do it again, I would have done a total "Kathak fusion" (not just the hands) where it just went right, left, right, left, etc. for footwork but I instead performed the proper footwork which was right, left, right, left heel, left, right, left, right heel, right etc. Susan, when you asked us about this during the presentation, I thought you were talking about the heel step, in which case, I would have students potentially come up with a way to represent that (e.g. hole in the graph or some other indicator). Additionally, students might pick up on the fact that I stay at centre position for much longer during the first portion, but it gradually becomes more like a sine graph as you get faster (because you have to pick up your feet faster to get more steps per beat). When that happens, the amplitude should get shorter as well (you can't lift your knee as high when you have to do 4 taps in one beat!) and so on, so there are a lot of exercises that come out of this that deal with different features of sine - but I should have mentioned these in the slides. 

One of my favourite discoveries through this project was that Aryabhata referred to Rsine as half-chords and that sine is actually a translation mistake as half-chord made its way from India to the Arab world, and finally to Europe in Latin as "sinus." Ptolemy had also done a half-chord table, but the Indian version was unrelated to it. Also, Aryabhata chose R = 3438' as his radius so that the circumference of the radius would be as close to 21600 = 360 x 60, so one unit along the arc of the circle would correspond to one minute (Berlinghoff & Gouvêa (2015). Math through the ages). I still wasn't able to figure out or make the connection between why this would be helpful exactly (i.e. why measure length in degrees/minutes as opposed to a standard measurement), but it would be an interesting topic to explore. I would have loved to express these ideas during our presentation as well but it was difficult to fit everything we wanted into the allotted time. However, I still think the history and dance applications would be a great introduction to sinusoidal curves in a math classroom (and allow us to explore dances we enjoy already through a mathematical lens).