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Final Reflection

Even prior to this class, I liked to use a story from past to explain mathematical concepts to the students that I tutor. Some of my favourite stories are how Gauss added from 1 to 100 as a child and how Pythagoras drowned his student for proving square root of 2 is an irrational number. I am happy that I gained a lot of knowledge and stories to be added to my repertoire. Also there are a lot of things that I really appreciated learning from this course. One of the most surprising fact that I learned is how different cultures all across the globe knew Pythagorean theorem before the time of Pythagoras. Knowing about these facts really helps to bring social aspect of teaching which I thought was hard to do as a math teacher. I hope that through learning about mathematics from different cultures can bring a more inclusive classroom environment in the future and help the students realize that it wasn't just people from particular gender or race that led to mathematical advancement.  ...
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Math Art Project

 https://docs.google.com/presentation/d/1BUMhyiXpnr9p3GK512ws_xO2O_lZ0MeMH87IPfahHm4/edit?usp=sharing Chum Sung Dae was a celestial observatory that was built in 647 A.D. in modern day Kyeong Ju during the time of Queen Sun Duk of Silla. It is the oldest astronomical observatory in Asia and possibly in the world. Although form the name and some records of observations, it is believed to be a celestial observatory, but because of its location, height and inconvenient access, scholars believe that there could have been other purposes for the construction of Chum Sung Dae. One of the hypothesis is that it was built to symbolize ancient mathematical principles of the time because of several mathematical and astronomical attributes of the structure.  One of the most interesting mathematical attributes that can be found in Chum Sngdae is the ratio between its dimensions. The ratio of its outer diameters between the layers 1 to 27 is 5:3, and ratio of height of the tower above th...
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Truncated Icosahedron Sculpture Reflection

 Frankly, I am slightly pessimistic about Truncated Icosahedron Sculpture activity. There are definitely benefits to the activity. The major appeal to this activity is that the end product looks cool, and it can be beneficial for the students to develop idea of 3D objects and the relationship between its edges, vertices and sides. However, I see a few reasons why I would not try this in a classroom. First, it requires too much materials that are hard to find. This is not too much of a problem since the CD's can be replaced with other materials, but then it adds on to the second problem which is that it is very time consuming. It took about 23 math teacher candidates more than an hour and a half  to complete the sculpture. If the CD's were to be replaced by other materials it would have took longer. Also assuming that the students will be taking longer time, it would take up at least 2-3 classes to complete this class project. The biggest issue of this project is that it is ver...
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Solving Ancient Problems in Ancient and Modern Ways

 https://docs.google.com/presentation/d/1te_wD2kSOn9IYpelCzBh9eHjncd3a_rcMF5FSm0Nygs/edit#slide=id.g35f391192_00 While working on this project, I was surprised by the level of sophistication that the ancient Babylonians had in terms of mathematics. Before taking this course, I was not even aware that the any other ancients civilizations were even aware of Pythagorean theorem or some forms of quadratics. I was able to solve the question using the modern methods which definitely required more math and time than I believed any ancient civilizations had. Also, even with spending a lot of time and consultation with several people, we could not figure out how they would have been aware or express the theorem that they must have known to be able to figure out all the Pythagorean triples that were recorded on the tablets. 
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Numbers with Personality

  Numbers with Personality by Alice Major explores the linguistic aspect of numbers to show the impact of   narrative attached to the social relationships and cultural memories related to numbers. The article mentions different emotions attached to different numbers and how they differ in different cultures depending on the historical and linguistic differences. I do no think that this would be worthwhile topic to discuss for an entire class, but is beneficial for the students if mentioned through anecdotes such as Hardy-Ramanujan number 1729. As Hardy has thought previously before his conversation with Ramanujan, it is easy to think that numbers such as 1729 are boring, but by mentioning these anecdotal episodes, it could be an opportunity for the students to take a look at numbers from a different aspect which could pique their interest. Personally, I do not give any personalities to the numbers, I do think that it is interesting to analyze characteristics of numbers and th...
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Trivium and Quadrivium

 1. The subjects that were studied in the medieval universities were called liberal arts where liberal meant that they were for free men. As part of liberal "arts", it was surprising to see subjects such as grammar, arithmetic, geometry and astronomy which would be part of sciences to be considered to be arts.  2. The difference usages of the words logistic and logic: logistics meant practical and utilitarian usage of numbers and calculations and therefore were for children and slaves while logic meant liberal arts which corresponds to further study of numbers which were for the free men. 3. For Greeks, logistics was a study of dealing with sensible objects and doing computation, reckoning, the arithmetic of business while arithmetic was more advanced philosophical study of numbers that looked at the relations and nature of the numbers. This is quite contrasting to modern understanding of these words, as arithmetic often refers to brainless, repetitive calculations while logi...
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Dancing Euclidean Proofs

 The film Dancing Euclidean Proofs  is a video that I would like to show to students in class in the future. I think that there is a common misconception that math is a rigid subject where there are very set tools, methods of solving and presenting understanding. I think that by showing this video to the students, they can learn that there are diverse ways to understand mathematical principles and there are no set ways that they have to show their understanding. Also as a person who majored in mathematics from the faculty of arts, I think that it would be a great opportunity for the students to see the artistic side of mathematics. However, I do not believe that the physically proofs activity would be very effective in the school settings because of several constraints that the students face. First, they have to understand the principles and theorems from reading the Euclid's Element which could be too difficult to them since they are not experienced with reading mathematical ...
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