Heesung Yun EDCP442

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.  ...

 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...

 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...

 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. 

  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...

 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...

 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 ...

 Most interesting fact that I observed from the presentations was frequency of appearances of familiar names in different presentations which shows the influence of these mathematicians across diverse fields of mathematics. For instance, ancient Greek mathematicians like Pythagoras, Archimedes and Euclid were mentioned multiple times in Dion, Yiru, Mike and Victor's presentations as well as my own. More over, modern mathematicians such as Descartes and Cardano were mentioned in Crystal, Ivan, and Dion's presentations. Another thing which I noticed is that most of the mathematicians were also vastly invested in philosophy. I knew that there were not much differentiating in mathematics and philosophy for the ancient Greeks as they viewed math as a way of epistemology, but I did not know that these commonalities continued until more modern times. During Emilie's presentation, she mentioned that Gauss wanted to be a philosopher until he was 19, and Descartes mentioned in Crysta...

 There were lots of cool facts that I learned from the presentations on Wednesday. One thing that I found most interesting is the fact that almost all mathematical discoveries were made across different regions at different times. Also it is very interesting to see that at times, mathematical knowledge that was lost in certain  regions were kept in different cultures which then gets reintroduced to the same region. In Yi Wei's presentation it was interesting to learn that Chinese first translated Euclid's work and had originally had the word rational numbers which was mistranslated to Japanese as reasonable numbers and came back to China as reasonable numbers instead of its original name. Besides the anecdotal things, I thought that the Indian mathematician in 1300 from Andrew's presentation being able to come up with a version of mean value theorem without any knowledge of Calculus was very impressive. 

 Although his work was first written and organized almost two millenniums ago, but schools have continued to teach it as one of the most basic and integral part of the curriculum. The article argues that Euclid's Elements is one of the best math textbook that exists and continue to will be in the future. I believe that this is due to the fact that it provides simple, understandable geometric features that can be extended and applied in more complex situations. In the Element, Euclid provides a propositions and gives instructions that are very easy for the reader to follow which makes it a good textbook. The beauty of his work lies in the fact that it is gives fairly simple and clear instructions of proof that are easy to be reenacted. Unfortunately I do not think that it is possible to postulate and define beauty from the standard of Euclidean geometry. There are other forms that are quite different from the work of Euclid that could also be considered beautiful. Euclid's work ...

What stuck out the most for me in the poem was capitalization of Beauty which normally is not. By capitalizing Beauty, I think that the author is putting two different meanings to the word. She first uses the word as its original meaning as most people understands, and secondly I think that she may be referring to herself. Throughout the poem, she claims that Euclid was the only person who had genuine understanding of beauty, which the second poem by David Kramer questions if she had read and seen other forms of art from different artists/writers. However, by referring to Beauty as a proper noun which also could mean herself, she is claiming that Euclid is the only artist who understood and believed in the definition of Beauty the same way that she does, not because she is ignorant of other forms of art. 

I think that it is very important to acknowledge non-European sources of mathematics since there are many benefits that can follow from studying mathematics from different cultures. By learning that there were different ways that the different civilizations used and proved same mathematical concepts, students can learn that there are several ways to approach a question. Often the creativity is ignored in math classes and students are asked to reiterate what they saw on the board, but by acknowledging different styles and approaches of different cultures, the students can naturally comprehend that mathematics is a creative process. Also, by studying mathematics from different cultures, students can be more appreciative of different cultures as they see that there were other cultures that were just as intellectually advanced as the western societies.   When I first learned that Pythagoras was not the first person to discover Pythagorean theorem, I was shocked and thought about th...

As it can be seen from the posts, Egyptians would have had a very difficult time trying to divide 101 by  10. Since they would have had to kept on getting smaller and smaller fractions. They had access to unit fractions, so they could have found out that 10 fits into 101, 10 times and the remainder of 1 could be represented as 1/10, but just by changing the number to 102, it gets more complicated since they would have had to find way to represent 1/5 using by sum of unit fractions with different denominators. Either way, they could not have arrived at the solution by dividing by 2, so it definitely was not an efficient method. Also previous to trying to divide by 101 by 10, I tried to divide by 101 by 11 instead and as soon as the whole numbers part was finished, it ran into problem of 11/2 which they would not have had access to, so the method does not work very well with odd numbers as divisors.    

 If we actually add 1/2, 1/3 and 1/12 we end up with 11/12, so we find out that 1/2+1/3+1/12 is just an Egyptian fraction representation of 11/12. As a result, we can see that the father never really wanted to give all 12 of his horses to his son, since there would have been one horse left. The sons can assume that there are 12 horses, and Pat can take 6 horses, Chris takes 4 horses and Sam takes 1 horse which adds up to total of 11 horses. To be honest, I do not see how representing fractions in Egyptian way can be more efficient than today's method. 

 If we start to question the practicality of anything that we learn in school, I believe that there are not many things that all students will be using in their daily lives in the future. For instance, very few number of people read poetry or Shakespeare and even less students will ever talk about Canadian importance of the Battle of Vimy Ridge. The word problems given in the classrooms nowadays, during Babylonian times and ancient Egyptian times are most often not similar to real life situations at all. However, I do think that they have their place in education. First, relating to the article about Babylonian algebra, I think that the Babylonian teachers did not have a choice but to ask word problems to test their students’ knowledge since they did not have the concept of unknown variables, so they could not set up an algebraic equation as we know today. Besides the ancient times, word problems makes it easier for the students to visualize the problems which helps students to und...

  First possible reason why the Babylonians could have chosen a sexagesimal system is that 60 has a lot of factors, so it was easier to express as fractions as we discussed in class. Another possible benefit of using 60 as the base for a number system instead of 10 is that it can save up space when writing numbers down to for record purposes. As we learned in class, the Babylonians used place values unlike other ancient civilizations such as Roman or Chinese, and their method of recording was not as easy compared to modern paper or of course digital. Therefore, they may have wanted to fit as much as number as possible within limited space, and using base 60 would have been more efficient choice than base 10.   In the modern society, there are several occasions where we use 60 as the base number of certain system. Most commonly seen systems are when we keep time there are 60 minutes in an hour and 60 seconds in a minute, and an angle in an equilateral triangle is 60 degrees...

 Three things that surprised me from the article is as follows: 1, Herodotus, Proclus, Aristotle Thales, Pythagoras were all influenced by Egyptians, but early 1900's mathematicians claimed that "the history of mathematics cannot with certainty be traced back to any school or period before that of the Ionian Greeks" 2, Babylonians knew how to solve quadratics in different way and knew Pythagorian theorem.  3, Indians were very well-versed in trigonometry especially sine function. 1, It is understandable, given that the belief of white supremacy was widespread during the early 1900s, that the European scholars wanted to claim that ancient Greeks who they believed were culturally and racially unified group of people to be the basis of development of mathematics. However, it surprises me that they could ignore that they decided not to look deeper into the records of the ancient scholars above which clearly shows records of exchange of knowledge as mentioned in the article.  ...

      To be honest, I did not like math when I was growing up. Growing up in Korea where good grades were the only and ultimate goal of learning, good math teachers were the ones who had the most efficient way to help the students to get good grades which often involved memorization and repetitive practice. I did manage to get good results in the tests and classes, but the dislike carried on even after I moved to Canada. One thing that changed my view of mathematics is when my grade 11 pre-calculus teacher told me a story of young Gauss who used arithmetic series to add all natural numbers from 1 to 100. I was not interested in the teacher’s other lessons, but I certainly enjoyed the story since I still remember years after. Even now, as a math tutor, I tell my students the story of Gauss every time I introduce them to arithmetic series which never fails to grab their attention and by the end of the story they have naturally acquired the technique of how to calculate ar...