Final Reflection on EDCP 442

 

The EDCP 442 (History of Mathematics) course has been a very knowledgeable course for me as I gained knowledge about ancient math and how to use that history of math into the mathematics classrooms in the school setting in the form of dance, art, games etc. that I have never thought about before. I also learnt about the importance of the history of math in collaborating with other communities. While working on Assignment 1, I leant that how Pythagoras theorem has been developed in old math, and it inspires me to incorporate that knowledge into my extended practicum in math 8 class when I explore Pythagoras theorem. From our group discussions and working on assignments, I learnt that the one way to increase my knowledge about mathematics topics is to acknowledge the fact that I don’t have much knowledge about the origin of the topic and I need to be open to learning. As a future math teacher, I want to see the same ideology in my students as well. I also learnt with the help of this course to make sure that all students in the classroom are involved in social interactions to learn more about the topic as I learnt from my peers as well in this course. 

           In a nutshell, this course has provided me with a great experience and has enabled me to establish my identity as an educator. This experience has moulded my knowledge in a better way where I can help students to achieve their goals and be successful with their journey.

Reflection on Assignment 3 (Aryabhata and sine table)

 

    While working on this assignment, I found very fascinating information about the sine tables and how Arayabhata found the sine table using Rsine notation. Before this, I only had information of Vedic math and the tricks that Indian used in mathematics; but after working on this assignment, I came to know that Indian mathematics also plays an important role in the geometry and trigonometry as well along with algebra. Doing dance version (Kathak) of the sine function, It made me think that I should try other dance forms as well which will help all students because this classical dance will be hard to understand for all students. 

    I realize that during the interactive activity in the presentation, we should use the slow motion of the steps to understand the step positions. I should show the students the slow-motion of spinning the knee part of dance (Amrit's part) and then increase the frequency to see how it will look in the rotation. 

   I understand that there is not only one way of representing or expressing mathematical concepts in the classrooms. As a future teacher, I am looking forward to incorporating embodied languages in math classrooms.  

Slides for Assignment # 3 (Amrit and Karishma)

 

Here are the slides for the presentation on Aryabhata's sine table and dance:

https://docs.google.com/presentation/d/1iEmjNow8yfgkHtMMaSnLJlV4cBAnglOj-8MOcKZqfQs/edit#slide=id.ga7cb77dedb_0_8

Topic and References for Assignment 3

 

Assignment 3 Topic and References: Aryabhata and Dance Representation(s) of the Sine Function

Karishma and I are working together on Aryabhata and his sine table. We will represent sine graphs with Kathak dance representations. 

References

Aryabhata. (1976). Aryabhatiya of Aryabhata (K.S. Shukla, & K.V. Sarma, Ed. & Trans.). Indian National Science Academy. (Original work published circa 510 C.E.) https://archive.org/details/Aryabhatiya-with-English-commentary/Aryabhatiya-with-English-commentary/page/n101/mode/2up?q=Rsine.

Berlinghoff , W. P. & Gouvêa, F. Q. (2015). Math through the Ages: A gentle history for teachers and others, Expanded Edition. Mathematical Association of America.

Kalpana, I.M. (2015). Bharatanatyam and Mathematics: Teaching Geometry Through Dance. Journal of Fine and Studio Art. 5(2), 6-17. https://academicjournals.org/journal/JFSA/article-full-text-pdf/502FA2F55648.

NrityodaySiwan. (2013, May 24). How to do Knee Spin also called Krishn gat in Kathak Dance[Video]. YouTube. https://www.youtube.com/watch?v=d4skLxh2fsc.

O'Connor, J. J. & Robertson, E. F. (2000, November). Aryabhata the Elder. MacTutor History of Mathematics Archive. https://mathshistory.st-andrews.ac.uk/Biographies/Aryabhata_I/.

Tejsree. (2015, August 21). The Science of Mathematics in Bharata Natyam. Bharata Natyam – The forever legend. https://anju0590.wordpress.com/2015/08/21/the-science-of-mathematics-in-bharata-natyam/.

Blog on Trivium and quadrivium

 

The most exciting thing of this article is Recorde’s method (Page 273) that aroused curiosity in my mind to understand and explore the technique of multiplication. It seems the easiest and neat way of multiplication using base 10. Due to interest, I worked with a few questions on my own (examples in the picture above). While working on questions, I found that if you got the two-digit number by multiplying the right side number (top with bottom), then you can get the final answer by subtracting the left digit of two-digit numbers with the difference of the diagonals. I am not sure whether they were using the same method to solve these problems, but it is a fascinating aspect.

I like the thought of comparing education with the first 35 years of human’s life in the quote when the author said, “He would have the first twenty years spent on gymnastics, music, and grammar, the next ten on arithmetic, geometry, astronomy, and harmony, and the next five on philosophy.” (Page 264). I can elaborate on this quote by using my life experience. As my experience, I understand that people are energetic and had much more potential to learn and explore different things during the first 20 years. After that, they become a subconscious about their career and start to think about their family and then they became mature enough to handle the family and social stress.

The last quote that shocked me is about getting a master’s degree in universities during that time. The quote, “There were no examinations in the modern sense of the term. The student had to swear that he had read the books prescribed and attended the lectures. To qualify for a degree, he was required to participate in public disputations, either defending a proposition or opposing one defended by another student.” (Page 272) made me think that there was trust among the people; that is why the authorities just gave the master’s degree to the students on the swear that they had fulfilled all the requirements. It also made me wonder that there was no place of content in the education system.   

Reflection on Numbers with Personality

 

Source: https://mathworld.wolfram.com/Hardy-RamanujanNumber.html

 

I have read the biography of Srinivasa Ramanujan. One of the interesting things about Ramanujan’s life is treating numbers as his friends and make connections between personal life and the real world and numbers. Due to this personality, he came up with the number 1729 called “Hardy- Ramanujan’s number”. After reading Major’s article, I understand the term OLP and synaesthesia; I can say that Ramanujan had OLP. The article points out that many people have a different interpretation of numbers in terms of their personalities. 

           I feel that introducing numbers with their personalities to the students will help them to deal with the anxiety of numbers. For example, many students scared from number “0”. I think if we explain the story behind the innovation of numbers and their importance in the classroom, then it will help students to deal with their number's anxiety. One other way to overcome this problem is to tell students to share their cultural belief in the representation of numbers because each culture has a different representation of numbers.

           During my school years, I remember that I always felt that positive numbers are friendly than negative numbers and easy to use. Other than that, I do not have any personalities about numbers, but I want to share something interesting about personalities of days of the week. In India, people consider Wednesday as lucky day and Thursday as a misfortunate day for the brother-sister relationship. I remembered my mother always forbid me to wash my hair on Thursday because of the beliefs that washing hairs on that day will bring misfortunate in a brother-sister relationship. 

           

Reflection on Assignment 1

During this assignment, the most important thing that I learnt is the importance of collaboration. While working on this assignment, there were certain concepts that I was not clear about and with the help of my peers, I was able to understand those very efficiently. It also improves each other's motivation because, with the support and guidance of other peers, you can present your opinion in approaching way. Also, with the help of interaction among peers, everyone can learn something from each other that they can not learn on its own. 

    As I believe in engaging activities more than the lectures, I think, to improve this assignment, we could spend more time on the engaging activity by shortening the introduction and background. But overall, I enjoyed working with my group and came up with some interesting facts during this assignment.