Assignment 3 Reflection

Personal reflection: 

It is very interesting to research into the history of sundial. However I do find it a bit difficult to incorporate into my teaching directly since the extensive requirement for knowledge from other fields, such as physics and geography. It would be nice if the science and math teachers can do a joint class on this topic, where each introduce a different perspective into the sundials. It was a great experience to work with Sukie and Chloe as a team. We learned a lot from each other, and we were able to share our findings, putting everything together. 

I also really enjoyed the project did by all other groups! The variety in the forms (poems, dance, story telling, etc) gave me a lot of insights about how math can be presented to the public. Now I have better understandings regarding the topic presented, and this is a great resource for my own and my future students! 

End of Term Reflection

This is a very interesting course for the BEd program. I anticipated that math history will be a part of the program, but I was surprised to see a lot of focus on non-European math history. It is definitely rewarding to know how other cultures and nations contributed to the development of mathematics. This provides me a great opportunity to enrich my teaching through incorporating histories and examples from various sources. 

I also liked the arts projects we did throughout the course. I had little idea about how sundial works, but after preparing for the art work and the final presentation, I feel like introducing sundial to all my students. And this is also a type of activity that I can ask my students to do. 

The course is really well designed!  I would expect it to be more fun it it were in-person, but the blogs really worked out well as I can see many interesting thoughts from my classmates. 

Assignment 3 Math History

Our group chose to represent our topic, the history of sundial, through this piece of drawing. This is because sundials are usually artistic in their designs, and visual representation can easily differentiate the various types of sundials. In history, many nations have individually developed and used sundials to keep track of time. Since there was no direct linkage between all the nations in using sundials in history, we have decided to combine all our findings together in one drawing.

In this drawing, we have put the large sundial in the center with cardinal directions pointing at the geographic location of different regions. Although being a sundial, the large sundial tells a different story from the time. We are focusing on the history of sundial in ancient China, ancient Greek, Renaissance Europe, and Medieval Islam. For each region, we put down the most typical representative sundial used in the era by the mentioned nations.  On top of that, we are representing our findings with drawings that we think are symbolic of the history and development of corresponding sundials. We decided to place the sun at the east where it rises, and the shadow of the gnome separates the three regions that we are going to introduce in detail. 

In teaching, we can show this drawing to the class, and ask students to discuss the history and relations to the given topics. The topic of sundials can be used to explore how trigonometry was used to tell time and improve the accuracy and precision of sundials from different periods of time. This artwork can also be combined with geography or physics classes where it is relevant. We can also include a hands-on activity in class to engage students in making sundials.

References 

Berggren, J. L. (2007). Sundials: An Introduction to Their History, Design, and Construction. Hands on History: A Resource for Teaching Mathematics, (72), 19.

Berggren, J. (1999). Sundials in medieval Islamic science and civilization. Coordinates, 1(9), 6.

European association for astronomy education. Short history of sundials. Retrieved 07 Dec 2020, from https://www.eaae-astronomy.org/find-a-sundial/short-history-of-sundials

Sabanski, C. (n.d.). Equatorial Ring Sundial. Retrieved December 14, 2020, from https://www.mysundial.ca/tsp/equatorial_ring_sundial.html

Shell-Gellasch, A. (Ed.). (2007). Hands on history: A resource for teaching mathematics (No. 72). MAA.

Sundial Histrory - First Time Keeping Device. (n.d.). Retrieved December 14, 2020, from http://www.historyofwatch.com/clock-history/history-of-sundials/

Vincent, J. (2008). The Mathematics of Sundials. Australian Senior Mathematics Journal, 22(1), 13-23.

Response to "Episodes in the Mathematics of Medieval Islam"

I can resonate a lot with the line "a culture's acquisition of intellectual material from an alien culture is a complex process and not accomplished in one place by a few individuals" This happens in a lot of cultures through out history. In my own culture, when trains and railways were first introduced, they were considered as monsters that disrupt the peace of the land. The Qing dynasty (of China, ~1800 AD) paid their price for rejecting the industrial revolution from the West. It would be interesting to show students how intellectual material flows among countries and cultures, through either a peaceful way or a less academic way where politics or religions are involved.

The book also teaches me the structure of Arabic names, which I was totally not aware of. The fact that Arabic name links to their father, (great) grandfathers, place of origin, and tag/nickname is extremely valuable in the study of mathematics history in the Islamic world. This new knowledge will not only help me to know the Arabic students better, but might also guide me during reading literatures in the future. 

The last point where I find it funny is that the scholar complained about "where he lived people considered it lawful to kill mathematicians". And this connects with the following points where there was hardships but also respect for mathematicians. Showing students the brave mathematicians who suffered but still decided to do mathematics may bring more respects to this field. 

Group Project: History of Sundial (Draft)

Topic: The history of sundial

Art format: One painting and one hand-made sundial 

Reference list:

[1] 2,000-year-old sundial unearthed in southern Turkey's Denizli, Daily Sabah, 20 March 2020

[2]: Archaeologists find Bronze Age sundial dating back more than 3,000 years Ancient Origins, 07 Oct 2013

[3]: Sundials: An Introduction to Their History, Design, and Construction From Hands on history, a resource for teaching mathematics,  2007 J. L. Berggren, Simon Fraser University

[4]: Ancient Chinese Sundials Kehui Deng, 2015

[5]: A brief history of time measurement Feb 2011, University of Cambridge, By Leo Rogers

[6]: Short history of sundials European association for astronomy education

[7]: The mathematics of sundials Australian senior mathematics journal 22(1) Jill Vincent University of Melbourne

[8] http://cultureandcommunication.org/deadmedia/index.php/Sundial  (sundial timeline)

[9] https://equation-of-time.info/sundials-with-shaped-styles

Response to "The Arithmetic of The Medieval Universities"

In the section "Christianity and Liberal Arts", there is a distinction between logic and logistic defined by Christianity. "'Logistic is the theory which deals with numerable objects and not with numbers. It does not consider number in the proper sense of the term...' but rather the counting of flocks, addition, subtraction, multiplication and division, always dealing with sensible objects." This definition is very much the same as "useful math" defined by modern day people who question the education of mathematics beyond those mentioned operations. It is interesting to see how some people retain the same view of mathematics when this field has drastically changed and improved our life for hundreds of years. 

In correspondence with the above definition: "as for the quadrivium, as the science are called, since they have little to attract in themselves and produce only a meager profit, most of the students neglect them or else omit them entirely". Thanks to the development of technologies, mathematics nowadays is required more and more by other disciplines, rather than being a stand-alone subject. While there is still perceptions of math being "useless" once you graduate from college, this mindset is being altered gradually. 

Lastly, I really like what Augustine said about mathematics, where "the principles of logic as the inviolable foundations of knowledge ... Side by side with the logic we find the truths of mathematics .. all there truths are necessarily and unconditionally true; they cannot be contested." I am surprised that at A.D. 386, someone already had such confidence in the nature of mathematics, when there was no computer or any efficient ways to communicate with the rest of the world. The fact that some mathematics can be proven true for thousands of years (and stay true for possible eternity) fascinates me a lot. I really like the feeling of proving something to be true with 100% confidence, and I hope my future students could feel the same satisfaction when they are also able to do so with mathematics. 

 

Response to "Numbers with personality"

In Major's paper, it says "our brain creates a space where personal associations and broader social experience can mingle." This seems to be true in Ramanujan's case since he shows affections towards numbers by calling them friends. It's easy for mathematicians to talk in this way because they work with numbers all the time, however, I am not sure if it's a good idea to introduce this OLP to secondary math students. I would probably mention that numbers have personalities for some people, and students are welcomed to find numbers that's special to them by themselves. This is not a process that requires too much teacher involvement, in my opinion. 

There are some numbers that I don't feel comfortable with due to my cultural background, such as the number "four" as mentioned in the article. Although I do not believe in superstition ideas, I still try to avoid the number "four" when it is possible. I don't have particular affection towards other numbers, except numbers 2 and 5. The reason is simple, 2 and 5 are easier to work with in mathematics compared to numbers such as 7. It is usually easier to find patterns from 2 and 5.