course reflection

What fascinates me the most about this course is the range and depth of topics that we have covered. When I first saw the title of the course "Mathematics History for teachers",  I thought to myself, "history and math, how interesting can these two topics be". I thought we were going to read some long articles to find out how important mathematical theories were discovered in history. 

Surprisingly, the history component of this course turned out to be quite interesting. I like how we didn’t just learn about the history behind the developement of mathematics, but also the history of the nations and culturesthat contributed to mathematics. I also enjoyed the artistic aspects that were added to learning about the history of mathematics.

Throughout the course, we have worked on math problems that could be used as starter activities for high school students. For example, the locker problem and the magic square. I have asked my grade 8s to work on the magic square problem during my short practicum. Again, I like the range of topics and questions we have covered in this course. The way that this course is organized is also very interesting. It is my first time taking a course that asks students to write blogs. Anyhow, I think it is very creative and fun.

Since we are learning online, the level of interaction between classmates is limited. One suggestion I would like to make for this course is to have more in-class and blogging interaction and between classmates, so we can get to know each other better.

Thank you Susan and Amanda for a great term! 

self-reflction on assignment 3

 I really enjoyed working on this final assignment for the course with my group mates Chloe and Yiwen. Although we have not met each other live in person, but it seems like we have known each other for a long time. We also worked together on the first assignment, and we had no problem with communication and collaboration. 

We didn't know what topic to choose for this art - history project at first. Since we are all from China, we thought we would research an important Chinese figure that has made contribution to mathematics. However, we could not come up with creative artwork to do with such a figure. We then saw the email from our instruction Susuan suggesting on history of sundials. We thought it could be an interesting topic to work on. We also decided to compose a drawing/picture of sundials so we could each be in charge of one part of history and one part of the artwork. 

In all, the collaborative component went well and I can't wait to present our work to the class. 

Assignment 3

 

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.

Assignment 3 draft

 

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

Blogging on Mathematics of the Golden Age of medieval Islam

 In reading about Al-Khwarizmi's contributions, I am surprised by the fact that he also managed to contribute to geography and astronomy aside from mathematics. It is fascinating to see that many great mathematicians have also made contributions to astronomy. It makes me relate to how math may seem to be a little bit dull when it stands by itself. But when math is tied to other areas such as astronomy and sciences, it usually facilitates in finding and discovery of new concepts and new inventions. We can say that math is contributing to many areas of study implicitly. When teaching mathematics, I can tell my students that math can be applied to many other areas of study so it is important for us to learn math. 

Again, Al-Biruni's interests were wide and deep. He had contributed to astronomy, astrology, pharmacology, and of course mathematics. I am surprised by how some people are born to be geniuses and they are meant to be born to make contributions to the world. Without these smart people, the world wouldn't be moving forward. We need to thank and look up to these people for their contributions. 

Lastly, what surprised me is the fact that these great mathematicians/educators would dedicate their entire life to discovering and finding new things. Many of the works they have accomplished took them years to compile together before they were released. I truly respect their perseverance in all the hard work they have contributed to mathematic and scientific developments. 

Blogging on trivium & quadrivium

 

“Numbers were identified with the various gods. He considered the odd numbers to be male and the even ones to be female. He made a strange distinction between the "divine number," a sort of general concept of number which existed only in the mind of the creator-god, and scientific numbers, which were the common numbers known to men on earth”

It is interesting to see that Nicomachus of Gerasa (c. A.D. 200) personified numbers into male and female, but he also identified numbers with various gods. I am wondering if certain numbers would be identified to represent a specific male god or a female god. He also made some "divine numbers" in relation to god. How did he determine which numbers were divine and what did those divine numbers mean to people who were studying mathematics back then?

"Throughout the Middle Ages, university instruction was based on a lecture disputation method…there were no examinations in the modern sense of the term. The student had simply 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."

After reading this quote, the first thought that came to my mind was "Wow, how lucky were these people for they didn’t have to do tons of exams to get the university degree." Their only final "exam" was through disputation. I find this very similar to our education program because we also don’t have to write any exams, but we are required to do lots of reading and discussions. This type of lecture-disputation for granting a degree would be feasible in most majors in the Arts faculty, but most science degrees would probably require some examinations before granting the degree. I wonder if this lecture-disputation method was also adopted for students in medical schools back then.

"Although it is true that much of what was, in the medieval university, course material for a master's degree is today common knowledge for third-grade school children, and although some of the more profound medieval processes of ratio and proportion are today taught in eighth-grade arithmetic classes, medieval arithmetic must not be regarded as superficial or merely elementary.  Many of the concepts are as challenging to modern graduate students of number theory as they were to medieval students of arithmetica."

This quote here has truly amazed me. It shows how human knowledge has advanced from Medieval times to the current days. A university degree in the Medieval Times is somewhat equivalent to our modern-day elementary school level, but there are still some difficult concepts that remain challenged for our modern-day graduate students. Anyhow, it illustrates how intelligent people have always been. From this, we can tell that people are learning to improve, and have improved from learning. 

Blogging on Mayan and other numbers

" Each of the positive integers was one of his personal friends" 

#1729 = the smallest number representable in two ways as a sum of the two cubes

If we think deeply about any numbers we see in life, we are likely able to link them to something personal. The Hardy-Ramanujan number 1729 was only a taxicab number which would probably have no meaning to anyone other than the driver. However, Hardy and Ramanujan managed to think deep and came up a special property for this number. Through their finding, more people would know that 1729 is the smallest number that can be represented in two ways as a sum of the two cubes. Linking to Major's concept on how human make association to numbers and their personal experience, numbers can be more than just numbers, they can have their special meanings to those who would actually take time to learn about them.

• Is this something that you might want to introduce to your secondary math students? Why or why not? If you would use these ideas in your math class, how might you do so?

Yes, I find this topic quite interesting to get students thinking about math and how math is always around us. Math teachers often hear their students ask "When do I ever get to use this in life". This would be an interesting topic to discuss with students. I can conduct a conversation on how numbers play role in different parts in arts, cultures, and our in everyday lives. I can ask students to think about any number and explain to the class how it is special to them. This activity would really get students thinking about how math is everywhere. 

• Do numbers have particular personalities for you? Why, how, or why not? What about letters of the alphabet, days of the week, months of the year, etc.?

For those who have seen me in real life, no one would have guessed that I am a math major and math teacher. To be honest, I don’t consider myself as a math person because I don't have the math brain that is able to connect everything to math right away. Sometimes I would ask myself, "why did I study math?  How did I up end up with a math degree and I am going to math teacher soon?" Everything seems so unreal. 

 I have told the class in the beginning of the school year that my birthday happens to coincide with the well-known mathematical constant pi. Sometimes I wonder if this is some kind of hint or fate that in my life, I will have to deal with math. (*laugh*) It is probably meant to be that I will have to deal with math for my life (at least part of my life) because I was born on pi day? I really don’t have an answer to that, but for sure the number 314 has a meaning to me. But people don’t see it in me because they don’t see me as a mathematical person. Even I don’t see myself as a mathematical person, but one thing I know is that I was willing to learn and I have worked hard for that math degree.  I will definitely keep up that spirit for future challenges.