Final Reflection

Most importantly I have learned the importance of including and teaching math history at a high school level (or even lower should I teach lower grades). I had personally always enjoyed when teachers would add in bits of math history to lessons, but after taking this course I now understand the value math history can have on a students learning and classroom experience. I have also come away with many activities and ideas of how to incorporate math history into my classroom. Additionally I learned more about artistic interpretations of math and how I could include art projects or artistic interpretations into my classroom practice.

The idea that teaching math history can provide greater connection to the material for students is probably the idea that developed most for me. I had not considered that opportunity for students as a part of teaching math history. However, throughout this course I have realized that teaching math history can provide students with greater context for the material, greater connection to the material, greater understanding and potentially more interest in the material as it presents math in a way they may not be used to. Understanding that I could include word problems, or working in another base into my classes as a way to incorporate math history or as a way to engage the class in less traditional activities is something I will take with me into my teaching.

My suggestion for next year is having more in class time discussing readings and blog posts - I understand we were under a bit of a time crunch this year!

Assignment 3 - Personal Reflection

 While working on this project I was amazed at the complexity of the thinking that had to take place to formulate stick charts. As well the observations those creating the charts had to make and the memorization needed to remember the specifics they were trying to map. I learned that there were not explicit mathematical calculations taking place to create these stick charts, but there was complex mathematical thinking and understanding necessary. I also found it very interesting that usually only the person who created the stick chart would use it, as it was only relevant to their interpretation of the wind, swells and islands. 

I believe the idea of the mathematics of ocean navigation and stick charts would be a great cross-curricular lesson/activity to do in math and science classes as you could incorporate math and ocean science. It would also allow students to practice their artistic side by having them create their own stick chart.

Assignment 3 - Write Up, Slides, Photo of Artwork

 Write Up: 

For our project we chose to learn about the mathematics of ocean navigation and mapping of the traditional cultures of the Marshall Islands. Micronesians settled on these islands in the Pacific Ocean over 3000 years ago (Patowary, 2016). The Micronesians conducted ocean navigation through the use of stick charts (manoa). These stick charts “identified patterns in ocean conditions such as swells, waves, or wind” (manoa). Traditional stick charts were made out of “coconut strips, palm strips, and cowrie shells” (Knighton, 2020) and were usually around “60 to 120 cm by 60 to 120 cm” (Ascher, p.349, 1995) in size. There are three types of stick charts, namely meddo, rebellith and mattang, all serving slightly different navigational purposes (Ascher, 1995). The mattang stick charts are thought to represent wave interactions, wind patterns and swell movements all of which are happening around an island or atoll (Knighton, 2020). The navigational purposes of the mattang was demonstrated by highlighting directionality with respect to the wind as well as the land position, while isolating swells (Ascher, 1995). This type of stick chart is more abstract than the other two, with their symmetrically placed land masses and “four uniformly depicted swells from perpendicular directions” (Ascher, p.360, 1995). The next two kinds of charts, meddo and rebellith are considered more of a map than the mattang charts (Ascher, 1995). The rebellith charts are larger in size and scope, and “include the whole of the island group, or at least one of the two parts” (Lyons, p326). Despite their size, and the lack of obvious arithmetic in Micronesian society, the relative positions of the atolls and islands were accurate (Ascher, p362). The meddo stick charts represented currents and islands or atolls and the navigation between them (Knighton, 2020). They served the same purpose as the rebellith but were smaller in scope. Both the rebellith and the meddo stick charts “incorporate localized details about wave refraction, reflection, and diffraction and their interaction” (Ascher, p.366, 1995), lending to the mathematical thinking that took place by those that created and analyzed these charts. 

Following our research into the mathematics of ocean navigation, our group chose to create a meddo stick chart of a few islands off the west coast of Vancouver Island. To build the map we first drew a map on paper to have an idea of what we wanted to build. To build it we decided to use branches for the sticks and rocks for the island as it is easily available. The long sticks represent the possible routes to the islands and the short ones represent the current. 

Slides:

https://docs.google.com/presentation/d/17kcszIhtNFMpQqYDtq6tZE2k7U-1Scd37qJhZg4-7dA/edit?usp=sharing

Photo of Artwork:

Assignment 3 - Topic, Draft Reference List and Artistic Format

 Topic: 

The mathematics of ocean navigation and mapping from the traditional cultures of the Marshall Islands and other South Pacific navigators, including navigation by ocean swells and stars, mapping the south Pacific with stick and shell maps.

Reference List:

Ascher, M. (1995). Models and Maps from the Marshall Islands: A Case in Ethnomathematics.

Historia Mathematica, 22, 347-370.

Knighton, H. (2020, April). Navigating the Waters with Micronesian Stick Charts. Ocean find

your blue. https://ocean.si.edu/human-connections/history-cultures/navigating-waters-

micronesian-stick-charts 

Lyons, H. (1928). The Sailings Charts of the Marshall Islanders. The Geographic Journal, 72(4),

325-327. https://www.jstor.org/stable/1782371

Patowary, K. (2016, February). The Stick Chart Navigation of Marshall Islands. Amusing Planet.

https://www.amusingplanet.com/2016/02/the-stick-chart-navigation-of-marshall.html 

Traditional ways of Knowing Polynasian Stick Chart. (n.d.). Exploring our Fluid Earth Teaching

Science as an Inquiry. https://manoa.hawaii.edu/exploringourfluidearth/node/34

Artistic Format: 

We will be attempting to recreate a stick chart.

An Introduction to the Mathematics of the Golden Age of Medival Islam

 One thing that I was not aware of at least in terms of Islam civilization was the idea that it was permitted to kill mathematicians. The book mentions that the reasoning behind this could have been that it was because mathematicians were considered astronomers and were therefore also considered astrologers. I personally have always found the more personal, dramatic history of mathematics very interesting and loved when my professors would incorporate it into our lessons. Although I am not sure where I would place Islamic civilization and their beliefs within class material, I think I would just start a lesson with some quick interesting facts to get the students engaged for the day. I always found as a student I really enjoyed less ‘math’ related math content to start the class, so I think starting the occasional class focusing on different civilizations which are involved with the history of math, would be a way to incorporate these facts into my teaching of mathematics.

Another thing I learned that I was not previously aware of was the origin of the word algorithm. I knew there was Latin origin, however I was unaware of its Arabic heritage in that it came from the mathematician Al-Khwārizmī. I would incorporate this into my own teaching of mathematics by providing a brief background and origin of where the term algorithm came from. Doing this I believe would provide some context for the students, as I think sometimes math vocabulary can appear to come out of nowhere for students. I would try and do this occasionally for new math vocabulary, as a way for students to have interesting facts connected to a term, to provide context. 

Finally, I was introduced to the calculation of 2pi that  al-Kāshī’s determined. As the book notes, the interesting part about this calculation was the accuracy to which is was done, by deciding how close he wanted his approximation of 2pi to be. I would incorporate this information into my own mathematical teaching by introducing this approximation of 2pi and the goal of al-Kāshī’s approximation, when I first introduce 2pi in class. As well, I think  al-Kāshī’s strict approximation guidelines he set for himself are a good way to explain to students the importance of accurate approximations, so the overall answer of what you are calculating is not largely affected by the approximation being made.  

Assignment 3

 Topic Choice: Ocean Navigation and Mapping

Group Members: Max and Jennifer

Trivium and Quadrivium

 “Of the seven liberal arts, the quadrivium comprised what we might call the scientific studies of the day” (p.265-266). This quote made me stop simply because quadrivium was grouped as one of the liberal arts. Given that the quadrivium is made up of hard science based subject areas, I found it very surprising that it was grouped as a liberal art. However, putting into perspective the time the quadrivium was defined, I can see how it would have been considered a liberal art as that field was definitely more prevalent during that time, and the support for ‘hard sciences’ was not as great as it is now. 

“As for the quadrivium, as the sciences are called, since they have little to attract in themselves and produce only a meager profit, most of the students neglect or omit them entirely” (p.270). This quote made me stop due to the reasoning behind students choosing to not continue their education in the sciences. I found this quote quite relatable as a science student myself. While I was completing my science degree, there was often talk amongst students and students not in the science faculty that would comment on the lack of profit that could come from the completion of a science degree, without at least one extra degree after your undergrad. However, I found that the students who truly loved science were not worried about profit at the end of their schooling! Again I have to put this quote in the context of the times, where science was just starting to make a rise.

A general view of the medieval universities would seem to indicate that at any given time, whatever arithmetic was known was taught”(p.273-274). Finally, this quote surprised me in making me realize that there was a time where whatever arithmetic was known it was taught. While the amount of mathematical advancements and new fields created since that time is very large, it is still incredible to think that all known math was taught and available for students to learn. Now we are learning all different fields of math, but I can’t imagine learning about all of the arithmetic that was ever known, during my university education.