Reading for Sep 23

 It's an interesting exercise to try to imagine how general mathematical statements could be made without the use of algebra. I suppose the Babylonians use algebra implicitly in their statements, but discuss the relationships between quantities. Moreover, it almost feels like dependencies and relationships in Babylonian mathematics are almost parametrized by a time variable, t. When we write a mathematical statement with algebra, while it still reads left to right, it its on the page as one singular statement. Babylonian statements about math tend to read more like algorithms, or a series of steps (like example 4.8 in the handout).

I think that math is about whatever you decide to make it about. Without wanting to get too philosophical about it, statements about logic "exist" in a sense, and they'll be true or false. Our use of such statements and our exploration of mathematics is really what we make of it. For the Babylonians, it seems as though it's supposed to be practical. Perhaps in due time they would have developed further tools to explore the concepts of algebra and abstraction, as there was clearly an academic inclination study such topics.

One area of mathematics I think would be interesting to discuss without the use of algebra would be graph theory. If instead of using algebra, we simply discussed the relationships that different vertices have with each other, we could perhaps open up the world of graph theory to students who have yet to develop the algebra skills necessary to study the subject. For example, as is suggested in the name, the handshaking lemma can be explained not only with a simple drawing on the board, but by telling a story about how people might shake hands at a party.

Reading for Sep 21

 I thought the different explanations for why babylonians used based 60 to be super interesting. The argument for the relationship between the cyclic nature of day and night represents by a circle, and the development of longitudes and latitudes with the use of 360 degrees to move around the earth was novel to me. I thought the use of the 12 starts which signify total darkness during the equinox form a natural basis for the development of the hour. In which case we have 24 hours in the day. Where I wish the article expanded more, was the integration of the minute and the hour, because this necessarily forces the timespan of a second to consist of 3600 repetitions in an hour. 

The use of 360 degrees, and 60 seconds in an hour has certainly played a huge role in my development and understanding of geometry. Equilateral triangles, trigonometric identities, time keeping, and even the initial development of modular arithmetic was all made easier by the fact that 60 has many factors. Rational numbers, terminating decimals and easy-to-remember roots played a key role in my understanding of geometry. Moreover, there always seemed to be a natural progression from 360 degrees in as circle to 365 days a year - a fact which provides a sense of continuity from the second up to the year.

3 of the 18 stars represent dusk, 3 for dawn,
leaving 12 for night 

Babylonian Multiplication Table!

 

Reading for Sep 16

 The classic 'Eurocentric' trajectory assumes that the basis of modern science is strictly European, and neglects that many other cultures had their own scientific developments independent of western colonialism. An early fact I found really interesting was that to Aristotle, Egypt was the centre for mathematics. Reflecting on this, it follows that Egypt, Mesopotamia, and other civilizations of the area had their own development of mathematics. How could, as an obvious example, it be that the pyramids were made? Or, for that matter, how could any of the complex feats of building, architecture and engineering without a solid understanding of mathematics. I also found the alternative trajectories for the dark ages fascinating. In my view, the renaissance was about europe's rediscovery of what was lost from the greek times. Unfortunately none of the credit was given to China, India, and the Hellenistic world.

This reading also piqued my curiosity in Mayan astronomy, and that their knowledge with rudimentary tools surpassed europe's at the time. Integrating mathematics and astronomy would be something I'm very keen to continue to explore. In particular, I'd like to explore if there are recorded examples of indigenous astronomy, and how the study of geometry or gravity can be connected to cultural learnings.

EDCP 442 Reading 1

  1) Pre-reading: Why and how should math history be incorporated into my own math teaching?

In my view, learning about the history of mathematics can be beneficial in several ways. On the one hand, learning math history can add a cultural and historical element to a math class which might otherwise lack cultural context completely. The ways that societies and civilizations studied and developed mathematics not only tells us about their scientific endeavours, but about what things were important to them in thew world. For example, for many civilizations, math was deeply connected to astronomy and cosmology, and informs us about the civilizations faith, belief in higher powers or "greater forces at play". Indeed, we have all wondered whether math hints at some universal design which we look to for answers.

I think that math history can be incorporated as a background section to provide context or motivation for learning a module, but also can be used as a tool to learn about those cultures themselves. Using math from a civilization or culture can help us understand the culture better itself. Bringing math history into the classroom can add colour to a subject which many students view as being bland.

2) Three quotes/ideas/paraphrases from the article:

"A more accurate view of mathematics and mathematical activity may be provided by historically important questions, problems, and answers." 

Students learn that it's normal to have uncertainties, doubts. They can see that math was something that people have grappled with for centuries. This passage prompted me to reflect on the fact that student's may relate to those who developed the math they're studying. For those people it wasn't easy either, and that it's normal to struggle, but it's possible to understand!

"Understanding the advantages and/or disadvantages of modern forms of mathematics".

I paused here because I had not considered that some older forms of mathematics may have advantages over the modern ones. For example, old number tricks from ancient Indian mathematics do have their place in modern society when one must perform quick calculations without the use of technology.

3) How has my view changed after reading the article?

Studying the history of mathematics has more benefit than just by providing context for modern day mathematics. It can also provide ways for students learn math in different environments, tools which suite alternative learning needs, and opens avenues for students to explore other aspects of the cultures which produced the math they studied from that time and place.

 

Bibliography

Tzanakis, C., Arcavi, A., de Sa, C. C., Isoda, M., Lit, C.-K., Niss, M., de Carvalho, J. P., Rodriguez, M., & Siu, M.-K. (2002). Integrating history of mathematics in the classroom: An analytic survey. In J. Fauvel & J. van Maanen (Eds.), History in mathematics education: The ICMI study (pp. 201–240). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47220-1_7

Hello World!

 Excited to teach math with you all!