Dec 1 - Trivium & quadrivium

The first thing that made me stop was the poem on p.271. It made me wonder how them writing about arithmetic, since that was considered high level back then, whether there will come a time when someone will look back at what we are doing now (something like quantum mechanics) and find it cute as well. To my surprise, the author mentions the same thing at the end of the paper: Is it not possible that someday a high school student may laugh condescendingly and say, "And they got graduate credit for that!"

Another interesting aspect is how "there were no examinations in the modern sense of the term", and how students just had to give their word that they studied it. It made me wonder how way back then they were still learning stuff without really examining people, and people were gaining knowledge, so how come we have to do it these days? Could it be possible they were just learning for the sake of it? It's a long topic to discuss but definitely an interesting one.

"The teachers were often famous mathematicians, translators, commentators, and authors of texts". Sometimes I think whether this would be a good thing or a bad thing. Maybe at some point we will reach an asymptote in terms of how much knowledge we can gain in a lifetime. What would fame look like then? Someone with a Ph.D in mathematics today definitely knows way more than a lot of mathematicians in the past, yet they are not as famous. Another thing that comes to mind is whether students benefit from having someone famous teach them. I'm not sure yet if this is good.

Nov 24 - Alice Major on Mayan and other numbers

I don't think that assigning personalities to numbers is a bad thing. It can possibly make math more enjoyable and even give a sense of belonging, and thus enhance one's experience with mathematics. From the Alice Major article it's possible to deduce that it's human to attribute human characteristics to numbers.

I might introduce these ideas to my secondary math students in the case some of them have synesthesia. There are many types of mathematicians who have their own mathematical ways of thinking. We should encourage many ways of thinking about mathematics as there isn't no true way, and mathematics is developed from many different methods. For example, Freeman Dyson, a famous mathematician and physicist, splits mathematicians into "birds" and "frogs" (Source: https://www.ams.org/notices/200902/rtx090200212p.pdf). The "frogs" are mathematicians who are into puzzles and problem solving (i.e. Paul Erdős), while the "birds" are mathematicians who like big picture ideas, who unify things (i.e. Hilbert, Felix Klein). It should be noted that all these mathematicians have contributed to mathematics in some way. Therefore, we should attack mathematics education from multiple angles, and with regards to Alice Major's paper, Ordinal Linguistic Personification, and synesthesia are some of these angles.

For myself, I'd have to give the boring answer and say that I never attributed anything to numbers themselves. I am more inclined to liking shapes and abstraction, and don't want to make anything personal just in case someday I'd might have to discard it.

Assignment #2 presentation - History of Limits - Slides

 https://docs.google.com/presentation/d/1yWFzpDkV7HKEUfVvLMbDZSWjkzhpGqyl0mETGqezJkw/edit?usp=sharing

Oct 7 - Assignment 1 reflection

Doing this assignment was very interesting, as both of my colleagues have a slightly different background in mathematics than me. I also learned something that I could use in my future classes, as I did not know about the slicing of the pyramid in 3 parts, in order to derive the volume. I also did not know about part c) as well, which is basically a generalization of the previous parts. I proved the whole problem rigorously but then I realized it would be impossible to present it, given the time. Therefore, I showed only the important steps, and took out the technical details (i.e. finding the diagonal). The hardest part was presenting the history of how the Egyptians did it, since there is so much to say. Deciding what to keep and what to throw are key things in a successful presentation. Zoe and Jacob were easy to work with and we didn't have issues getting along.

Nov 17 - Dancing Euclidean Proofs

First stop: "Euclid's proofs(and geometric proofs in general) are visual in nature, and these visualizations can be embodied through artistic representation in one way or another(as drawings, sculptures, paintings, textile arts—and as artistic performances,including dance." I think this is amazing. It reminded me of  Sir Ken Robinson's TED talk on whether schools kill creativity: https://www.ted.com/talks/sir_ken_robinson_do_schools_kill_creativity?language=en . He mentions people have to move to think, and talks about dancing as something we must all do. What a great way to incorporate this idea and mathematics.

Second stop: "asking  ourselves  questions  such  as What  is  most  beautiful?  What  makes  the  proof  most  clear?  What  is practical?" This seems like a good way to get students to think outside the box. Sometimes we are stuck in the abstract world of math and drawn figures. Asking questions like these seems to be a new way of abstracting what is important, and more so what is "clear".

Third stop: "While  dancing  the  proofs adds a temporal dimension to Euclid’s original representation, the positionality of the dancers and audience(in the same plane)involves some loss of the third spatial dimension." This is so interesting I have no words to describe it. It is part of the above idea of thinking outside of the box. When we add other dimensions we see things from a completely new point of view which can aid in many things, especially when we are stuck working on a problem. About the idea of showing them to a live audience, maybe a simple mirror could work?

Assignment #2 topic: Calculus 12 - Limits

 I will look into the history of limits.

Nov 9 - Euclid Poems

Euclid was a Greek mathematician who came up with the first axiomatization of mathematics. Euclid's Elements, were the first books where axioms and mathematical proofs were used widely in order to find other mathematical concepts.

Edna St. Vincent Millay's poem talks about how Euclid's work is the epitome of beauty, and that it's unmatched by any other endeavor to capture beauty, such as those who "who prate of Beauty". The anatomization of light is a metaphor of his axioms, but I am unsure what she's referring to about the "sandal set on stone."

The second poem compares (rather rudely) mathematics with poets, and implies mathematics has more beauty than poetry as the poets have only seen her with clothes on.