Margot's EDCP 442 Blog

Overall, this course was a great refresher to all the business courses I am usually enrolled in. It was eye-opening to be able to relay all this profound information to my peers and family members and teaching them about where all the important mathematical concepts came from (they might have enjoyed this course as much as I did from the sidelines haha).  I honestly had no idea that ancient civilisations such as the Egyptians and Babylonians were the main leaders in groundbreaking theories and proofs. The fact that the Babylonians used a base of 60 was the main shock to me as I had no idea how to interpret their system into the base 10 that we use today. Another one of my favourite readings was the "Is Pythagoras Chinese" reading as it showed how in both Asian and Western cultures, they were coming up with the same ideologies and proofs but by using different methodologies of both teaching and solving. That reading also opened up my understanding of the different language bar...

Never in my 21 years of living, have I ever needed to understand the history of mathematics. From a young age, my parents enrolled me in Kumon which is a Japanese educational tutoring institutional that aims to teach young students mathematics. At Kumon, the method was very similar to how I was taught in school; the method was based around repetition and doing the same problems over and over again until it was muscle memory. Therefore looking back at my school days, we were never introduced into any history behind the findings, and rather focused on the technique per say.  After reading the article, and enrolling in this class, I do truly think that understanding the origins of mathematics would be interesting to add to learning and should be added into school curriculums. We are very prone to figuring things out and getting to the bottom of different technologies such as figuring out how to safely come up with a vaccine to be able to prevent COVID-19 from spreading more. So why wo...

 The three quotes that stood out to me the most from this reading was:  1. “Paris, Oxford, and Cambridge "systematically discouraged all technical instruction, holding that a university education should be general and not technical." I think that this quote is referring to how our education system, especially the prestigious institutions are failing to teach knowledge and theories for the sake of teaching and passing on this information. It is rather taught as a way to apply this knowledge to what the students are trying to do as an occupation in the future and making sure they are taught the necessary skills for it. I do understand that this is what institutions are set out to do, however, not everything in life is about learning for a specific outcome but instead learning should be a universal privilege that people can just ponder on and observe what has been taught to them.  2. “Logistic was practical and utilitarian, a study for children and slaves; logic was a libera...

I was very excited to see if there were similarities in this reading with the topic Jennah and I had done on Assignment 3 with our own Hindu mathematical research on the history of Brahmagupta.  I wanted to first talk about Al-Kwarizmi as his book on The Addition and Subtraction According to the Hindu Calculation which we also spoke about in our presentation was what introduced the numerical demical system into the Western world. The reading also mentioned that his book was later translated into Latin and this is what aided the spread of this knowledge to the rest of the world and why we use it today. In our own research, we also found out that Al-Kwarizmi was also the one to translate Brahmagupta's work and incorporated it into the same book.  Secondly, I found ‛Umar al-Khayyāmī's work on the calendar reform and his book on the Explanation of the Difficulties in the Postulates of Euclid interesting as he discussed the foundations in geometry that was later also translate...

I thought that the creative aspect of all the presentations, helped me understand each groups topic better and thus, would be a great way to incorporate creativity in the classroom. From Jennah and I's presentation of the History of Bhramagupta, I was able to tie together his various academic achievements into one painting.  What I found most provoking and a big take-way was when we talked about how this theories and ideologies were spread across the world, first through Arabic kingdoms and then secondly, through the translation to Latin where they spread across Medieval Europe. I think this again, shows how much our modern educational system lacks in teaching the origins and the stories behind mathematical proofs or formulas.  Apart from this, I was not aware that Bhramagupta was the famous mathematician to begin the conversation of the concept of zero. I remember when I was being taught basic multiplication in junior school no teacher could explain to me why every number mul...

Prior to reading this paper, I was aware of Synesthesia but not OLP. I think that Major's paper touches upon important aspects that I hadn't thought about before. Specifically, when she spoke about social numbers and how letters such as 'A' are associated with more popular colors such as A. This could be due to the fact that when we are taught the letter system from a young age in western cultures, the letter 'A' is associated with a an apple -  they tend to associate the letters with another object to familiar the children and thus, that is where red comes into the picture. However, when reading that example, I saw it more as we associate letters that are more frequently used with colours that are more frequent as well and that is why the letter 'y' or 'u' would be associated with the colours brown or beige.  I think that students should be given the opportunity to link numbers with another form of sensory or cognitive pathways such as colours o...

 Something that stood out to me specifically from this text was the mention of the different methods the Babylonians and the Greeks used when teaching. More specifically, the point made by Høyrup about how "Greek mathematicians grew out of problems" as opposed to how "nearly all the Babylonian texts" were "problem texts". His idea of the "useless second-degree problems" in Babylonian scribal mathematics where students were taught to problem solve using the methods at hand could be an example of pure mathematics whereas the Greeks and their focus on solving problems practically by applying methods could be seen an example of applied mathematics.  I do think that both of these teaching methodologies focus on practicality and generality as they were taught to subsequent generations however, I think that Babylonian word problems carry more weight in practicality. This can be seen by the type of word problems they as they were focused on real life app...

  I found this activity rather fun as it reminded me of Sodoku! I used to play Soduku all the time when I was younger to be able to train my brain to problem solve and expand my brain capacity. I was able to solve the problem above rather quickly using a trial and error method and I think this speaks to how memorization and muscle memory of my Sodoku hobby aided this. Again, this might be an example of how muscle memory from doing repetitive problems in school allows us as students to be able to fully execute problems without hesitation and therefore might be the reason that understanding where math ideas and theories came from and the history behind them is not incorporated into math cirriculums.   When doing some additional research into the magic square, I also came across this musical violin piece from  Šarūnas Nakas Ziqquratu (1998) that incorporated the magic square of 5. I think that it is interesting to see how rhythm and mathematics go hand in hand together....

For assignment #3 I will be working with Jennah and we will be exploring the world of Indian Mathematics, specifically looking at the history of the mathematician, Brahmagupta.  We will touch upon his insights and what he discovered during his lifetime and try to see if we can tie it with the European and Arabic time periods which we already learnt about in class. Our creative aspect of the presentation and findings will be expressed of a painting. Therefore we will have a visual piece to bring all our ideas together.  Painting / Drawing:  Since Brahmagupta was an astronomer, we decided to portray his main ideas and theories on a space-like looking background. Attempted stars and planets were drawn to emphasize this creative idea. On the left, I drew a painting of what historians believed Bhrahmagupta looked like during 598 CE - 668 CE. His main two books that he had written; the Khandakhadyaka and Brahmasphutasiddhanta are listed on the green pot that he is holding ...

Firstly, I think that the use of our bodies as a form of expressing mathematical proofs and theories is well justified. The report and video did a great job at portraying the different benefits this visual and kinesthetic learning style can have on understanding the content better. Milner and Duque's mentioned that by going through each part of the dance, creating a flow of movements they are able to mimic how "proof's unfold over time". This was interesting to me as I had forgotten that proofs were solved through different interpretations, trial and error alongside, piecing together the different axioms.  Moreover, I enjoyed how they were able to explain that with expressive content there is a certain level of intuition and reasoning that you have to consider in order for the rest of the audience to understand where you are coming from. They did this by listing their different assumptions that they had thought of before videoing the different proofs. As seen in the s...

It was a beautiful yet confusing poem for me at first as part of the poem uses biblical allusions such as "O Holy". It wasn't until I dug deeper into the history of Euclid to understand where this background and purpose of the biblical ties came from.  As mentioned in the title of the poem: Euclid or otherwise known and Euclid of Alexandria was a Greek mathemetician that was given the title: The Father of Geometry. Many of his geometric theories stemmed from a series of axioms. This implied that, given an assumption that a statement is true, it is a starting point for exploration and rational thinking. I believe that this poem written by Edna St. Vincent Millay truly captivated the nature of geometry that Euclid was known for by adopting the use of an iambic pentameter structure with the occasional " strategically placed occurrences of dactylic meter, which successfully slow down the poem where new ideas begin or old ones end." (McGee, n.d.). This musical meter ...

Upon visiting various different Egyptian exhibitions, I had always come across the Horus eye symbol but never looked much into the meaning behind it. I had assumed that the eye carried some sort of importance in keeping spirits away similar to the Greek's however, I had never imagined it to carry the importance of such rich history and mathematical properties.  Interestingly enough, not only does each part of the eye symbolize a different fraction, but it also portrays different senses in which the Egyptians believed there to be six; Hear, Taste, Smell, Touch, See and Thought as seen below.  The egyptians believed that this eye was considered the 'whole' eye. However, it is important to note that the sum of each of the fractions, which can be seen as a geometric series today, only adds up to 63/64. When researching I found that some academics believed that the 1/64 missing from the 'whole' eye could be intentional as no mortal human being can re-create something so ...

Upon reading this paper, it is clear that both the Greeks and Chinese had their own mathematical discovery triumphs despite the lack of communication between both civilizations. As noted by Ross Gustafson, the Greeks were more focused on the understanding of the different proofs and how they were able to solve the different problems such as the right-angle triangle or the verification of the square root of 2 to be an irrational number.  Even though my career doesn't involve traditional teaching, from a students perspective who has has to learn about mathematics, I will say that learning the methodology has more emphasis in school cirriculums than understanding where the actual math came from. Therefore I would make the slight comparison that the way in which we teach students mathematics today follows a similar sturcture to those of the Chinese. The texts states that the  Jiu Zhang suahshu "was not to prove beyond argument the material but to guide the reader (student) on the ...

A SaveOnFoods supply manager counted a total of 32 apples in stock delivered from apple farmers based in Yakima, Washington.  They noted that they had received 1/7 of the order four days post the expected delivery date. What was the original quantity that was delivered?  Solution:  1) We need to find a convenient integer answer that has been obtained through multiplying it by 1/7. Therefore we can choose the number 7.  2) (1 + 1/7) * 7 = 8  3) Therefore 8 = 32  4) The number 4 is used to multiple 8 giving us an answer of 32.  5) Therefore we can use 4 to multiply by 7 to allow us to gain the answer of the unknown quantity.  4 * 7 = 28  --> Therefore 28 is the quantity that was delivered  6) Checking if this is the correct answer: 1/7 of 28 is 4:  (1/7)*(28) = 4 --> 28 + 4 = 32 

  Our presentation was based on problem 79 of the Rind Papyrus (1650 BCE). We were able to denote the three different word problems that have developed over time in different parts of the world. Ultimately, St. Ives was a nursery rhyme that originated from the Egyptians in problem 79. Interestingly enough, before Arabic numerals were introduced into Europe as seen below in 1202, arithmetic problems were solved used a counting instrument called the Abacus.  Here is the link to our presentation:  https://docs.google.com/presentation/d/1Wqyy652vSVV6qoujA1cfXZ33vjY7iq_9q8HN_-qXx14/edit?usp=sharing Reflection:  From this assignment, I was able to fully gage how knowledge is passed down through different generations, not only within the same community but also by demographic spread. It was interesting to see how different cultures were able to interpret arithmetic problems or sequences using a variety of different methods such the Italians through the use of the Abacus ins...

Upon reading this extract, I found it interesting to understand how the Babylonians were able to interpret word problems through the use of different images and symbols on the tablet. In the 4.7 example, we were able to see a solution distinction between the two groups and how we use an entirely different type of notation today. Alongside this, all this time learning the Quadratic Formula in school and I did not know that it was interpreted by the Babylonians when they had no formal algebraic system set in place. They were able to adopt different types of questions and solve up to three unknowns whether it be linear, quadratic or exponential.  The system we adopted today was derived from their findings, however, the notation we use is much more generalized in my opinion. We use the same symbols such as 'x'. 'y', 'a', 'b', or 'c' for unknowns in most mathematical practices around the world today or even greek symbols in different areas of knowledg...

 

Upon reading this extract, I was especially inspired by the flow of events and knowledge that circulated our world of mathematics today. The three things that stood out to me most were:  1. In our education system today, we tend to ignore historical facts from all cultures and countries in certain academic disciplines, especially mathematics. Most of the figures found in the text illustrate how we have evidence that suggests mathematics has been a contributable subject from many regions and dates back to 800 - 500 BC with the Sulbasultras. Steering us away from the Eurocentric viewpoint we typically engage within our curriculums.  2. Majority of the ending of the chapter focused on the Mayan civilization. I found it interesting that they were more than 12,000miles away from Babylon, but produced a similar numerical system consisting of similar symbols. However, instead of using a base 60 system as discussed in our previous classes, they were the founders of the number zero and...

As we managed to see in class, the Babylonian mathematics time table was on a sexagesimal system. Naturally, when comparing both the numbers 60 and 10, I was able to distinguish their mathematical differences between them. Sixty is divisible by all numbers 1-6 (on the other hand: 10, 12, 15, 20, 30, 60) whereas 10 is only divisible by 1, 2, 5 and 10 (itself) maybe making it easier to mathematically divide or use fractions. Alongside this, I remember in my chemistry classes we always used to focus on Fullerene's which are Carbon allotropes. Interestingly enough, Buckminsterfullerene has a formula of C60 and its natural composition of carbon atoms are arranged in hexagons and pentagons, both shapes being a division of 60.  In today's world, the number 60 has also been prominent in keeping our clocks on the correct path. Each hour and minute consists of this number and both military (non-integer) and regular time (whole number) clocks are divisible with little error. We again see ...