Babylonian Algebra from “Crest of the Peacock"

 

                        Source: https://www.goodreads.com/book/show/2189976.Babylonians

Table 4.2 in the reading “Babylonian algebra” surprised me that how peoples used words to represents quantities in ancient time when algebraic notations were not discovered. I noticed the word problems in the reading are related to fields and measurement. I think the words such as “ush”, “sag”, “lagab”, “sukud”, “asha”, “sahar” reflects their everyday lifestyle and culture. They used these kinds of words to solve math problems in their daily lives. It also tells us that in math, real-world issues play an essential role. In modern word problems, we also use words and number that represent our background and knowledge. For example: When we tell students to come up with an expression for “The sum of two numbers is equal to fifteen”, they know the meaning of “sum”, and they also know that a number should have a value.

           I believe that generalization and abstraction both play a significant role in developing mathematical knowledge. The tangible things can turn into abstraction, which helps to generalize the idea of mathematics. Generalization and abstraction help students to understand the concept behind what they are learning. For example: During my volunteer experience, a teacher used different sizes of cereal and cookie boxes to teach nets and surface area of the rectangular prisms. Using this approach, students can form their generalization to understand the concept.

           I think imagining geometry or graph theory without algebra is reasonable because these require visual representation to solve the problem. But calculus without algebra seems a bad nightmare for me. For example: in the question “2x – 400 = 244”, students can quickly find the number (x) by using algebraic steps. But if the problem is “How old am I if 400 reduced by two times my age is 244?” they will struggle with the words in the first place, and maybe they come up with the wrong equation that will give the wrong answer as well.

Factors of 45 using Base 60

 

Reflection on “The Crest of the Peacock”

 

 

This article reveals the ability of human beings to think mathematically and create inventions. While reading this article, the figure about “the classical Eurocentric trajectory” surprised me that there is no acknowledgement of other countries who contributed to math history. Later in the article, the figure about “An alternative trajectory for the Dark Ages” attracts me how Baghdad served as a meeting place to other countries to collaborate on their researches during dark ages. The diagram about “the spread of mathematical ideas down the ages” represents the interconnection between the countries on the development of math, whether it is confirmed or unconfirmed two way or one-way transmission. It helps me to understand the transmission of knowledge quickly and clearly.

Secondly, the “Caliph al-Mansur at Baghdad”, where the manuscript library was built, make me think about the obstacles faced by the mathematicians to the exchange of knowledge between many cultures or countries. During that time, there were no technology or instruments to gather information, and there were no means of transport to travel from one country to another. Whereas nowadays, new inventions or technology make life easier to gain knowledge or collect information. 

The discoveries about place value and the use of zero in the article reminds me of my research on the history of zero in my university course. It tells how a place holder becomes a zero in a number system. Each culture has its meaning of zero, such as in Arabic “sifr” means nothing, in Sanskrit “Shuunya” means empty or dot. 

This article makes me excited to learn and explore the history of mathematics and inventions.

Knowledge about Base 60

Speculative Phase:

When I was in India, my grandparents always fascinated me by telling me their experiences about counting numbers and recognising time by looking at the sun and stars. Because they were uneducated, they do not know any math conversions or terminology. They were only familiar with dozen because they used a thumb to count on each finger. Each finger represents three different parts and total we have 12 parts. I think 60 represents times because each hour has 60 minutes, and each minute has 60 seconds. It is easier to count by skipping by 10 rather than skipping by 60.

Research Phase:

After doing research, I came to know the history that Babylonian mathematics passed by Sumerians, who originated base 60 as a sexagesimal system. They used base 60 in geometry, counting, and measuring time. I also find out that they used 60 because it is easy to break into the fraction because of its divisors (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60).

References:

Gill, N.S. (2020, August 27). Babylonian Mathematics and the Base 60 System. Retrieved from https://www.thoughtco.com/why-we-still-use-babylonian-mathematics-116679

Sweeney, J.F. Why Base 60. Retrieved from https://vixra.org/pdf/1407.0062v1.pdf

Why teach math history?

 

 

I think that math history should incorporate into teaching math. I believe that teaching the history of the topic that will teach in the class will motivate students to learn more and help them develop positive attitudes towards their learning. By incorporating the history of mathematics in teaching, math will allow students to understand how the concept has been introduced and developed over time. By looking at the mathematician struggle, the students will learn that they are not the only ones who struggle. It also helps students to adapt to multicultural approaches to solve the problems.

            After reading the article, the objections made me wonder whether it is useful to teach math history in the classroom or not. In the semester system of education, the lack of time would be a considerable obstacle to teach math history. But the given pieces of evidence in the article provide me assurance that teaching math history in the classroom will help students learn from their mistakes and clear their doubts by going into the depth of the topic.

            I still believe that teaching the history of math will motivate students to achieve their goals. A teacher should need to focus on the method of implementation of the history of math into the classrooms. Giving a research project to the students as their assignments or showing a short video in the class will overcome the lack of time.