Why do We Teach Math History

When talking about history, I think most of us would have a sense of curiosity and admiration. Reading about the history of math would give us a claerer view of "whys" and "hows". Teaching the history of math will help students to explore the "whys" behind the math we are talking about today, letting them to appreciate the ins and outs behind all the formulas.

I would think students who don't like math wouldn’t take any interest in learning the history of it, but if educators could introduce math via the medium of teaching history, students might take another look at what is math in a different perspective. Math was created from our daily lives which is closely tied to human history, students should be able to notice the beauty of math from learning its history first. I think one of the most common reasons that math was not the most liked subjects in school is because it seems so far away from our daily life, students think there is no use of math. However, it's actually the opposite as math was created from people for practical purpose in their daily lives. Teaching students about it would hopefully help them to see the importance of math and math education. 

Re: Constructing a Magic Square

 This question reminds me of Sudoku I used to enjoy playing. 

To start with the first number, I decided to start with the number in the center. I picked 5 as my first tray-on number for the center number since it's the middle number among 1-9. Since now the middle number is determined to be 5, we know that A,D & B,C should be from the following numbers, 

15-5=10

1,9

2,8

3,7

4,6

Then I tried to put 9 on the upper right corner then realized that it won't work since the number is too big that there won't be so many options left for other spots in the square. Then I tried to put 9 in the middle spot on the top row, then I solved the whole squre. 

See below, 

Re: Research online the significance of the Eye of Horus and unit fractions in ancient Egypt.

    The Eye of Horus reminded me of the pineal gland in our brain which in some regions was called the "third eye". The pineal gland looks like the Eye of Horus and it's the part of the human's brain, the primary function of the pineal gland is to produce melatonin. Melatonin has various functions in the central nervous system, the most important of which is to help modulate sleep patterns. It's interesting how I personally take melatonin sometimes when having trouble sleeping. 
   
     The human pineal gland grows in size until about 1–2 years of age, remaining stable thereafter, although its weight increases gradually from puberty onwards. The abundant melatonin levels in children are believed to inhibit sexual development, and pineal tumors have been linked with precocious puberty. When puberty arrives, melatonin production is reduced. That's why in some cultures, "the third eye" is considered as the symbol of purity and soul. 

    Interestingly enough, there is some math behind this as well. the Eye of Horus was thought to be used by the ancient Egyptians to represent one divided by the first six powers of two

The right side of the eye = ​¹⁄₂

The pupil = ​¹⁄₄

The eyebrow = ​¹⁄₈

The left side of the eye = ​¹⁄₁₆

The curved tail = ​¹⁄₃₂

The teardrop = ​¹⁄₆₄

This reminds me of the golden ratio as well just with different base numbers, which is essentially everywhere in our lives. 

Re: Reading Article Was Pythagoras Chinese - Revisiting an Old Debate

 •Does it make a difference to our students' learning if we acknowledge (or don't acknowledge) non-European sources of mathematics? Why, or how?

Yes, most of math theorems/theories are similar across different cultures. However, they are not totally the same/duplicate of each other. Every culture has its own perspective in terms of understanding the theorems and the purpose of developing the theorems are also different. I think it's important to let students view/understand the same theorem from different perspectives will help them to foster the ideas into their more practical learning. As Canada is such a multicultural country, It's important to introduce non-European sources of mathematics to the class so that students will learn to appreciate the versatility of mathematics around the world. Mathematics is truly a great lens to see the world not only mathematically but also historically! 

•What are your thoughts about the naming of the Pythagorean Theorem, and other named mathematical theorems and concepts (for example, Pascal's Triangle...check out its history.) 

I personally don't feel it's wrong to use someone's name for the theorem, but It can mislead sometimes as that person might not be the first one who discovered the math behind it. However, as we are teaching/learning in a western country, it's understandable to first introduce the western version of the theorem which makes it's even more important to share the non-European sources of mathematics in class. Sadly, schools most likely only introduce westernized mathematics in schools in Asian countries and forgot about they have their own history of mathematics! We should at least introduce them to the students so that they are reminded of their roots which should be embraced by people all around the world. Math is not just some formulas that were recorded in books, it's rather a part of the history that witnessed the development of cultures and human beings. Math doesn't belong to "someone", it belongs to all of us!

Re:Ancient Egyptian 'algebra': The method of 'false position' (estimate, check, adjust)

 

Amy just got paid from her part-time job working as a sales assistant in a clothing store. Her paycheque for two weeks was $1500. Her friend Sara asked her how much does she spend on her outfits, Amy answered "I don't know how much exactly but the money I spent on clothes is half of the money I spent on my food and rent, and I already spent all of the money I got from my current paycheque." How much did Amy spend on her outfits? 

Modern Solution: Let x be how much Amy spent on her outfits. 

x+2x=1500

3x=1500

x=500

False Position: Let x be how much Amy spent on her outfits. 

Try x=100, x+2x=100+200=300

We need the answer 1500, which is 5 times as big as the current answer, so x must be 5 times as big as the trial number. (100*5=500)

Check: If x=500, x+2x=500+1000=1500

Re: History of Babylonian Word Problems

I really enjoyed reading the chapter! When I finished reading the first two pages of all the word questions. I made some notes aside, I saw there was a pattern to them! Every word question has a subject (you, I, she, he, and they) and a verb (doing something), and there's always a time and a place for the word problem. While reading the problems, I begin to have a picture of in my head, illustrating the event/problem is being described. That's so interesting because I would not have the same "picture" of the problems if they are simply a theory/concept like greek math was mainly about! Here we see the importance of having word problems that are familiar in our life as it's easy to read our own experiences rather than thinking in someone else's shoes.

I would think Babylonian math would be the "first-class math" if I didn't keep reading since it's relatively real-life related and in order to have the ability to solve those problems, they will have to know the reasoning behind it, right? However, after finishing reading the whole chapter, I then realized that in order to come up with some sort of theory/theorem like how greek did, it's unquestionable that they will have to know the ins and outs of it first. On the other hand, knowing how to solve problems doesn't necessarily require any deeper understanding of the concept. In another word, solving word problems is like training yourself to imitate Claude Monet's paintings, you can have your tweaks here and there but it's not your creation. However, the authentic meaning of education is to deeply understand the fundamentals behind all the "whys", or at least the encouragement to achieve that! 

In my own experience, it's very challenging for both students and teachers to translate mathematical theories/theorems into a language that most students can understand without doing any word problems, or we can say without imitating a sample solution. Relating back to the article, I don't think there is such thing as the first/second class of math. Pure, applied or practical math are related, it's like building a skyscraper, every piece of concrete counts. As educators, we should encourage students to understand math in their own ways. There is a right/wrong answer but not in terms of how we learn.