Nanxi EDCP 442 Blog

Similarities: Both systems use symbols to represent numbers. The Babylonians used wedge-shaped marks, while the Egyptians used pictures, like lines and symbols, for different amounts. Both systems had separate symbols for larger numbers. There is no single numbers like 2,3,4… The Egyptians used one symbol for 10,100,1000,10000…while the Babylonians used their base-60 system to handle large numbers. Differences: The Babylonian system is a positional system, where the value of a symbol changes based on its place in the number, similar to our system today. The Egyptian system is an additive system, where you simply add the symbols together to get the number. Each symbol represents a fixed value (e.g., 1, 10, 100) regardless of where it appears.Base system: The Roman numeral system is similar to the Egyptian system because it's also additive. However, Roman numerals use some subtraction rules (e.g., IV for 4), which the Egyptian system does not. Advantages and Disadvantages: Egyptian ...

I believe students often avoid word problems because they find concepts like taxes or interest intimidating, especially when decimals are involved. After learning more about the history of word problems, I’d like to incorporate both that history and students' everyday lives into my teaching. I’d start by discussing with students where they might already encounter math without realizing it. For example, I might ask if they’ve ever thought about how much a discounted item costs or how long it takes to travel a certain distance. These are practical problems they’ve likely faced but don’t necessarily associate with math. Together, we’d turn these situations into word problems, helping them see that math is already a part of their daily lives. For the more challenging topics, like calculating taxes or interest, I’d create scenarios that are relatable. Instead of giving a generic tax problem, I might ask them to imagine buying a new phone with an option to pay in installments. We’d ca...

It's fascinating to consider how the ancient Egyptians were able to construct precise structures using only simple tools like measuring ropes and rulers. This made me reflect on whether our modern society is overly reliant on high technology and overlooks the ingenuity of simple tools and methods. The "stretching the cord" technique and the precise alignment of the pyramids showcased the ancient people's manual skills and spatial imagination. Another point that stood out to me was the role of astronomical observations in measurements. It made me realize that ancient people's observation of nature was so smart and their connection with heaven and earth was closer. While we rely on high-tech means like GPS today, I wonder if we have lost some of the wisdom of 'looking up at the stars' and the connection with nature.  My two questions: 1. How did the Egyptians maintain such precision in their surveying methods, especially when constructing pyramids and temple...

 

 

When students ask me, “Teacher, why do I need to learn this? Am I going to use functions or calculus when I buy groceries?” or similar questions, I am initially at a loss for words, and then I fall into deep thought. As the text says: “Are word problems used primarily to train students in the use of methods without necessarily providing an understanding of those methods? Are problems chosen simply to illustrate the "methods at hand"? This actually resonates very truthfully with my experience in previous jobs. In my past work, I often felt torn and conflicted. On the one hand, direct teaching methods allow for efficiently achieving teaching goals within a limited time. On the other hand, explaining the logic behind these methods helps cultivate students' deeper thinking and genuine understanding of the essence of mathematics. Teaching methods are efficient, but in the long run, students may lose interest in mathematics or fail to apply what they have learned in broader con...

The Babylonian system used a base-60 system for numerals, which still influences how we divide time into 60 seconds and 60 minutes. The second article discusses how divisions of hours, minutes, and seconds evolved for practical reasons. Unlike natural time divisions, which feel fluid and seasonal to me, these modern measurements have more rigidity, shaped by human needs. Reflecting on these, I see a tension between time as an infinite continuum versus the imposed grids of hours or minutes—human inventions that attempt to control something fundamentally uncontrollable. The two perspectives make me reconsider how much time-keeping systems blend arbitrary invention with natural rhythm, and how my daily life sometimes feels constrained by one more than the other. Combined with the life experience of the Chinese people, the measurement of time in agricultural societies relies more on natural cycles and astronomical phenomena, such as the four seasons and the twenty-four solar terms. Thi...

I'm so amazed! The Mesopotamians had such advanced mathematical knowledge so long ago! Their invention of the place value system and methods for solving quadratic equations are still incredible today. Not to mention, they even discovered the Pythagorean theorem! This completely overturns my understanding of ancient mathematics. It turns out that human intelligence was so brilliant even in the distant past, which is truly admirable! This image makes me wonder how people in ancient times gradually built up mathematics. Mathematics is not the sole possession of any civilization; it is the collective fruit of human intellect. Between different civilizations, people formed a vast network, their understanding of the world flowing like rivers, intertwining and expanding, eventually shaping the grand tapestry of mathematics. In my history studies, I've long focused on politics, economics, and culture. We often concentrate on tangible technological advancements like papermaking and th...

  Speculative Phase: When I think about why the Babylonians might have chosen base 60, one of the first things that comes to mind is how divisible the number 60 is. It can be division by so many numbers—1, 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30. This makes it really convenient for doing calculations, no matter odd numbers, even numbers, multiples of five. In comparison, base 10 is much simpler, but it only divides easily by 2, 5, and 10. Using 60 would have made dividing things like goods, land, or even time much easier and more precise. I also think about how we still use 60 in modern life. For example, we divide an hour into 60 minutes and a minute into 60 seconds. Maybe they noticed patterns in the movements of the stars or planets that led them to use 60. In some ways, it reminds me of how the Chinese zodiac is based on a 60-year cycle, and the traditional 60-year cycle , known as the Ganzhi or sexagenary cycle, is used to track years. This system combines 10 heavenly stems...

  Whether math history should be incorporated into my teaching: I think math history should definitely be part of the classroom, even though I haven’t used it much in my teaching so far. Back when I was a student, those little historical stories at the end of each chapter always caught my attention, even if my teachers never really talked about them. I’d read them and think, “Hey, if I lived in ancient times, maybe I could have been a mathematician too!” The way they solved problems wasn’t all that different from how I would’ve done it—kind of amusing to think about. Why math history should be incorporated: In my own experience, math history made me really curious about how those formulas and theorems came to be. Without calculators, how on earth did they manage such complex calculations? I couldn’t even wrap my head around it. I’m sure a lot of today’s students have similar questions when they’re learning, and introducing the history behind these discoveries could make math fe...