9.18-Babylonian-style base 60 multiplication table for 45

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9.18-Reflection - Babylonian word problems

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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...
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9.23-Response-Ancient Egyptian mathematics: Numeration

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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 ...
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9.16-Response-History of time calculations, base 60 and base 12

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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...
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