Did Mesopotamian scribes have algebra?

Without algebra and algebraic notation, I think general mathematical principles could still be explained, but they would be much more wordy. Instead of saying a variable, I think people would describe things similarly to how the Babylonians described quantities with ush, sag, lagab, etc. Unless we’re talking about before the Babylonians even had these traces of syncopated algebraic terms to use, then I think they would somehow use words to describe the idea of the quantity. Making generalizations very wordy but still possible. 

I don’t necessarily think mathematics is all about generalization and abstraction. A lot of mathematics, especially at the high school level, can be generalized into formulas and processes, but mathematics is such a broad subject that I don’t think everything is expressed that way. Without algebra, I think I would have a really hard time solving problems because symbolic notation is so ingrained in how I think. Reading the worksheet, I had a hard time wrapping my head around their solutions, and kept wanting to refer to modern notation because that's the language I'm used to. Especially as they also use base 60 while I’m so accustomed to base 10. Though I can imagine for them, this rhetorical algebra and base 60 felt very natural, just as symbolic algebra and base 10 feel to me

I definitely think students go through similar stages as they learn algebra. Many students can solve a word problem when the unknown is described in words, but when variables are introduced, they don’t always make the connection immediately. I’ve seen it happen often when tutoring, and it can take time for students to learn this new way of representing unknowns. 

History of Time Calculations

I never really questioned the way we divide time because 24 hours, 60 minutes, and 60 seconds feel so natural to me. When I think about hours, I picture a clock with 12 numbers, even though there are actually 24 hours in a day. It made me think about how much of the way I understand time comes from human-made systems. I also wonder whether there could be a more optimized way to divide time. Our current system seems so fixed, but it’s not perfect, as the Scientific American article discusses how there can be a minute with 61 seconds. 

When I think about a year, I usually picture 12 months, but I also think of the 4 seasons. Since I’ve always lived in Vancouver, the seasons are fairly noticeable, so I tend to experience a year more as a cycle through spring, summer, fall, and winter rather than as 365 consistent or different days. I hadn't really thought about these different ways of visualizing time before, but I can imagine everyone visualizes something different based on their own background. For example, I believe Americans use the 12-hour AM/PM format, while people overseas are more accustomed to using military time. 

I found the differences between the two articles interesting when discussing the Babylonian base-60 system. The Scientific American article focuses more on why 60 is useful, since it has many factors and can be divided in many different ways, which the Babylonian numerals article mentions too. However, the Babylonian numerals article also discusses several theories about why 60 was actually chosen in the first place, without there being one definite explanation. I was also surprised to learn that the Babylonians inherited the base-60 system from the Sumerians, and I think it’s so interesting that there are so many theories as to why the number 60 was chosen. It makes me wonder if the actual reason could be something historians haven’t even thought about yet.

45 multiplication table!

 

Crest of the Peacock introduction

When reading, one thing that surprised me was how intertwined the flow of mathematics was between different civilizations. I didn't realize there was so much cross-cultural exchange happening, especially considering how much harder communication and travel between different nations would have been at the time. I usually think of mathematical ideas as being developed by individual civilizations, so it was interesting to learn about how ideas could be shared and built upon across different cultures.

I also found it interesting that the words “algebra” and “algorithm” have Arabic roots. I never really thought about where these words that we use often even came from, and I did not realize how much the Arabic and Islamic world contributed to mathematics. I was already aware of some of the major contributions from India, but I hadn’t considered the contributions from the Arabic world to the same extent. It made me realize the history of mathematics is so global and vast. Even though I’ve taken a course on the history of mathematics before, I think I barely even touched the tip of the iceberg.

Another thing that surprised me was learning about the Maya and their astronomical observations and calendar construction. As I read it, I wondered how they were able to accomplish such an impressive feat with the technology available to them at the time.

 

Why teach math history?

 I believe math history should be incorporated into math teaching because it allows students to explore the “how” behind what they are learning, rather than focusing on the final answer or formula. I think it’s important to understand the history of how things happened and the process of figuring it out. Learning the background and reasoning behind ideas could also lead to a deeper understanding, especially with more complex topics. It could also show students that math is more than just numbers or formulas they’re memorizing; rather, it has a history that’s been developed over a long period of time through the efforts of countless groups and people. 

After reading the article, I liked how the author provided unique examples of different ways we can incorporate the history of mathematics into teaching. I particularly liked the ideas under “experiential mathematical activities”. I think these could be interesting and memorable ways for students to learn about the history of mathematics because they allow students to actually experience how mathematics was done, and it incorporates more fun into their learning. Some of these ideas were also not what I would have initially thought of, as I would first think of using worksheets or other media. I especially liked the idea of using games to explore the history of mathematics, and I appreciate that the author provided specific examples of what these activities could look like.

I was also interested in how history can be used as a “bridge between mathematics and other subjects”. This reminded me of what I’ve been learning in IB about making subjects interdisciplinary. I agree that history is an interesting way to bridge mathematics with other subjects that may appear unrelated, because when I previously thought about making math interdisciplinary, I would first think of more direct numerical connections, such as connecting math to physics. 

Hello World!

 This is a corner in the nest!!