In the first article by Scientific American, Michael A. Lombardi (2007) reflects on the origins of the sexagesimal system, proposing that the base-60 system may have developed from observations of the positions and intervals of the sun, moon, and stars. In contrast, O'Connor and Robertson (2000), writing for MacTutor, present multiple theories- including Theon's divisor explanation, Neugebauer's weight system reasoning, and their own interpretation. They suggest that the Babylonians may not have chosen base-60 by looking to the heavens, but rather adopted it in a way similar to how we arrived at our base-10 system- by simply observing their hands.
While Lombardi's (2007) explanation feels more "scientific" in its astronomical reasoning, I find O'Connor and Robertson’s (2000) argument more intuitive. It seems likely that the need for a counting system emerged from everyday practical needs, long before anyone began carefully studying the movements of celestial bodies. This also makes me think about how deeply ingrained our understanding of "how to count" is. We’re accustomed to counting to ten using our fingers, but other cultures—such as those in China or the Middle East—have developed entirely different counting methods.
The idea that number systems could have originated from something as simple and universal as counting on one's hands makes the subject feel much more human. While we may think that counting to 60 using our finger joints is strange, perhaps we should also question our own entrenched assumptions about what “counts” as counting or mathematics. It reminds me that foundational mathematics is not only shaped by abstract reasoning, but also rooted in the tangible, lived experiences of people trying to make sense of the world around them.
This could also be a fun and engaging classroom activity at the beginning of the year: simply asking students how they count. It would open up a space to explore the diversity of counting methods across cultures and encourages students to reflect on their own assumptions about numbers. From there, the class could dive into the sexagesimal system- perhaps by working with fractions or time measurements- as a way to show how different systems can be both practical and deeply rooted in history. Activities like this can help students see math not just as a set of rules, but as a reflection of human creativity, culture, and problem-solving across time.
Jagatia, A. (2021, September 3). How the way you count reveals more than you think. BBC Future. https://www.bbc.com/future/article/20210902-how-finger-counting-gives-away-your-nationality
Lombardi, M. A. (2007, March 3). Why is a minute divided up into 60 seconds, an hour into 60 minutes, and only 24 hours in a day? Scientific American. https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/
O’Connor, J. J., & Robertson, E. F. (2000, December). Babylonian numerals. MacTutor History of Mathematics. University of St Andrews. https://mathshistory.st-andrews.ac.uk/HistTopics/Babylonian_numerals/
This is an excellent reflection that weaves together the readings, your personal interpretation, and meaningful classroom applications. I especially appreciate how you highlight the cultural diversity of counting and propose a creative activity for students. It shows deep engagement with the material and practical insight as a future teacher. One way to enhance your reflection even further would be to briefly connect back to the historical details (like the sundial or water clock) to balance the cultural perspective with more of the historical context from the articles.
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