Response to the Readings on Time and Base 60

The first point that I noticed was the difference between the two articles in explaining why base 60 was used. I do not think there is a direct factual inconsistency. The Scientific American article explains that 60 is very convenient for expressing fractions, while the St Andrews article agrees with this mathematical advantage but questions whether it can explain the historical origin of the system. If divisibility were the only reason, then we might also ask why people did not choose 12 or 30 as a base. I think this is an important point for teaching. When we teach the history of math, we should tell students clearly whether we have solid evidence for a fact or only a well-supported explanation. More importantly, we should help them understand how mathematical ideas may develop through practical needs. The educational value is not only knowing who invented something or why a system was chosen, but learning how mathematics is connected to real human activities and why my students are learning math.

The second point that I noticed was that the Babylonian system could still work even though it had no true zero and no clear sexagesimal point. That reminds me of a problem in teaching. In many textbooks, we can find expressions saying that the limit of a function “equals DNE.” Strictly speaking, this is incorrect, because DNE is not a number. However, at the beginning, teachers sometimes need to balance students’ understanding with a fully rigorous definition. I think we should tell students that this notation is not formally correct, but we can temporarily allow them to write it when everyone understands what it means and there is no ambiguity. On the other hand, if a notation can cause ambiguity, it must be treated more seriously. For example, in trigonometry, if an angle is written without a degree symbol, it is normally understood to be measured in radians, and I must explain this clearly in class. Therefore, the Babylonian example makes me think that mathematical notation does not need to be perfect as long as it works, but teachers need to help students understand when an informal notation is acceptable and when precision is necessary.