The first stop… the third word problem??? “A woman dies leaving a husband, a son, and three daughters” is the starting line??? But in all seriousness, word problems listed at the start of the chapter are all very practical situations that I can see multiple civilizations encounter. Some of those questions are definitely not appropriate to be used in the classroom nowadays, but it’s very interesting to see the shift from practical word problems into more “theoretical ones.” For example, we have the dad buying 200 watermelons as part of a word problem. Another interesting point in the chapter is how Babylonian math is based on methods while Greek math is based on problems. This feels like the difference between relational and instrumental understanding in the ancient times. Seems to me that the Babylonians focused on instrumental while the Greeks focused on relational. Just like how many modern mathematics focuses on knowing how to calculate something instead of why we calculate something, the Babylonians seem to focus on the arithmetics of math more. Their word problems reward those who are good at doing straight up calculating, whereas the Greeks seem to reward those who understand the concepts of math and those who can extend their understanding to other problems. This seems pretty logical, since the Greeks excel at geometry and the discovery of many modern mathematical concepts.
This begs of the question of the types of word problems we should use in our classrooms. I think it’s quite interesting that the Babylonians use the more practical word problems, since back then, before the modernization of technology, math can almost be life or death to them. If they don’t figure out the optimal crop configurations, they might starve the next winter. Whereas now, if we don’t figure out the area of an elliptical farmland that we probably can’t afford to buy, it doesn’t affect our survival. The ancient Babylonians needed to be proficient in those calculations to make sure that their civilization is held up together. Practical word problems are just as important as the more theoretical word problems, since practical problems is what we prepare the future generation with when they become adults. So as a teacher, it’s important to implement topics such as estimation taxes in the percentages unit, understanding the unlikeliness of winning the lottery in the probability unit, and predicting the value of compound interest in the exponents unit.
Interesting comments. I always wonder whether Babylonian mathematical discoverers/ inventors only wrote down the practical solutions, but also discussed the more theoretical ideas -- but when it came to the knowledge level of each scribe, it may have been largely instrumental! Good points about students today being able to calculated in certain areas to be able to thrive in the world.
ReplyDelete*calculate, not calculated!
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