I almost found it humorous that the practice of doing "impractical" problems has outlived the Babylonian number system. And not just the Babylonians, but many diverse groups over generations of time spread out from all over the world. First thoughts is that explaining mathematical concept is a "human" problem, and for all of the inventions and technologies that have improved over time, it is surprising that we couldn't find a way around explaining mathematical concepts. I definitely feel the "empathy" that Gerofsky brings up, and something feels good knowing that humans thousands of years ago, living in much more primitive times, have faced the same abstract problems.
Much of the reading led to more questions, What exactly is it that made it hard for the Babylonians to theorize, like what about the abstractions was hard to express exactly? How did it help having to explain it in problem form? How much "theory" did they really understand? How different is it to understand math in the context of made up problems? Did they have a need for a more general mathematical thinking approach? What is it about the Greeks is it that made theorizing easier? I have more questions than I did before reading the chapter, and I am excited to dig in to these concepts.
Your reflection is curious and insightful. I appreciate how you connected the persistence of “impractical” problems across history with the human struggle of explaining mathematics, and how you captured the sense of empathy with learners across time. The questions you raise about Babylonian abstraction and the shift to Greek theorizing show deep engagement with the reading.
ReplyDeleteTo strengthen your response, you might focus on developing one or two of your questions further, connecting them more clearly to the chapter’s central debate about word problems as method-training versus concept-building.