It does appear that we have continued to use word problems throughout all of our math history, from the Babylonians to our modern classrooms. I agree that the ancient people of Babylon probably used word problems as a way of practicing problem types. I think that it’s unlikely that the ancient Babylonians had a good system of creating problems the way we have, and so putting a problem into words was the best way to convey the problem. Even in more recent times a problem would be given in words. The following is a recreation of a math problem and its solutions. I think that this helps to highlight that these problems (which would not have been expressed algebraically) are ways for earlier mathematicians to work on complex problems. https://old.maa.org/press/periodicals/convergence/recreational-problems-in-medieval-mathematics-men-buying-a-horse
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To expand on the idea that I was trying to get at previously, in modern day we can express many problems in abstraction through algebra. A problem like A^2 + B^2 = C^2 is abstracted from the graphical format which it originated with algebra. If we wanted to consider the same problem in the ancient world, we might have to begin by explaining the rules of our problem and drawing it. We have also reduced the need for explanations through a long history of education, a quadratic does not need a context for it to have a solution or root. Given a problem like x^2 -2 =0 we know how to solve it without context or explanation, but in the ancient world people would not readily know the type of problem simply from numbers. To that end they needed context and diagrams to better understand the problems which appeared in their lives, or math that solely existed for fun.
Benn, you make a clear point about how word problems served as practice tools before algebraic notation. To strengthen your reflection, you might compare their role in Babylonian times with how we use them in classrooms today.
ReplyDeleteThanks for the link to the interesting piece on the classic 'men buying a horse' problem too.
ReplyDeleteThanks Ben! I appreciate how you expanded your earlier idea by contrasting ancient and modern approaches to abstraction in mathematics. Your explanation of how algebra reduced the need for context while ancient mathematicians relied on narrative and diagrams demonstrates a solid grasp of the historical and conceptual shift. The final point about math existing for fun nicely ties back to the spirit of the Babylonian problems discussed in the reading.
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