Response to Gerofsky, "The History of the Word Problem Genre"

 I would wager to bet that outside of a few specialists and students of the history of mathematics, the response to finding out that mathematical word problems have a history as long as the history of human written records would be one of surprise and perhaps even incredulity. "Why would word problems be that important?" is the question I imagine many people would ask. It is also the question I found myself asking as I read the opening portion of Gerofsky's chapter.

First I must confess that though I was aware the Babylonians had a sophisticated mathematics, before this class, I was unaware that the word problem genre had been a part of it. When I learned that it was, my next assumption was exactly the one Gerofsky identifies early in the chapter: that Babylonian mathematics (including word problems) was "'merely practical' as opposed to later Greek abstract, theoretical mathematics. So the main "stop" for me in this reading was the insight of Eleanor Robson (as explained by Gerofsky) that the problems in Babylonian mathematics "functioned on two levels...On one hand, they taught practical skills and tested methods to future scribes; on the other, 'many of those methods no longer had real-life applications.'" As Gerofsky summarizes it, Robson's concept was of a Babylonian mathematics which was "at one potentially useful and obviously impractical."

This, it seems to me, could stand as a summary statement about mathematics as I have experienced it and intend to teach it. It reminds me that the point of mathematics is not to be "practical," though astonishing real-world applications have followed from many branches of mathematics, sometimes quite unexpectedly. When my 14-year-old daughter asks, as she does somewhat regularly, "When will I need to use this in real life?" my reply is straightforward: "Probably you won't. You should find other reasons to study math."

I answer in this way because I think - and it seems the Babylonians also thought - that there are benefits to doing mathematics that go beyond "practical" daily life application. I'm not sure how they would have explained it, but for me, math is a way of looking at the world, a way of stretching and training our minds - even a way of appreciating beauty. And it's fun, which I can't help but think was part of it all in Babylonian times too.

I recognize that one could debate whether "word problems" themselves are fun. Perhaps not as we usually encounter them in mathematics textbooks today. But part of the insight of Gerofsky's chapter is that for the Babylonians, such problems (often impractical) were the only means of discourse available for the expression of mathematical ideas. My question coming out of this reading is: what in our mathematical discourse is the equivalent? Perhaps emphasizing the abstract side of math has done some of our students a disservice. Is there a way we as mathematicians and teachers of math can use "word problems" or something similar to express deeper mathematical thinking, even to lead our students forward in their understanding, rather than merely "disguising" routine math in a way that leaves many students feeling tricked? Perhaps I can find out more by reading the rest of Gerofsky's chapter someday!