The best answer

The other day, E, who is in third grade, had math homework. One of the problems read as follows:

Patrick purchased 12 books. He needed four books for each of his research projects at school. How many projects did he have? _____

The space designated for the answer was a short black line about one centimeter long. There wasn't enough room to write "This is a seriously messed up question," so E wrote "3."

The word problem asks a complex question, worth deconstructing. What assumptions are we to make about Patrick and his research projects in order to obtain what test-designers would likely call "the best answer"?

Consider: Who is Patrick? Presumably he is a student, for part of his life is spent "at school." There is, of course, the possibility that Patrick is a grown-up. Maybe he is a bearded Duke social scientist in a tweed jacket, or a bright, enthusiastic doctoral student in Education at UNC, conducting research projects on third graders. But since the whole point of word problems is to simulate real-life situations in which knowing rudimentary math is a useful skill, the pupil needs to be able to identify with Patrick. Let us assume, then, that Patrick is a third-grader, like E.

Where did Patrick get the money to buy 12 books? Even if they're cheap little paperback books, like the popular Pixi books in Germany, they probably cost at least $1 apiece. Where does a third grader get $12 to blow on books? Why doesn't Patrick want to spend his money on Legos instead? Perhaps Patrick is rolling in dough because he's engaged in a profitable little sales ring at Before- and After School. What is he selling that the other kids want? Is it legal? Why aren't responsible adults intervening?

But a third grader conducting illicit money-making schemes is hardly a third grader who would be responsible about schoolwork. Clearly, Patrick values education. Perhaps he bought the books because his wealthy parents have him so over-scheduled with character-building activities--violin lessons, soccer, dressage--that he does not have time to go to the library.

Or perhaps Patrick can't use library books for his research projects because he needs to deface the books. For a science project, he needs to distill the covers: Patrick will find that the liquid component smells like artificial smoke flavoring, and he'll capture the gaseous component (oxygen) in an inverted test tube, light a match under it, and produce water. For an art project, he'll make a collage out of ripped up pages, gluing them down and painting over them with acrylics or shellac. Patrick doesn't need to use brand new books for such projects, so he chose to shop at the used books store. Smart Patrick.

But is a collage necessarily "research"? And what elementary school has a science lab and the instructional expertise to allow third graders to distill anything? No, Patrick likely bought these books in order to read and glean information from them. Apparently Patrick lives in a community where funding for the public library ran out long ago: he has a better chance of finding relevant texts at the dusty used books store, so that is where he shops, even though it requires picking through a lot of duds before he finds the gems.

The wording of the math problem--four books for each project--hints that Patrick will use every book for one and only one research project. Poor Patrick has to do three completely different projects at once, and he's only in the third grade. None of the teachers at his school has ever heard of integrated thematic instruction. Patrick's school isn't great.

Or perhaps Patrick's teachers have reached their limit with third graders who think copying information from the internet and pasting it into a Word document constitutes research. Unlike E, Patrick knows how to type and how to surf. His teachers are wise to insist on bibliographies that include at least four print sources. They thought Patrick would go to the library, but instead he went to Amazon.com because he's part of the screen generation, glued to the chair in front of his computer, unable to find useful information without the help of Google.

Obviously, E couldn't fit all of these concerns onto the short black line; aside from which, they were my concerns, not his. He knew the authors of his math book wanted him to write "3."

Sometimes the math word problems do ask students to "Explain," and space is provided for a written response. Consider, for example, another problem from E's homework:

Explain It Evan told his class that the people in his family have 14 legs altogether. Quinton said that there must be 7 people in Evan's family. Is Quinton correct? Explain.
________________________________________
________________________________________
________________________________________

E does not care much for writing, so he wrote: "yes 2+2+2+2+2+2+2=14," and then, for good measure, "14 / 7 = 2." Then E and I had an interesting discussion about "underlying assumptions" and Quinton's assumption that everyone in Evan's family has two legs. Is Quinton correct?