Marc Vidulich recently posted a paragraph or two (written by a former student of his who is now a freshman at USC) about word problems.
We should observe that this student is unusually articulate, even for a college freshman. At the risk of being flamed for bringing up standardized tests, I would like to point out that just about everyone I've ever met who was successful at mathematics had rather high verbal scores (frequently even higher than their math scores) on the SAT or similar exams. My own experience in having students write journals in college mathematics courses at the freshman/sophomore level suggests that there is a high correlation between verbal strength and the ability to succeed at mathematics. We probably should not be surprised to find that students who solve word problems well also handle semantics well; after all, the troublesome part of most word problems for most students is the essentially *semantic* transformation from natural language to formal language.
Someone recently posted some remarks (which I seem to have deleted in an uncharacteristic bout of housecleaning) lamenting deficiencies in students' formal training in grammar. I think that's another piece--the syntactic piece--of the puzzle, though my memory of the post was that I thought it was a little off the mark. I think that the connection that author seemed to perceive between grammar and linguistic skills wasn't the important one. Having taught both algebra and programming, I'd say that the important connection is in a student's ability to handle syntax; the student who makes consistent troublesome syntactic errors in programming is the same student who mishandles algebraic transformation consistently. (Other people have remarked on this phenomenon, too--especially folks in the Calc-Reform movement who've been trying to integrate computer algebra systems with calculus.) But I think that this has little bearing on the word-problem problem, because the word problems we usually pose in our algebra courses involve very little syntactic difficulty *once one has made the necessary semantic transformation*.
These are, I am sure, only pieces of the puzzle, but important pieces. I haven't a clue how they fit together, nor what other pieces there may be. Where the observation that linguistic abilities are important in mathematics takes us, I don't know.
The big paradox here is that the students who need help the most are seemingly the very ones who aren't articulate enough to describe their troubles...