Recently I wrote one of my ex-students, a freshman at USC. Lou Talman had responded to Ron Ward (I think) and had mentioned a term I use all the time (bag o' tricks) in my class and I knew she would think it was funny. Anyway, I included some of the text of the letter and here is her response to the discussion about word problems:
"Okay, my little non-big worded brain didn't quite get the jist of what RON was talking about, but I'll just tell you what I think about word problems. I absolutely love them. Most kids hate them, because they like it all spelled out for them what's going on and how to go about solving them. Word problems make you think about what's happening, and then decide from there how you're going to approach the problem. I look at one, and if a particular stategy from class or from what I know makes sense, then I will try that way. If not, sometimes I will guess and check. Sometimes I have no idea what I'm doing on them, but when I sit down and think mathmatically about how the numbers fit together, I can figure out what its asking. As for teaching types of strategies, I think that every kid needs a basis for drawing ideas on how to solve a problem. I do not, however, think that word problems should be put into certain types, nor do I think that kids should not have leeway to solve the problem however it makes sense to them. Plus, if a teacher relys too heavily on teaching certain general ways to solve these problems, the kids are going to stop thinking through the problems, which is the purpose of them, and start "plugging in" different taught ways, like guess and check, much like you would plug and chug into a normal boring equation. I never had much trouble with word problems, because I guess from an early stage I knew that I needed to interpret the english on the page into a mathematical language that I knew how to solve. That's all word problems really are, I think. As for different methods and stuff, I really don't know what I did. I think I went more on intuition that drawing from a list of pre-determined ways to go about the problems."
Just for information: this student scored a 36 on the math part of the ACT and was in the low 700s on the SAT; ranked #3 in a class of 570 at a fairly academic public school; scored a 5 on the A.P. Math Exam (AB test); and is THE best student, both in creativity and in quality of work, I've ever had in 15 years of teaching.