Most students fear word problems.

I would believe that if the statement were re-worded to say "A great many high-school students feelings about word problems range from dislike through hatred and fear."

But the statement begs the question of why is that so. And it is that question that is important. If you have difficulty doing the highly stylized and unnaturally simplified problems called "word problems," you will never be able to apply mathematics to the actual problems to which mathematics can give answers or help to give answers.

My personal feeling is that the inability to master word problems comes from a defect in teaching. We do not stress, at least not enough, that mathematics is a language the purpose of which is to find an answer from what is already known. Now I do not believe that there is a universal technique to translating a problem described in a natural language into the language of mathematics. Indeed, many problems cannot be translated at all, such as what should I get my wife for her 75th birthday. So perhaps the first step outside a classroom is to ask yourself, "Might I be able to translate this problem into a mathematical problem that I know how to solve?' So, I might suspect that a problem could be solved by measure theory. I have not a clue about measure theory. When I hear that some theory is based an atomless measure space, I know that I must (1) give up, (2) take a course, or (3) find an expert.

Now this of course is not an issue for students in a class or reading a text. Their word problems are specifically designed to let them exercise techniques that they have already been exposed to. So, given that I suspect math can help me, my next question is whether I can translate what I do know into mathematical language. If the answer is yes, then I do that and

**write it all down**.

students should be strongly encouraged to do this. I might go so far to say that it ought to be a requirement on homework for high school students. At least it would stop them from saying "I don't even know where to start."

My next question is whether I can translate what I am looking for into mathematical or quasi-mathematical language. If the answer is yes, then I

**write that down**. In an algebra class, that would usually be something like

\(\displaystyle x = \text {a numeral}\) or \(\displaystyle x = \text { an algebraic expression.}\)

Now we no longer have a word problem. We are now concerned only about what mathematical techniques are in our tool box let us go from what we know to what we want.

I have worked with students who can do mechanics til the cows come home, but (to retain my bovine metaphor) are buffaloed by translation. That indicates to me a serious deficiency in how the subject is taught.