Word Problems

When I was growing up, we had math problems. Somewhere between my grade-school experience and my daughters', a distinction arose. There were math problems that consisted of simply numbers and operations...and there were word problems. The former variety were simple; all you had to do was add, subtract, multiply or divide the given numbers till you came up with an answer. The latter were a different story. (Oddly enough, they are also called 'story problems'.) These are the legendary questions that begin "A train leaves Southville at 10:45 am; a second train leaves Northville a half hour later..." These are the problems of which nightmares are made. Not only do you have to perform the right operations, but you have to figure out what the operations are, and often, what the numbers themselves are. The possibilities for error are limitless. These problems were made for the invention of 'partial credit'.

Now, I always used to enjoy the challenge of this type of problem--though I realize many of my compadres did not. I liked figuring out the puzzle of what stood for what, and how to convert real-life activity to neat numerical representations. (Imagine the thrill when I found out that calculus allowed me to figure out the volume of a doughnut, or some other fanciful shape!) I majored in chemistry, and the math involved only made that study more amazing to me.

But..back to real life and the mathematical transcription thereof. My students, when faced with this type of problem, always moaned and groaned that they hated word problems! Of course they did. They demanded more; insisted that they really understand what was going on...Horrors! My patented response was that life itself was a word problem--and it is. There is hardly ever a clear-cut equation or set of operations that will answer any of the questions that arise in day-to-day living. The problems are always messy variations of Northville and Southville, with limited time and resources available, and you've got to come up with some sort of answer, whether you understand all the parameters or not. If nothing else, word problems teach us how to set out what we know in an organized fashion--and then think about what we need to find out before we try to build a bridge from here to there.

Sometimes the Northville train ends up on a siding, or Southville's takes a detour, depending on our level of competence. Sometimes we throw up our hands in dismay, and walk away down the track. The problems vary in importance from what to have for dinner to how to deal with aging parents, from deciding where the safest place is for retirement funds to life-or-death medical decisions. Nothing is easy, but unlike the situation in your math workbook, there is usually more than one good enough answer: not perfect, not all-encompassing, not incontrovertible, but good enough, all the same. I can live with that.