Monday, July 02, 2007

Word Problems Are Not That Much of a Mystery

Most of it is just common sense

Many times, my students are surprised by how simple some problems seem when I explain them. They go "Is that all there is to it? Can it be that simple? You didn't use any formula!"
A big part of the difficulty students often have with word problems is they think there is or there should be a special type of formula suited for each particular problem. But, for many word problems out there, that is not the case.
If your first reaction to a word problem is trying to remember a formula that would solve that problem, chances are you are never going to remember such a formula, because you have never seen it, because it is not there in any book, and no teacher teaches it as "the" formula for this problem.
There may well be a formula for that particular problem, but the formula is nowhere to be found on record. Because nobody has bothered to figure it out or to pass it down, because even if they did, the formula would be applicable only to that particular word problem and to no other problem. It would be a very limited, almost useless formula.
So, the first thing you have to do with word problems, is to forget about formulas altogether and just read the problem, over and over and over again, as many times as you need to understand what the problem is talking about, what situation it is describing.
You want to really understand the situation, the process described in the problem. You want to understand it as clearly as you see sunlight. You want to be able to express it in your own words, you want to be able to imagine it, you want to be able to tell a story about it, you want to be able to draw a complete picture of it.
Once you do that, the solution presents itself to you naturally, the numbers practically work themselves out. When you really know what is going on, you know what to do, you know what operations to perform, they make sense.
So, again, it's not how to mechanically make the problem fit into a canned formula, but how to make your very own mind wrap itself around the problem completely, with total abandon, accuracy and precision

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