Tuesday, February 1, 2011

How to Answer a Question 101

Some of the most highly respected people in this world are the fictional characters in word problems – those people who need to double recipes, buy enough fencing for their yards, or sell enough tickets to generate a certain profit, and ask for our help because they haven't learned the math themselves. And by "respected" I don't mean "admired."  I mean a more basic kind of respect, like respecting other people's decisions.  Most of us have probably shown more respect to these people than we would to anyone who asked the same questions in real life. 

In an algebraic equation, you have variables that you need to solve for, but the rest of the numbers are fixed factors.  In word problems, we treat each piece of information the same way.  If Mark wants to bake enough double-layer cakes to serve 100 people and one double-layer cake serves 10 people, we would say that Mark needs to bake 10 cakes to serve everyone.  We don't suggest that he make a sheet cake or cupcakes instead of a double-layer cake, or that he ditch the cake idea altogether and bake cookies instead.  We accept Mark's choice as a fixed factor. 

But things don't work that way in real life.  Just to ask a question, just to bring up a problem, you have to be prepared to defend your position - to explain why you want to fence in your entire yard, or repaint every room in your house, or bake and frost 10 double-layer cakes to feed 100 people.  Sometimes it seems like the only place where we accept each other's decisions, where we don't act as if other people owe us an explanation for their actions just because they're not doing what we would have done, is in the fictional world of a word problem.  I hope that one day we can show each other the same respect that we once showed to the people in our homework assignments.


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