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nonroutine problemsolving
Posted:
Dec 19, 2000 12:39 PM


The issue of importance to me is not whether a particular problem is routine to the mathematical community. It is whether we confront students with problems that are not routine _to them_.
I have seen many texts in which all the exercises are exact copies, except for the numbers, of one of the examples. Students have only to identify the appropriate example and then work several exercises in exactly the same way  they do not even need to read the problems!
This practice of presenting students only with problems quite close to those they have seen has, I fear, become quite common. I have had students, even in nondevelopmental courses, object that a problem on a test was not like any example we worked in class. Less commonly, I have had students who tried to work every problem on a test in exactly the way we worked the last example in class. These students clearly are not thinking about problemsolving; they are performing a mindless ritual.
Perhaps this is off the point, perhaps not. A psychologist at my school recently told me that students who have problems with authority are frequently very mathanxious. My first reaction was, I had (have) problems with authority! I always liked math because I didn't need no stinking authority to tell me what was right.
Another possibly tangential comment. I have occasionally watched a math for the GED presentation on the state network  never for long, I admit; it's just too dull. The teachers do a fine job of explaining _what_ to do; but as far as I can tell, they never say a word about _why_ we do that.
If I can tie these disparate threads together, it looks to me as though mathematics education has really lost its bearings. Students are learning procedures and algorithms that will give the correct answer, but they are not learning what makes the answer correct or how to judge it correctness for themselves.
Forsan et haec olim memenisse juvabit. (Someday even this may be a pleasant memory.) Aeneid Virgil
>  > From: RWW Taylor > Sent: Tuesday, December 19, 2000 11:07 AM > To: mathedcc@mathforum.com > Subject: A vanishing breed... > > Jodi Cotten recently asked on this forum: > > > Please give an example of what you consider to be a nonroutine > problem. > > **************************************************************************** * To post to the list: email mathedcc@mathforum.com * * To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.com * * Archives at http://mathforum.com/epigone/mathedcc/ * ****************************************************************************



