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New about realworld problems
Posted:
Oct 27, 1995 8:19 PM


`Journal for Research in Math Education'. Jack Price's article `President's Report: Selling and Buying Reform: If we build it, will they come ?' P.488: ``We already have consensus from the major mathematics organizations and have mounted extraordinary efforts to help teachers understand and use the standards.<...> it is only the beginning if we wish to sustain the efforts necessary to realize our vision.''
A few days ago some members of this list (who usually do not participate in the exchange of opinions) claimed `for the record' that President Price does not insist on implementation of the `standards'.
P.488: ``Many people, both inside and outside the mathematics community, have made some strong, but uninformed, accusations about the standards <...> At best, these statements are misinformed; at worst, they are meanspirited or selfserving.''
So, there has been NO valid criticism of the `standards'.
P.489: ``Second, some problems do have one right answer arrived at through one specific method. But in real life, far more problems are encountered that may have two or more right answers or may have one right answer but permit multiple solution methods. Remember George Polya's fourstep method of solving problems; the last step is ``look back''.''
Problems with two or more right answers certainly exist, for example, many quadratic equations. What is so exciting about it ? And what does Polya do here ? Did he ever classify mathematical problems into `reallife' and `nonreallife' ones ?
Problems which can be solved in two different ways certainly exist and are useful. Collections of olympiadstyle problems contain good examples. But in the Standards such problems are rare. Can somebody find a problem, which is solved in two different ways in the `Standards', so that we could enjoy and discuss it ?
Andrei Toom toom@thecollege.iwctx.edu



