Dear Editor: Word Problems: Applications vs. Mental Manipulatives

Thank you for giving place to articles on word problems [1, 2]. I am concerned with word problems very much and would like to say something about them also. First of all, in my opinion, any discussion should include a definition of the subject and in such situations it is better to keep as close as possible to the exact meaning of the words. I suggest that a non-word problem is a problem, which is formulated using mainly mathematical symbols and only a few special words like " Solve the equation... " Correspondingly, a word problem is a problem which uses non-mathematical words to convey mathematical meaning. At the K-12 level non-word problems tend to be technical exercises, which are necessary, but not exciting. It is only natural that most interesting and non-standard problems are word problems. It does not mean that all word problems are difficult, but all of them need understanding of the natural language and ability to translate between different modes of representation: in words, in symbols, in images. This is similar to Thomas' main idea [2], although I do not quite agree with his treatment of solving equations. In America word problems are often considered difficult and unpleasant. There is a well-known cartoon of the 'Far Side' series, which shows Hell's library, consist