The Specific Type of Problem in Arithmetic versus the General Type of Problem

Abstract

To what extent does the solving of a specific problem in arithmetic develop general problem-solving ability; that is, to what extent does the solving of a certain specific problem develop ability which will function in the solution of similar problems? In other words, to what extent are pupils, after solving a certain specific problem, able to formulate a general conception whereby the principle involved in solving the problem will become generalized and thought of as applying to all problems of a similar nature? Do problems that contain numbers and thereby become specific and problems that contain no numbers but are of a general nature have different effects on the pupil? Are problems containing numbers easier or more difficult than problems which do not contain numbers but are.more general in type and involve general principles? Many teachers think that, if they give a sufficient number of specific problems, the pupils will draw conclusions from the solving of these problems and make generalizations. On the other hand, many teachers think that pupils should be given practice in solving problems of a general nature; they think that it is not enough to give practice on specific problems, that pupils should have some practice in solving problems of a general nature if they are to be successful in thinking in general terms and in applying arithmetical principles. The writer attempted to devise a test to determine whether problems with numbers or problems without numbers are more readily understood by pupils. Two lists of problems were prepared. List A contained problems of a specific nature, problems with definite values expressed in numbers. List B contained problems of a general nature, problems with no definitely expressed values. Three of the problems from each list follow.