Algebraic word problems: Role of linguistic and structural variables

Abstract

No adequate theory of instruction suitable for constructing instructional programs in problem solving has yet been created. One of the reasons for this is the fact that despite intense investigation, much about the sources of problems difficulty still remains to be learned. However, there are a number of studies that examine the effect that problem variables may have on the difficulty of word problems in arithmetic. A basic assumption of this approach is that the structure of the problem itself, to a large measure determines its difficulty level. It was assumed that the relative difficulty of word problems in arithmetic could be determined by analyzing the construction of the problem statement itself. Most of such variables fall into one of the two following groups: (1) those that describe the textual statement of the problems, and (2) those that describe a standard solution algorithm for the problem. A more detailed sets of variables for arithmetic word problems are presented, among others, in Suppes, Loftus and Jerman (1969); Jerman and Rees (1972); Jerman and Mirman (1974). The main purpose of this paper is to report the attempts made to identify and define variables that affect performance of studies on algebraic word problems. If arithmetic word problems are solved using one or more arithmetic operations, then algebraic word problems demand the use of formulae or equations for translating the problem situation from natural language to the corresponding mathematical expression. The variables considered were many, but the variables defined and used for the arithmetic problems in above mentioned studies were examined. It was decided to concentrate on defining variables which describe the textual statements of the problem. In order to describe a solution algorithm for the problem several addtional variables were formulated.