Key Contextual Features of Algebra Word Problems: A Theoretical Model and Review of the Literature.

One of the four algebra word problem structures found in K-12 textbooks is the propositional relation structure (Mayer, 1982). This type of problem asks students to establish equivalences between the variables or noun referents in the problem. The literature available indicates that students have inordinate difficulties, when trying to solve a propositional relation type of problem. The literature says little about how key context features are assigned to the text of the algebra word problem and how these features affect student performance or preference of algebra problems in general. Three key context features of algebra word problems were identified: familiarity, imageability, and variable type (discrete or continuous). These three key contextual features have been shown to have performance effects on arithmetic and algebra problems. The analysis in this paper examines these key context features of algebra problems in relationship to pictorial, symbolic, and verbal representational formats. In addition, an information processing model of the algebra word problem solving process is presented. The ways in which key contextual features may influence problem processing and the construction of solutions is discussed. This paper supplies a rationale, definitions, and a procedure for assigning key context features to an algebra word problem of the propositional relation type. These procedures were used to construct a set of 16 algebra word problems that systematically varied the key contextual features identified. These problem are proposed to be used to study several variables that may be important to understanding the nature of difficulties students face when solving a problem with a propositional relation structure. The model developed and presented could be generalized to other algebra problems of different structures or other domains. (Contains 45 references.) (MDH)