Aspects of Word-Problem Context That Influence Children's Problem-Solving Performance
Wiest, Lynda R., Focus on Learning Problems in Mathematics
Students tend to deem word problems one of the most distasteful and anxiety-inducing tasks in the mathematics classroom. They--at least those in the United States--perform poorly on solving word problems (e.g., Kouba, Brown, Carpenter, Lindquist, Silver, Swafford, 1988). Educational-equity issues also surface in relation to this important ability. Girls perform more poorly than boys in solving word problems (Fennema, 1989), particularly the less routine types, and other student subgroups may respond differentially to word problems as well.
Because word problems are difficult for students and play a key role in mathematics instruction, it is worthwhile to seek improved ways of constructing them. The result can lead to enhanced student thinking and insight into which problem aspects impact students' problem-solving performance and in what manner. One aspect of word problems that some researchers have found to impact student performance is problem context, or "non-mathematical meanings present in the problem statement" (Kulm, 1984, p. 17), for example, the "story" in which the mathematics problem is set. The influence of problem context is an important area that has not been studied extensively (Chipman, Marshall, & Scott, 1991; Harvey, 1987). Context as used here refers to the verbal aspect of word problems only (including numerals). It does not encompass other modes of problem presentation, such as concrete or pictorial formats, or the environment in which problems are solved (e.g., classroom climate).
In this article, I discuss aspects of word-problem context that appear to influence students' problem-solving performance. These aspects are gleaned mainly from a study conducted with fourth-and sixth-grade students (Wiest, 1996/97), but also from literature detailing similar work by other researchers.
Kuhn (1984) says problem context may help problem solvers give meaning to the mathematical content in a problem and that it is likely to influence, in particular, the problem-solving stages of understanding a problem and planning its solution. In addressing the potential influence of word-problem context, Ross, McCormick, and Krisak (1986) say, "Learners bring different knowledge structures to a task ... what comprises a meaningful presentation for one student may not be very meaningful to another" (p. 245). Bickmore-Brand (1990/1993) says context is foundational to mathematical activity: "Context is paramount to the construction of meaning the whole way through. It is the backdrop against which the parts have to make sense" (p. 3).
One way problem context may influence problem-solving performance is through the degree of interest and, hence, motivation it sparks. It may inspire problem solvers to engage to a greater degree in a problem and to persevere longer in solution attempts (cf. Boaler, 1993b, 1994; Murphy & Ross, 1990). Thus, affective variables, in addition to problem-solving success measured by correct solutions and answers, are worth considering.
Hembree (1992) conducted a meta-analysis of 44 studies, including study samples ranging from students at the fourth-grade through undergraduate levels, in which problem context was varied while mathematical structure was held constant. He classified the context manipulations as abstract vs. concrete, factual vs. hypothetical, familiar vs. unfamiliar, imaginative vs. ordinary, personalized vs. impersonal, and preferred vs. nonpreferred (indicating whether or not students chose or were assigned problems they solved). Hembree concluded that better performance was most strongly associated with familiar contexts, a finding corraborated by Kouba et al. (1988) in examining the results of the Fourth National Assessment of Educational Progress. Concrete and imaginative problems in Hembree's meta-analysis, the latter using fantasy or unusual circumstances, showed borderline significance in having positive effects upon students' problem-solving performance. …