Solving arithmetic word problems: Role of reading and computational skills.

Abstract

Investigated how children cope with some of the demands imposed on them by arithmetic word problems by administering problems modeled after those used by the National Assessment of Educational Progress to 200 6th-graders. A computational demand was imposed on the Ss by adding extraneous information to the problems, whereas a reading demand was imposed on them by increasing the syntactic complexity of the problems. Multiple regression analyses indicated that the Ss' computational ability and reading ability together accounted for 54% of the variance in solution accuracy: Eight and 14%, respectively, of this variance was unique, whereas 32% was common to the abilities. In addition, the analyses indicated that the presence of extraneous information in the problems reduced the accuracy of Ss' solutions. The use of complex syntax had no significant effect on accuracy. The findings suggest that reading ability and computational ability both play important roles in children's successful solution of word problems. The findings also suggest that the presence of extraneous information in word problems can impose a formidable demand on children's limited processing capacities. (14 ref)

Individual differences in the development of skill in mental addition: Internal and external validation of chronometric models

“…This latter finding may imply the existence of a common retrieval component that activates items in long-term memory (cf. Horn 1988) and is consistent with results reported by Muth (1984), who found a moderate relationship (r2 = .37) between reading ability and computational skill. On the other hand, rather than forcing an interpretation on the relation between Addition Efficiency and Reading Skills, we presume that, if a cognitive component score reflecting word retrieval had been available on all subjects, the path from Addition Efficiency to Reading Skills would have been greatly attenuated.…”

A cognitive analysis of number-series problems: Sources of individual differences in performance

“…Similarly, striking individual differences exist in manipulating numerical information (e.g., Hunter, 1977). Recognition of memorized series and calculation may well be domain-specific forms of knowledge, but they probably are not task-specific: both procedures may be applicable to a wide variety of tasks that require numerical skills (Holzman et al, 1982;Muth, 1984). In contrast, checking and self-termination are related to efficiency and may well be both task-and domain-independent, but neither characteristic appeared to be related to skill in Experiment 2.…”

Contextualization in Perspective

“…Renninger, Ewen, and Lasher (2002) showed that when the domain is personalized to student's own interests, such as training dogs or ballet turnout, this can potentially limit strategies and mask a lack of knowledge. Part of learning in any domain is distinguishing between relevant and irrelevant information, the addition of extraneous information that might be confused for relevant information can easily increase demand (Muth, 1984).…”