József Kontra: The role of linguistic and structural variables in solving mathematical word problems

Most theories of mathematical problem solving hold that students' performance on algebraic word problems is best interpreted by assuming that there are differences between the text base, i.e. an elaboration of the verbal formulation of surface structure into propositions, and the situation model, i.e. the representation of the situation presented in the text. The first section of this paper addresses issues of problem categorisation and representation. Three aspects of mathematical word problems found in textbooks are discussed, namely, content, generalisation and abstraction. The empirical findings presented tend to confirm the important role of linguistic and structural variables which describe the textual statements of story problems. 32 problems on uniform rectilinear motion, arranged into 4 tests, were administered to 630 students in the 9th grade. The system of 31 variables developed by Lepik (1990) was applied in the research reported, complemented with several additional variables newly introduced. The ratio of correct responses to the individual items was used to assess student performance. Reliability issues are emphasised in the discussion of the results, including an examination of the effects of the above-mentioned variables on reliability (in order to make it possible for teachers to construct more reliable classroom tests by modifying certain task characteristics under their control). The results regarding difficulty levels are consistent with those of Lepik, i.e. most variables appeared to be good predictors of the performance measure used. These findings suggest that an appropriate readability level cannot be a neglected component of student success with word problems. However, in order to comprehend a problem, students must see how the bits of information (variables) fit together in a coherent whole (schema). Finally, it was found that the number of formulae required to be applied in solving the problem may influence task reliability. In this context, another significant factor appears to be the proportion of words with 9 or more letters. Some implications of the findings are discussed with regard to teaching.

MAGYAR PEDAGÓGIA 101. Number 1. 5-45. (2001)

Levelezési cím / Address for correspondence: Kontra József, H-7400 Kaposvár, Ezredév u. 10.

 
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