【導(dǎo)讀】(.,Lean&Clements,1981;Presmeg,1992).Inthisstudy,weclarify. 1990;McGee,1979;Sherman,1979;Smith,1964).Forexample,Kaufmann,1990,forareview).

　　

【正文】 of spatial transformations of a spatial representation. Items vary in difficulty (., number of spatial transformations to be imagined), and the limiting factor in performance on these tests is difficulty, which is in contrast to tests of spatial relations wherein the items are relatively easy and the limiting factor is speed (Carroll, 1993。 Lohman, 1988). Spatial visualization has sometimes been interpreted as the ability to construct high quality representations that are resistant to decay when plex transformations are carried out on the representations (Lohman, 1988). The construction of schematic spatial representations in solving mathematical problems might also be thought of as the construction of high quality spatial representations, in that they represent the essential information relevant to solving the problem and omit superfluous details. This research was carried out in an allboys school. Given that there are welldocumented sex differences in spatial ability, we might be concerned about the generality of the findings. However, sex differences in spatial and mathematical ability do not emerge until puberty (McGee, 1979), so these differences are not observed in the age group studied in this research. Second, sex differences in spatial ability have been found primarily in tests of spatial relations and are not found in tests of spatial visualization (Linn amp。 Peterson, 1985), which were most predictive of use of schematic representations in this study. Third, a recent study of physics problem solving carried out with male and female college students replicated this research, showing that high spatial ability students constructed more schematic spatial representations and low spatial ability students constructed more concrete pictorial images (Kozhevnikov, 1999). Therefore, we expect our results to generalize to other populations, although it is important to test this expectation empirically. Our research clearly shows that some visualspatial representations promote problemsolving success and others may present an obstacle to mathematical problem solving. Regardless of a student39。s spatial ability, it might be possible to teach students productive ways of representing problem information spatially. Instructing students to try to visualize mathematical problems will probably not be successful. Instead, instruction should encourage students to construct spatial representations of the relations between objects in a problem and discourage them from representing irrelevant pictorial details. References Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal of Research in Mathematics Education, 21, 4760. Carroll, J. (1993). Human cognitive abilities: A survey of the factoranalytic studies. 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