外文翻译---视觉-空间表征的类型和数学问题解决
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1、PDF外文:http:/ Journal of Educational Psychology, 1999, 91, 4, 684-689. Types of Visual-Spatial Representations and Mathematical Problem Solving Mary Hegarty and Maria Kozhevnikov University of California, Santa Barbara Although visual-spatial representations are used extensively in mathematics
2、and spatial ability is highly correlated with success in mathematics education, research to date has not demonstrated a clear relationship between use of visual-spatial representations and success in mathematical problem solving. The authors distinguished 2 types of visual-spatial representations: s
3、chematic representations that encode the spatial relations described in a problem and pictorial representations that encode the visual appearance of the objects described in the problem. Participants solved mathematical problems and reported on their solution strategies. The authors were able to rel
4、iably classify their visual-spatial representations as primarily schematic or primarily pictorial. Use of schematic spatial representations was associated with success in mathematical problem solving, whereas use of pictorial representations was negatively correlated with success. Use of schematic r
5、epresentations was also significantly correlated with one measure of spatial ability. The research therefore helps clarify the relationship between visual imagery, spatial ability, and mathematical problem solving. Visual imagery refers to the ability to form mental representations of the appearance
6、 of objects and to manipulate these representations in the mind (Kosslyn, 1995). Most researchers agree that such visual representations are important in mathematics education because they enhance an intuitive view and an understanding in many areas of mathematics (e.g., Krutetskii, 1976; Usiskin, 1
7、987). There is a significant relationship between spatial ability and achievement in mathematics (e.g., Battista, 1990). However, the wide use of visual images by students is not always effective in problem solving and can lead to erroneous solutions (e.g., Lean & Clements, 1981; Presmeg, 1992).
8、 In this study, we clarify the relationship between visual imagery, spatial ability, and mathematical problem solving by identifying two different types of visual-spatial representations used in solving mathematical problems schematic and pictorial representations and by showing that they are differ
9、entially related to success in mathematical problem solving. Visual-Spatial Representations in Mathematical Problem Solving There is extensive research in mathematics showing a correlation between spatial ability and mathematical performance (e.g., Battista, 1990; McGee, 1979; Sherman, 1979; Smith,
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