外文文献资料Journal of Educational Psychology, 1999, 91, 4, 684-689.Types of Visual-Spatial Representations and Mathematical Problem SolvingMary Hegarty and Maria KozhevnikovUniversity of California, Santa BarbaraAlthough visual-spatial representations are used extensively in mathematics 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: schematic 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 reliably 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 representations 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 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, 1987). 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). 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 problemsschematic and pictorial representationsand by showing that they are differentially related to success in mathematical problem solving.Visual-Spatial Representations in Mathematical Problem SolvingThere is extensive research in mathematics showing a correlation between spatial ability and mathematical performance (e.g., Battista, 1990; McGee, 1979; Sherman, 1979; Smith, 1964). For example, Sherman (1979) reported that the spatial ability factor was one of the main factors significantly affecting mathematical performance. This correlation increases with the complexity of mathematical tasks (see Kaufmann, 1990, for a review).Other investigations have focused on the mental processes used in solving mathematical problems, particularly the role of diagrams and visual-spatial images in mathematical problem solving. In these studies, students reported their solution processes after solving problems or while solving problems. On the basis of such studies, Krutetskii (1976) concluded that individuals can be classified into three groups according to how they process mathematical information. The first group consists of verbalizers, who prefer verballogical rather than imagery modes when attempting to solve problems; the second group, visualizers, involves those who prefer to use visual imagery; and the third group, mixers, contains individuals who have no tendency one way or the other.Following the Krutetskii model, Moses (1980), Suwarsono (as cited in Lean & Clements, 1981), and Presmeg (1986a, 1986b, 1992) recognized that individuals could be placed on a continuum with regard to their preference for using visual imagery while solving mathematical problems.The authors of these studies defined mathematical visuality as the extent to which a person prefers to use visual imagery or diagrams when attempting mathematical problems. Suwarsono developed an instrument to measure an individuals level of visualitythe Mathematical Processing Instrument (MPI), which has been used extensively in further research on this topic. A surprising result from this literature is that the wide use of visual images is not always effective and can sometimes lead to erroneous solutions of mathematical problems. Finding a negative correlation between mathematical visuality and both spatial ability and mathematical performance, Lean and Clements (1981) concluded that verbalizers outperform visualizers on both mathematical and spatial ability tests. On this point, Presmeg (1986a, 1986b) identified five kinds of imagery used by high school students in solving mathematical problems: (a) concrete pictorial imagery (pictures in the mind); (b) pattern imagery (pure relat