【正文】 oblem representation, whereas other kinds of imagery may play a more positive role. Presmeg ascribed the most essential role in mathematical problem solving to pattern imagery, in which concrete details are disregarded and pure relationships are depicted. This kind of imagery was also identified by other researchers (Johnson, 1987。 the second group, visualizers, involves those who prefer to use visual imagery。外文文獻(xiàn)資料 Journal of Educational Psychology, 1999, 91, 4, 684689. Types of VisualSpatial Representations and Mathematical Problem Solving Mary Hegarty and Maria Kozhevnikov University of California, Santa Barbara Although visualspatial 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 visualspatial representations and success in mathematical problem solving. The authors distinguished 2 types of visualspatial 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 visualspatial 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 (., Krutetskii, 1976。 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 amp。 Krutetskii, 1976). However, none of these researchers examined the quantitative relationships between use of different types of imagery and mathematical problem solving, nor have they examined the relationship between spatial ability and use of different types of imagery. In summary, although spatial ability correlates positively with mathematics achievement, preference to process information visually correlates with neither mathematical performance nor spatial ability tests. These results have cast doubt on the usefulness of classifying students as visualizers or verbalizers, and as a consequence, the number of educational studies related to the visualizerverbalizer cognitive style has declined rapidly over the past decade. Types of Visual Imagery Ability The current research differentiates between two different visual imagery abilities identified in cognitive psychology and neuroscience research. This research suggests that visual imagery is not general and undifferentiated but posed of different, relatively independent visual and spatial ponents (., Farah, Hammond, Levine, amp。 Lean amp。 Lohman, 1988). The PMA Space test is a mental rotation test. On each trial, participants are shown a standard figure on the lefthand side of the page and six parison figures on the righthand side of the page. Their task is to indicate whether each of six parison figures is a planar rotation of the target figure (as opposed to its mirror image) as quickly and accurately as possible. This test is a measure of the spatial relations factor, also referred to as speeded rotation (Carroll, 1993。 Lean amp。 D. N. Osherson (Eds.), Visual cognition: An invitation to cognitive science (Vol. 2, pp. 267296). Cambridge, MA: MIT Press. Kozhevnikov, M. (1999). Students39。 Clements, M. A. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267299. Linn, M., amp。 Presmeg, 1986a, 1986b, 1992) found no relationship between use of visualspatial representations and mathematical problem solving. Characterizing students as visualizers and verbalizers is too general a classification. There are, in fact, two types of visualizers: schematic types, who are generally successful in mathematical problem solving, and pictorial types, who are less successful than schematic types. In this study we also began to examine the relationship between use of types of visualspatial representations and different spatial ability factors. Use of schematic imagery was associated with high spatial visualization ability, as measured by the Block Design test, but not with a test of spatial relations (the PMA Space test). Tests of spatial visualization, like the Block Design test, are the most plex tests of spatial ability, involving a sequence 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。 visualspatial representations were schematic or pictorial. For each problem on which a person used a visualspatial representation, the representation was scored as either primarily schematic or primarily pictorial. A visualspatial representation was scored as primarily schematic if the student drew a diagram, used gestures showin