【正文】 ry is not general and undifferentiated but posed of different, relatively independent visual and spatial ponents (., Farah, Hammond, Levine, amp。 further, spatial imagery is not limited to the visual modality (., one could have an auditory or haptic spatial image). Cognitive studies have provided evidence for a dissociation between these two aspects of imagery. First, dualtask studies have shown that visual imagery tasks are impaired by concurrently viewing irrelevant pictures but not by moving one39。 Lean amp。 Educational Research Centre, 1968). This test was designed to measure general verbal intelligence and was developed as part of a large study of the effects of standardized testing in Ireland (Kellaghan, 1976). It is made up of sections on analogies, the identification of words opposite in meaning to a given stimulus, the identification of concepts as belonging to a single category, and inductive and deductive reasoning. The DVRT is standardized for children aged 10 years to 13 years, with reliability estimates ranging from .94 to .98 for different ages. 3. The Ravens Progressive Matrices Test (Raven, 1958) was used as a measure of nonverbal reasoning. Each item on this test shows a 3 X 3 matrix of figures with one missing cell. The figures in each row and column differ by some rule or set of rules. The task is to induce these rules and apply them to choose the missing figure from a set of eight choices. 4. Spatial ability was measured by two tests, the Block Design subtest of the Wechsler Intelligence Scale for Children— Revised (WISCR。 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。 hence, this problem was omitted from further analyses. We, serving as two independent raters, scored 20 of the participants39。 Lean 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。 D. N. Osherson (Eds.), Visual cognition: An invitation to cognitive science (Vol. 2, pp. 267296). Cambridge, MA: MIT Press. Kozhevnikov, M. (1999). Students39。 Agnoli, F. (1986). Are spatial visualization ability and visual imagery ability equivalent? In R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 3, pp. 255296). Hillsdale, NJ: Erlbaum. Presmeg, N. C. (1986a). Visualization in high school mathematics. For Learning of Mathematics, 63, 4246. Presmeg, N. C. (1986b). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297311. Presmeg, N. C. (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23, 595610. Raven, J. (1958). Standard progressive matrices. London: H. K. Lewis. Sherman, J. A. (1979). Predicting mathematical performance in high school girls and boys.。 Clements, M. A. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267299. Linn, M., amp。 Calvanio, R. (1988). Visual and spatial memory: Dissociable systems of representation. Cognitive Psychology, 20, 439462. Johnson, M. (1987). The body in the mind: The bodily basis of meaning, imagination, and reason. Chicago: University of Chicago Press. Kaufmann, G. (1990). Imagery effects on problem solving. In P. J. Hampson, D. E. Marks, 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。 in fact, this measure is significantly negatively associated with one of the spatial measures. As is to be expected, the psychometric tests were highly correlated with each other and with mathematical problem solving. We now consider the relationship between t