【正文】 of questions, asked by the experimenter, about the strategy used to solve the problem. This method of questioning was adopted because we found that children of this age vary considerably in their ability to give concurrent verbal protocols while solving these types of problems. All students were asked all of the questions, unless they had already spontaneously provided the information asked in a question. The problems are presented in Appendix A, and sample acpanying questions are presented in Appendix B. 2. Verbal reasoning ability was measured by the Drumcondra Verbal Reasoning Test (DVRT。s attention from the main relationships in the problem statement. Second, we hypothesize that spatial ability is positively associated with use of schematic imagery but not with use of pictorial imagery. Finally, to test the alternative hypothesis that use of schematic imagery is related to general intelligence, rather than spatial ability specifically, we include measures of verbal and nonverbal general intelligence. Method Participants Thirtythree boys in sixth class (sixth grade) in an allboys primary school in Dublin, Ireland, took part in this study. The mean age of the participants was 12 years, 1 month (range = 11 years, 6 months13 years, 1 month). Materials The following measures were administered to the students: 1. The MPI consists of 15 problems, either taken from previous studies (Krutetskii, 1976。 Logie, 1995). Visual imagery refers to a representation of the visual appearance of an object, such as its shape, color, or brightness. Spatial imagery refers to a representation of the spatial relationships between parts of an object and the location of objects in space or their movement。s attention from the main elements in the original problem 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。 (b) pattern imagery (pure relationships depicted in a visualspatial scheme)。 the second group, visualizers, involves those who prefer to use visual imagery。 Presmeg, 1992). In this study, we clarify the relationship between visual imagery, spatial ability, and mathematical problem solving by identifying two different types of visualspatial representations used in solving mathematical problems— schematic and pictorial representations— and by showing that they are differentially related to success in mathematical problem solving. VisualSpatial Representations in Mathematical Problem Solving There is extensive research in mathematics showing a correlation between spatial ability and mathematical performance (., Battista, 1990。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。 McGee, 1979。 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。 (c) kinesthetic imagery, which involves hand movement and other gestures。 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 image