Abstract
Spatial diagram representations such as hierarchies, matrices, and networks are important tools for thinking. Our data suggest that college students possess abstract schemas for these representations that include at least rudimentary information about their applicability conditions. In Experiment 1, subjects were better able to select the appropriate spatial diagram representation for a problem when cued to use general category information in memory about those representations than when cued to use specific example problems given during the experiment. The results of Experiment 2 showed that the superior performance in the general category condition was not based on a comparison of the test problems with examples in memory. The results of Experiment 3 showed that the superior performance was not due to learning that occurred during the experiment or to transfer appropriate processing. The General Discussion section considers the nature of students’ representation schemas and the question of why college students have only rudimentary schemas for common and widely applicable diagrammatic representations.
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Anderson, J. R., Farrell, R., &Sauers, R. (1984). Learning to program in LISP.Cognitive Science,8, 87–129.
Bartram, D. J. (1980). Comprehending spatial information: The relative efficiency of different methods of presenting information about bus routes.Journal of Applied Psychology,65, 103–110.
Barwise, J., &Etchemendy, J. (1991). Visual information and valid reasoning. In W. Zimmermann & S. Cunningham (Eds.),Visualization in teaching and learning mathematics (pp. 9–24). Washington, DC: Mathematical Association of America.
Bransford, J., Sherwood, R., Vye, N., &Rieser, J. (1986). Teaching thinking and problem solving: Research foundations.American Psychologist,41, 1078–1089.
Butler, D. L. (1993). Graphics in psychology: Pictures, data, and especially concepts.Behavior Research Methods, Instruments, & Computers,25, 81–92.
Carroll, J. M., Thomas, J. C., &Malhotra, A. (1980). Presentation and representation in design problem-solving.British Journal of Psychology,71, 143–153.
Cheng, P. W., &Holyoak, K. J. (1985). Pragmatic reasoning schemas.Cognitive Psychology,17, 391–416.
Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., &Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems.Cognitive Science,13, 145–182.
Chi, M. T. H., Feltovich, P. J., &Glaser, R. (1981). Categorization and representation of physics problems by experts and novices.Cognitive Science,5, 121–152.
Day, R. S. (1988). Alternative representations. In G. H. Bower (Ed.),The psychology of learning and motivation (Vol. 22, pp. 261–305). San Diego: Academic Press.
Francis, M. (1995).Symbolic representations: Relations among four measures of knowledge. Unpublished master’s thesis, Vanderbilt University, Nashville.
Gick, M. L., &McGarry, S. J. (1992). Learning from mistakes: Inducing analogous solution failures to a source problem produces later successes in analogical transfer.Journal of Experimental Psychology: Learning, Memory, & Cognition,18, 623–639.
Goldin, G. A. (1985). Thinking scientifically and thinking mathematically: A discussion of the paper by Heller and Hungate. In E. A. Silver (Ed.),Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 113–122). Hillsdale, NJ: Erlbaum.
Guri-Rozenblit, S. (1988). The interrelations between diagrammatic representations and verbal explanations in learning from social science texts.Instructional Science,17, 219–234.
Hegarty, M., &Just, M. A. (1993). Constructing mental models of machines from text and diagrams.Journal of Memory & Language,32, 717–742.
Holyoak, K. J. (1985). The pragmatics of analogical transfer. In G. H. Bower (Ed.),The psychology of learning and motivation (Vol. 19, pp. 59–87). New York: Academic Press.
Kaplan, C. A., &Simon, H. A. (1990). In search of insight.Cognitive Psychology,22, 374–419.
Kindfield, A. C. H. (1993/1994). Biology diagrams: Tools to think with.The Journal of the Learning Sciences,3, 1–36.
Koedinger, K. R., &Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry.Cognitive Science,14, 511–550.
Larkin, J. H., &Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words.Cognitive Science,11, 65–99.
Levin, J. R. (1989). A transfer-appropriate-processing perspective of pictures in prose. In H. Mandl & J. R. Levin (Eds.),Knowledge acquisition from text and pictures (pp. 83–100). Amsterdam: Elsevier.
Lewis, A. B. (1989). Training students to represent arithmetic word problems.Journal of Educational Psychology,81, 521–531.
Lynch, M. (1990). The externalized retina: Selection and mathematization in the visual documentation of objects in the life sciences. In M. Lynch & S. Woolgar (Eds.),Representation in scientific practice (pp. 153–186). Cambridge, MA: MIT Press.
Malt, B. C. (1989). An on-line investigation of prototype and exemplar strategies in classification.Journal of Experimental Psychology: Learning, Memory, & Cognition,15, 539–555.
Mayer, R. E., &Gallini, J. K. (1990). When is an illustration worth ten thousand words?Journal of Educational Psychology,82, 715–726.
McGuinness, C. (1986). Problem representation: The effects of spatial arrays.Memory & Cognition,14, 270–280.
Medin, D. L., &Ross, B. H. (1989). The specific character of abstract thought: Categorization, problem solving, and induction. In R. J. Sternberg (Ed.),Advances in the psychology of human intelligence (Vol. 5, pp. 189–223). Hillsdale, NJ: Erlbaum.
Morris, C. D., Bransford, J. D., &Franks, J. J. (1977). Levels of processing versus transfer appropriate processing.Journal of Verbal Learning & Verbal Behavior,16, 519–533.
Novick, L. R. (1990). Representational transfer in problem solving.Psychological Science,1, 128–132.
Novick, L. R., &Hmelo, C. E. (1994). Transferring symbolic representations across non-isomorphic problems.Journal of Experimental Psychology: Learning, Memory, & Cognition,20, 1296–1321.
Novick, L. R., &Holyoak, K. J. (1991). Mathematical problem solving by analogy.Journal of Experimental Psychology: Learning, Memory, & Cognition,17, 398–415.
Novick, L. R., & Hurley, S. M. (1997, November).College students’ knowledge about three spatial diagram representations. Paper presented at the annual meeting of the Psychonomic Society, Philadelphia.
Polya, G. (1957).How to solve it (2nd ed.). Princeton, NJ: Princeton University Press.
Reed, S. K., &Bolstad, C. A. (1991). Use of examples and procedures in problem solving.Journal of Experimental Psychology: Learning, Memory, & Cognition,17, 753–766.
Ross, B. H., &Kennedy, P. T. (1990). Generalizing from the use of earlier examples in problem solving.Journal of Experimental Psychology: Learning, Memory, & Cognition,16, 42–55.
Schoenfeld, A. H., &Herrmann, D. J. (1982). Problem perception and knowledge structure in expert and novice mathematical problem solvers.Journal of Experimental Psychology: Learning, Memory, & Cognition,8, 484–494.
Schwartz, D. L. (1993). The construction and analogical transfer of symbolic visualizations.Journal of Research in Science Teaching,30, 1309–1325.
Schwartz, S. H. (1971). Modes of representation and problem solving: Well evolved is half solved.Journal of Experimental Psychology,91, 347–350.
Schwartz, S. H., &Fattaleh, D. L. (1972). Representation in deductive problem solving: The matrix.Journal of Experimental Psychology,95, 343–348.
Smith, E. E., Langston, C., &Nisbett, R. E. (1992). The case for rules in reasoning.Cognitive Science,16, 1–40.
Sweller, J., Chandler, P., Tierney, P., &Cooper, M. (1990). Cognitive load as a factor in the structuring of technical material.Journal of Experimental Psychology: General,119, 176–192.
VanderStoep, S. W., &Seifert, C. M. (1993/1994). Learning ”how” versus learning “when”: Improving transfer of problem-solving principles.The Journal of the Learning Sciences,3, 93–111.
Wertheimer, M. (1982).Productive thinking (Rev. ed.). Chicago: University of Chicago Press. (Original work published 1959)
Winn, W. (1989). The design and use of instructional graphics. In H. Mandl & J. R. Levin (Eds.),Knowledge acquisition from text and pictures (pp. 125–144). Amsterdam: Elsevier.
Winston, M. E., Chaffin, R., &Herrmann, D. (1987). A taxonomy of part-whole relations.Cognitive Science,11, 417–444.
Zimmermann, W., &Cunningham, S. (1991). Editors’ introduction: What is mathematical visualization? In W. Zimmermann & S. Cunningham (Eds.),Visualization in teaching and learning mathematics (pp. 1–8). Washington, DC: Mathematical Association of America.
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Novick, L.R., Hurley, S.M. & Francis, M. Evidence for abstract, schematic knowledge of three spatial diagram representations. Memory & Cognition 27, 288–308 (1999). https://doi.org/10.3758/BF03211413
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DOI: https://doi.org/10.3758/BF03211413