Solving problems using matrix, network, and hierarchy diagrams: The consequences of violating construction conventions

In order for a diagram to be useful for solving a problem, it must be constructed so that its perceptual features facilitate inferences relevant to that problem. In Experiment 1, we established the construction conventions, which relate to how information is assigned to different parts of the diagram, for three spatial representations—networks, hierarchies, and matrices. In Experiment 2, participants solved problems using diagrams that either followed or violated these conventions. As hypothesized, participants took longer to draw inferences from convention-violating matrix and network diagrams than from their convention-following counterparts, and these inferences were less accurate. Convention adherence did not affect reasoning time or accuracy for hierarchy diagrams. The authors concluded that the construction conventions are related to perceptual features that facilitate certain types of inferences for matrix and network diagrams, and they discussed why this might not have been the case for the hierarchy.

[1]  M. Scheerer,et al.  Problem Solving , 1967, Nature.

[2]  Steven H. Schwartz,et al.  Modes of representation and problem solving: Well evolved is half solved. , 1971 .

[3]  P. Wright,et al.  Written information: Some alternatives to prose for expressing the outcomes of complex contingencies. , 1973 .

[4]  William G. Holliday,et al.  Teaching verbal chains using flow diagrams and texts , 1976 .

[5]  Patricia Wright,et al.  Presenting technical information: A survey of research findings , 1977 .

[6]  E. Kay,et al.  Introductory Graph Theory , 1978 .

[7]  D. Bartram,et al.  Comprehending spatial information: the relative efficiency of different methods of presenting information about bus routes. , 1980, The Journal of applied psychology.

[8]  W Winn,et al.  Perceptual Strategies Used with Flow Diagrams Having Normal and Unanticipated Formats , 1983, Perceptual and motor skills.

[9]  Herbert A. Simon,et al.  Why a Diagram is (Sometimes) Worth Ten Thousand Words , 1987, Cogn. Sci..

[10]  Sarah Guri-Rozenblit,et al.  The interrelations between diagrammatic representations and verbal explanations in learning from social science texts , 1988 .

[11]  J. Barwise,et al.  Visual information and valid reasoning , 1991 .

[12]  Matthew Flatt,et al.  PsyScope: An interactive graphic system for designing and controlling experiments in the psychology laboratory using Macintosh computers , 1993 .

[13]  Daniel L. Schwartz,et al.  The construction and analogical transfer of symbolic visualizations. , 1993 .

[14]  M. Just,et al.  Constructing mental models of machines from text and diagrams. , 1993 .

[15]  L. R. Novick,et al.  Transferring symbolic representations across nonisomorphic problems. , 1994 .

[16]  K. Holyoak,et al.  Mapping conceptual to spatial relations in visual reasoning. , 1996, Journal of experimental psychology. Learning, memory, and cognition.

[17]  Robert L. Goldstone,et al.  Reuniting perception and conception , 1998, Cognition.

[18]  R. Cox Representation construction, externalised cognition and individual differences , 1999 .

[19]  Jeffery. M. Zacks,et al.  Bars and lines: A study of graphic communication , 1999, Memory & cognition.

[20]  Sean M. Hurley,et al.  Evidence for abstract, schematic knowledge of three spatial diagram representations , 1999, Memory & cognition.

[21]  L. R. Novick,et al.  Folding a fish, making a mushroom: The role of diagrams in executing assembly procedures , 2000, Memory & cognition.

[22]  Paul U. Lee,et al.  Lines, Blobs, Crosses and Arrows: Diagrammatic Communication with Schematic Figures , 2000, Diagrams.

[23]  Laura R. Novick,et al.  Spatial diagrams: Key instruments in the toolbox for thought , 2000 .

[24]  Uwe Oestermeier,et al.  Verbal and visual causal arguments , 2000, Cognition.

[25]  Laura R. Novick,et al.  To Matrix, Network, or Hierarchy: That Is the Question , 2001, Cognitive Psychology.

[26]  M. Gattis Structure mapping in spatial reasoning , 2002 .

[27]  Merideth Gattis,et al.  Mapping relational structure in spatial reasoning , 2004, Cogn. Sci..

[28]  Justus J. Randolph Free-Marginal Multirater Kappa (multirater K[free]): An Alternative to Fleiss' Fixed-Marginal Multirater Kappa. , 2005 .

[29]  Christof Körner,et al.  Concepts and misconceptions in comprehension of hierarchical graphs , 2005 .

[30]  Laura R Novick Understanding Spatial Diagram Structure: An Analysis of Hierarchies, Matrices, and Networks , 2006, Quarterly journal of experimental psychology.

[31]  Laura R. Novick,et al.  Context and structure: The nature of students' knowledge about three spatial diagram representations , 2006 .

[32]  L. R. Novick,et al.  Understanding phylogenies in biology: the influence of a Gestalt Perceptual Principle. , 2007, Journal of experimental psychology. Applied.

[33]  T. P. Carpenter,et al.  Professional development focused on children's algebraic reasoning in elementary school , 2007 .