This experiment investigated the effect of format (line vs. bar), viewers’ familiarity with variables, and viewers’ graphicacy (graphical literacy) skills on the comprehension of multivariate (three variable) data presented in graphs. Fifty-five undergraduates provided written descriptions of data for a set of 14 line or bar graphs, half of which depicted variables familiar to the population and half of which depicted variables unfamiliar to the population. Participants then took a test of graphicacy skills. As predicted, the format influenced viewers’ interpretations (...) of data. Specifically, viewers were more likely to describe x–y interactions when viewing line graphs than when viewing bar graphs, and they were more likely to describe main effects and “z–y” (the variable in the legend) interactions when viewing bar graphs than when viewing line graphs. Familiarity of data presented and individuals’ graphicacy skills interacted with the influence of graph format. Specifically, viewers were most likely to generate inferences only when they had high graphicacy skills, the data were familiar and thus the information inferred was expected, and the format supported those inferences. Implications for multivariate data display are discussed. (shrink)

Three studies were conducted to examine the relation of spatial visualization to solving kinematics problems that involved either predicting the two‐dimensional motion of an object, translating from one frame of reference to another, or interpreting kinematics graphs. In Study 1, 60 physics‐naíve students were administered kinematics problems and spatial visualization ability tests. In Study 2, 17 (8 high‐ and 9 low‐spatial ability) additional students completed think‐aloud protocols while they solved the kinematics problems. In Study 3, the eye movements of fifteen (...) (9 high‐ and 6 low‐spatial ability) students were recorded while the students solved kinematics problems. In contrast to high‐spatial students, most low‐spatial students did not combine two motion vectors, were unable to switch frames of reference, and tended to interpret graphs literally. The results of the study suggest an important relationship between spatial visualization ability and solving kinematics problems with multiple spatial parameters. (shrink)

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, Volts, Ohms, (...) Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, Volts, Ohms, (...) Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)

Diagrams are a form of spatial representation that supports reasoning and problem solving. Even when diagrams are external, not to mention when there are no external representations, problem solving often calls for internal representations, that is, representations in cognition, of diagrammatic elements and internal perceptions on them. General cognitive architectures—Soar and ACT-R, to name the most prominent—do not have representations and operations to support diagrammatic reasoning. In this article, we examine some requirements for such internal representations and processes in cognitive (...) architectures. We discuss the degree to which DRS, our earlier proposal for such an internal representation for diagrams, meets these requirements. In DRS, the diagrams are not raw images, but a composition of objects that can be individuated and thus symbolized, while, unlike traditional symbols, the referent of the symbol is an object that retains its perceptual essence, namely, its spatiality. This duality provides a way to resolve what anti-imagists thought was a contradiction in mental imagery: the compositionality of mental images that seemed to be unique to symbol systems, and their support of a perceptual experience of images and some types of perception on them. We briefly review the use of DRS to augment Soar and ACT-R with a diagrammatic representation component. We identify issues for further research. (shrink)