Graphical revelations: comparing students' translation errors in graphics and logic

Richard Cox*, Robert Dale, John Etchemendy, Dave Barker-Plummer

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

7 Citations (Scopus)


We are interested in developing a better understanding of what it is that students find difficult in learning logic. We use both natural language and diagram-based methods for teaching students the formal language of first-order logic. In this paper, we present some initial results that demonstrate that, when we look at how students construct diagrammatic representations of information expressed in natural language (nl) sentences, the error patterns are different from those observed when students translate from nl to first-order logic (fol). In the nl-to-diagram construction task, errors associated with the interpretation of the expression not a small dodecahedron were manifested much more frequently with respect to the object's size than with respect to its shape. In the nl-to-fol task, however, no such asymmetry was observed. We hypothesize a number of possible factors that might be implicated here: differences between the nl-to-diagram and nl-to-fol tasks; the reduced expressivity of diagrams compared to language; scoping errors in participants' nl parsing; and the visuospatial properties of the blocks-world domain. In sum, constructing a diagram requires the student to provide an instantiated representation of the meaning of a natural language sentence; this tests their understanding in a way that translation into first-order logic does not, by ensuring that they are not simply carrying out a symbol manipulation exercise.

Original languageEnglish
Title of host publicationDiagrammatic representation and inference
Subtitle of host publication5th International Conference, Diagrams 2008, Herrsching, Germany, September 2008, proceedings
EditorsGem Stapleton, John Howse, John Lee
Place of PublicationBerlin
PublisherSpringer, Springer Nature
Number of pages9
ISBN (Print)3540877290, 9783540877295
Publication statusPublished - 2008
Event5th International Conference on Diagrammatic Representation and Inference, Diagrams 2008 - Herrsching, Germany
Duration: 19 Sep 200821 Sep 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5223 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349


Other5th International Conference on Diagrammatic Representation and Inference, Diagrams 2008


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