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Diagrams Affect Choice of Strategy in Probability Problem Solving

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Diagrammatic Representation and Inference (Diagrams 2016)

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Abstract

We investigated whether diagrams influence strategy choice and success in solving elementary combinatorics problems. Generic diagrams (trees or two-way tables) were provided to solvers as aids. Participants’ coded solution strategies revealed that problem solvers tended to utilize mathematical structures and solutions that easily mapped to the diagrams’ visuospatial relations. For example, when provided with an unlabeled N-by-N table, solvers tended to proceed by defining an equally-likely outcome space (an “outcome-search” solution); when provided with a binary tree, solvers tended to adopt a “sequential” solution defining stage-wise simple or conditional probabilities; when provided with an N-ary tree cuing equally-likely outcomes, choices were split between the two solution types. Furthermore, the tree and the table showed different patterns of characteristic errors, and perhaps for this reason, the tree led to higher accuracy for one problem that involved sequential sampling without replacement, while the table was best for the other problem, involving independent events. The results support arguments that the content and structure of diagrams must be congruent to that of the problem at hand and be easily and accurately perceived to be effective, and demonstrate that diagrams can influence strategy choice in problem solving.

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Authors and Affiliations

  1. Teachers College, Columbia University, New York, USA

    Chenmu Xing & James E. Corter

  2. Council for Aid to Education, New York, USA

    Doris Zahner

Authors
  1. Chenmu Xing
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  2. James E. Corter
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  3. Doris Zahner
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Correspondence to Chenmu Xing .

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Editors and Affiliations

  1. The University of Cambridge , Cambridge, United Kingdom

    Mateja Jamnik

  2. The University of Tokyo , Tokyo, Japan

    Yuri Uesaka

  3. Millersville University , Millersville, Pennsylvania, USA

    Stephanie Elzer Schwartz

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Xing, C., Corter, J.E., Zahner, D. (2016). Diagrams Affect Choice of Strategy in Probability Problem Solving. In: Jamnik, M., Uesaka, Y., Elzer Schwartz, S. (eds) Diagrammatic Representation and Inference. Diagrams 2016. Lecture Notes in Computer Science(), vol 9781. Springer, Cham. https://doi.org/10.1007/978-3-319-42333-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-42333-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42332-6

  • Online ISBN: 978-3-319-42333-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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