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Identification of Errors in Mathematical Symbolism and Notation: Implications for Software Design

  • Seyeon Kim
  • Marco Pollanen
  • Michael G. Reynolds
  • Wesley S. BurrEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)

Abstract

Mathematical user interfaces for authoring, collaboration, problem-solving and reasoning invariably rely on the ability to read, write and manipulate complex mathematical expressions. However, very little research has been done on how people read mathematical expressions, let alone how they are understood by the mind. One technique which researchers use to gain insight into how people read and comprehend symbols and complex phenomena are studies using eye-tracking hardware: focus on, and tracking of, pupils in order to determine the reader’s attention and fixation. In this paper we will explore the results of a study on two classes of students: mathematically “expert” (mathematical sciences students) and non-expert (Faculty of Science majors from outside the mathematical sciences). Each participant was presented with a series of mathematical problems (stimuli) and their eyes and attention/focus tracked as they worked through the problems mentally. We will discuss the differences in the two classes, both with respect to the correctness of responses to the problems and the structure of the scanning and identification of important components within the problem. This study has applications in mathematical software usability, accessibility, and design of interfaces, as comprehension of mathematical notation and formalism is assumed in the implementation of the modified symbolism inherent in structured mathematical software interfaces.

Keywords

Mathematical notation Symbolism Eye-tracking Problem identification Mathematical software interfaces 

Notes

Acknowledgments

This work was supported by research grants from eCampus Ontario and Trent University’s University Research Grants Program (URGP).

References

  1. 1.
    World Medical Association: Declaration of Helsinki: ethical principles for medical research involving human subjects. JAMA 310(20), 2191–2194 (2013)CrossRefGoogle Scholar
  2. 2.
    Clifton, C., Staub, A., Rayner, K.: Eye movements in reading words and sentences. In: Van Gompel, R.P.G., et al. (eds.) Eye Movements, pp. 341–371 (2007)CrossRefGoogle Scholar
  3. 3.
    Holmqvist, K., Nyström, M., Andersson, R., Dewhurst, R., Jarodzka, H., Van de Weijer, J.: Eye Tracking: A Comprehensive Guide to Methods and Measures. OUP, Oxford (2011)Google Scholar
  4. 4.
    Kohlhase, A., Fürsich, M.: Understanding mathematical expressions: an eye-tracking study. In: FM4M/MathUI/ThEdu/DP/WIP@ CIKM, pp. 42–50 (2016)Google Scholar
  5. 5.
    Bone, M.: A gaze into the mind’s eye: gaze as an indicator of cortical reinstatement during mental imagery. Unpublished doctoral dissertation, University of Toronto, Toronto, ON, Canada (2015)Google Scholar
  6. 6.
    Blostein, D. and Grbavec, A.: Recognition of mathematical notation. In: Handbook of Character Recognition and Document Image Analysis, pp. 557–582 (1997)CrossRefGoogle Scholar
  7. 7.
    MacGregor, M., Stacey, K.: Cognitive models underlying students’ formulation of simple linear equations. J. Res. Math. Educ. 24(3), 217–232 (1993)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Seyeon Kim
    • 1
  • Marco Pollanen
    • 1
  • Michael G. Reynolds
    • 2
  • Wesley S. Burr
    • 1
    Email author
  1. 1.Department of MathematicsTrent UniversityPeterboroughCanada
  2. 2.Department of PsychologyTrent UniversityPeterboroughCanada

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