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Insights into numerical cognition: considering eye-fixations in number processing and arithmetic

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Abstract

Considering eye-fixation behavior is standard in reading research to investigate underlying cognitive processes. However, in numerical cognition research eye-tracking is used less often and less systematically. Nevertheless, we identified over 40 studies on this topic from the last 40 years with an increase of eye-tracking studies on numerical cognition during the last decade. Here, we review and discuss these empirical studies to evaluate the added value of eye-tracking for the investigation of number processing. Our literature review revealed that the way eye-fixation behavior is considered in numerical cognition research ranges from investigating basic perceptual aspects of processing non-symbolic and symbolic numbers, over assessing the common representational space of numbers and space, to evaluating the influence of characteristics of the base-10 place-value structure of Arabic numbers and executive control on number processing. Apart from basic results such as reading times of numbers increasing with their magnitude, studies revealed that number processing can influence domain-general processes such as attention shifting—but also the other way round. Domain-general processes such as cognitive control were found to affect number processing. In summary, eye-fixation behavior allows for new insights into both domain-specific and domain-general processes involved in number processing. Based thereon, a processing model of the temporal dynamics of numerical cognition is postulated, which distinguishes an early stage of stimulus-driven bottom-up processing from later more top-down controlled stages. Furthermore, perspectives for eye-tracking research in numerical cognition are discussed to emphasize the potential of this methodology for advancing our understanding of numerical cognition.

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Notes

  1. Besides the reading times of numerals, eye-tracking was also employed to investigate the readability of different number formats which seem to differ with regard to their comprehensibility. Rello, Bautista, Baeza-Yates, Gerv, and Herv (2013) found that participants with dyslexia improved in text comprehension when digits and percentages were used instead of number words and fractions, respectively.

  2. While further investigating the mental representation of arithmetic facts, Zhou, Zhao, Chen, and Zhou (2012) employed horizontal electrooculography (HEOG) in single-digit addition and multiplication problems. This method only provides information about the horizontal direction (i.e., left/right) of eye-movements. In their HEOG data the authors found converging evidence for a preferred operand order in the representation of arithmetic facts. In particular, the HEOG data indicated that participants preferentially fixated the larger operand first. Again relying on HEOG, Yu, Liu, Li, Cui, & Zhou (in press, in this issue) showed that the direction of eye movements in mental arithmetic is influenced by the relative magnitude of the operands.

  3. Please note that there is an ongoing debate on whether symbolic and non-symbolic presentation formats address the same underlying representation of numbers or not (e.g., Cohen Kadosh & Walsh, 2009 for an overview and discussion). However, this is beyond the scope of this article.

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Acknowledgments

Julia Mock was supported by the German Research Foundation (DFG) providing funding to Korbinian Moeller and Elise Klein (MO 2525/2-1). Stefan Huber was supported by the Leibniz-Competition Fund (SAW-2014-IWM-4) providing funding to Elise Klein. Elise Klein was supported by a Margarete von Wrangell fellowship from the Ministry of Science, Research and the Arts Baden-Württemberg. Korbinian Moeller is principal investigator at the LEAD Graduate School [GSC1028], a project of the Excellence Initiative of the German federal and state governments. We wish to thank Margarete Ocker for proofreading our manuscript.

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  1. Leibniz-Institut für Wissensmedien, Schleichstraße 6, 72076, Tuebingen, Germany

    J. Mock, S. Huber, E. Klein & K. Moeller

  2. Section Clinical Cognition Research, Department of Neurology, University Hospital, RWTH Aachen University, Aachen, Germany

    E. Klein

  3. Department of Psychology, University of Tuebingen, Tuebingen, Germany

    K. Moeller

  4. LEAD Graduate School, University of Tuebingen, Tuebingen, Germany

    K. Moeller

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Mock, J., Huber, S., Klein, E. et al. Insights into numerical cognition: considering eye-fixations in number processing and arithmetic. Psychological Research 80, 334–359 (2016). https://doi.org/10.1007/s00426-015-0739-9

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