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Exploring mental representations for literal symbols using priming and comparison distance effects

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Abstract

Higher-level mathematics requires a connection between literal symbols (e.g., ‘x’) and their mental representations. The current study probes the nature of mental representations for literal symbols using both the priming distance effect, in which ease of comparing a target number to a fixed standard is a function of prime-target distance, and the comparison distance effect, in which ease of comparing two numbers depends on the distance between them. Can literal symbols that have been assigned magnitude access mental representations of quantity to produce distance effects? Forty participants completed number comparison tasks involving Arabic numerals and literal symbols, a training task, and a working memory task. While both distance effects were present with Arabic numerals, there was no evidence of either with literal symbols. Results suggest that literal symbols may not share the same mental representations of magnitude as other number formats or may access them differently. Additional research is needed to understand mental representations utilized in higher-level mathematics (e.g., algebra), which includes both Arabic numerals and literal symbols.

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Notes

  1. The meaning of an Arabic numeral could be dependent on its place-value (e.g., 3, 30, 0.03). However, above we refer to the Arabic numeral as a whole, rather than the role of individual digits.

  2. For brevity, we do not report the CDE for the Arabic numerals only condition or pairwise comparisons for each distance related to error rate and reaction time. Results are available from the authors by request.

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Acknowledgments

We thank Dr. Gigi Luk for her assistance with research design, analysis, and feedback on previous versions of this manuscript. We also thank Dr. Kurt Fischer, George Spencer, Janine de Novais, and three anonymous reviewers for feedback on prior versions of this manuscript. This research was funded by the Graduate Student Award from the Mind, Brain, Behavior Interfaculty Initiative at Harvard University to CP and the Harvard Graduate School of Education Dean’s Summer Fellowship to CP.

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  1. Harvard Graduate School of Education, Appian Way, Cambridge, MA, 02138, USA

    Courtney Pollack, Sibylla Leon Guerrero & Jon R. Star

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  1. Courtney Pollack
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  2. Sibylla Leon Guerrero
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Correspondence to Courtney Pollack.

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Pollack, C., Leon Guerrero, S. & Star, J.R. Exploring mental representations for literal symbols using priming and comparison distance effects. ZDM Mathematics Education 48, 291–303 (2016). https://doi.org/10.1007/s11858-015-0745-9

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