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Approximate Number System and Mathematics

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Front. Psychol. | doi: 10.3389/fpsyg.2018.01801

Task Constraints Affect Mapping from Approximate Number System Estimates to Symbolic Numbers

 Dana L. Chesney1* and Percival Matthews2
  • 1Psychology, St. John's University, United States
  • 2Educational Psychology, UW Madison International Division, University of Wisconsin-Madison, United States

The Approximate Number System (ANS) allows individuals to assess non-symbolic numerical magnitudes (e.g., the number of apples on a tree) without counting. Several prominent theories posit that human understanding of symbolic numbers is based – at least in part – on mapping number symbols (e.g., 14) to their ANS-processed nonsymbolic analogs. Number-line estimation – where participants place numerical values on a bounded number-line – has become a key task used in research on this mapping. However, some research suggests that such number-line estimation tasks are actually proportion judgment tasks, as number-line estimation requires people to estimate the magnitude of the to-be-placed value, relative to set upper and lower endpoints, and thus do not so directly reflect magnitude representations. Here, we extend this work, assessing performance on nonsymbolic tasks that should more directly interface with the ANS. We compared adults’ (n = 31) performance when placing nonsymbolic numerosities (dot arrays) on number-lines to their performance with the same stimuli on two other tasks: Free estimation tasks where participants simply estimate the cardinality of dot arrays, and Ratio estimation tasks where participants estimate the ratio instantiated by a pair of arrays. We found that performance on these tasks was quite different, with Number-line and Ratio estimation tasks failing to the show classic psychophysical error patterns of scalar variability seen in the Free estimation task. We conclude the constraints of tasks using stimuli that access the ANS lead to considerably different mapping performance and that these differences must be accounted for when evaluating theories of numerical cognition. Additionally, participants showed typical underestimation patterns in the Free estimation task, but were quite accurate on the Ratio task. We discuss potential implications of these finding for theories regarding the mapping between ANS magnitudes to symbolic numbers.

Keywords: approximate number system, symbolic number mapping, number-lines, ratios, Estimation

Received: 14 May 2018; Accepted: 05 Sep 2018.

Edited by:

Marcus Lindskog, Uppsala University, Sweden

Reviewed by:

Evelyn Kroesbergen, Radboud University Nijmegen, Netherlands
Bert Reynvoet, KU Leuven, Belgium  

Copyright: © 2018 Chesney and Matthews. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Dr. Dana L. Chesney, St. John's University, Psychology, New York, 11439, New York, United States,