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General Commentary ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Psychol. | doi: 10.3389/fpsyg.2018.02259

Commentary on: Pinheiro-Chagas, P., Didino, D., Haase, V.G., Wood, G., & Knops, A. (2018). The Developmental Trajectory of the Operational Momentum Effect.

  • 1Cognitive Science, Universität Potsdam, Germany
  • 2Ariel University, Israel

Recently, Pinheiro-Chagas and colleagues (2018) studied the development of the operational momentum (OM) which denotes a tendency to accept larger than correct outcomes in addition and smaller than correct outcomes in subtraction. The authors reviewed some theories of OM and derived two competing predictions. First, they described the attentional account, according to which OM results from an overshoot of an attentional spotlight when moving along the spatially oriented mental number line (MNL) in accordance with the magnitude of the second operand. Given that “formal schooling …might consolidate a systematic movement direction during the acquisition of arithmetical skills” (p.3), older children should show more OM. Secondly, they described the compression account of OM according to which linear operations (addition, subtraction) are performed on logarithmically compressed operand representations. Referring to a log-to-linear developmental shift in the placement of numbers on visually presented number lines, they predicted that older children should show less (un-) compression and thus less OM. Their results from 8-12-year olds showed a gradual increase of OM starting at 9 years and thus supported the attentional account.
The clear performance pattern reported by Pinheiro-Chagas and colleagues makes a useful contribution to the literature on OM development but their report also misrepresents the state of knowledge about OM. It might leave readers unnecessarily misinformed about the multi-faceted origin of this bias generally, and more specifically about the status of reverse OM for our understanding of cognitive biases in formal reasoning. We draw attention to these points below.
First, the authors acknowledged early OM in 9-month-olds (McCrink & Wynn, 2009) as well as reverse OM in 6-year-olds (Knops et al., 2013), thus recognizing a problem with their result of late-emerging and gradually increasing OM. While the authors mentioned the work of Pinhas and colleagues they did not convey its full impact with regard to this point. First, Pinhas and Fischer (2008; see also Shaki et al., 2018) observed larger OM in zero problems (such as 4+0) compared to non-zero problems (e.g., 3+1). This alone suffices to discredit the compression account because the logarithm of zero is not defined. Thus, the compression account was arguably a mere strawman pitted against the attentional account. But if attention shift magnitude is “… a distance corresponding to the magnitude of the second operand” (p. 2), how does this account explain larger OM with zero problems?
Further inconsistencies are reflected in the methods: From an attentional perspective, repeated downward movements of both addends, as well as upward movements of the subtrahend, constitute inconsistencies with the vertical MNL. More generally, why were operations along a horizontal MNL primed with vertical movements? The fact that subtrahends moved away from the area of interest in the display centre removed attention from the place of mentally simulating the outcome, thus impeding subtraction.
Secondly, Pinhas and Fischer (2008) proposed multiple sources of OM, including the operands, the operator, and the result. Taking into consideration evidence from biased quantitative reasoning, estimation heuristics and spatial-numerical associations, we have since developed this proposal into a comprehensive model of arithmetic heuristics and biases (AHAB; Shaki, Pinhas & Fischer, 2018; see also Shaki & Fischer, 2017; Fischer & Shaki, 2018). This model can explain the complete range of findings reported in the literature, including reverse OM, as a weighted contribution from an anchoring effect, an estimation heuristic, and spatial associations of operands and operators. Pinheiro-Chagas et al.’s report created the false impression that reverse OM is an anomaly. Instead it was found repeatedly (Charras et al., 2012, 2014; Knops et al., 2013; Pinhas, Shaki & Fischer, 2015, Blini et al., 2018; Mioni et al., 2018) and can be understood as reflecting anchoring bias in non-zero problems.
One further strength of AHAB is its ability to account for both spatial and non-spatial biases in mental arithmetic, regardless of whether computational uncertainty originated from encoding non-symbolic operators or results, as in studies by Knops and colleagues, or from mapping of perfectly identifiable operators and results onto a continuous response dimension, such as horizontal lines or time intervals (Shaki, Sery & Fischer, 2015; Mioni et al., 2018). It would be interesting to learn whether Pinheiro-Chagas and colleagues replicated the spatial bias in response selection previously observed in this paradigm by Knops et al. (2009).
Finally, the authors mention also an heuristic account of OM: a tendency to accept more than the correct outcome for additions and less than the correct outcome for subtractions because addition leads to “more” and subtraction to “less” (McCrink & Wynn, 2009). They compare it to the attentional account and state that “… the two accounts provide equivalent predictions” (p. 3). This is in conflict with the recent analysis offered in McCrink and Hubbard (2018, p. 240) that “… the use of heuristics is generally increased when attention is decreased”. We think that heuristics are triggered by operators. Yet, OM only emerges late, i.e., when both operator and second operand have been processed (Liu et al., 2017; Masson et al., 2017; Blini et al., 2018; D’Ascenzo et al., 2018). Results obtained from procedures where operators even preceded the first operand (cf. Knops et al., 2009) or multiple quantities are presented during responding (cf. Pinheiro-Chagras et al., 2018) must be interpreted cautiously because the normal ingredients of OM are dis-ordered or diluted.

Keywords: Embodied Cognition, operational momentum, SNARC effect, Mental arithmetic, Numerical cognition

Received: 27 Aug 2018; Accepted: 30 Oct 2018.

Edited by:

Krzysztof Cipora, University of Tubingen, Germany

Reviewed by:

Catherine Thevenot, Université de Lausanne, Switzerland
Jérôme Prado, Centre national de la recherche scientifique (CNRS), France  

Copyright: © 2018 Fischer, Miklashevsky and Shaki. 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: Prof. Martin H. Fischer, Universität Potsdam, Cognitive Science, Potsdam, D-14476, Germany,