Abstract
The operational momentum (OM) effect describes a systematic bias in estimating the outcomes of simple addition and subtraction problems. Outcomes of addition problems are overestimated while outcomes of subtraction problems are underestimated. The origin of OM remains debated. First, a flawed uncompression of numerical information during the course of mental arithmetic is supposed to cause OM due to linear arithmetic operations on a compressed magnitude code. Second, attentional shifts along the mental number line are thought to cause OM. A third hypothesis explains OM in 9-month olds by a cognitive heuristic of accepting more (less) than the original operand in addition (subtraction) problems. The current study attempts to disentangle these alternatives and systematically examines potential determinants of OM, such as reading fluency which has been found to modulate numerical–spatial associations. A group of 32 6- and 7-year-old children was tested in non-symbolic addition and subtraction problems, in which they had to choose the correct outcome from an array of several possible outcomes. Reading capacity was assessed for half of the children while attentional measures were assessed in the other half. Thirty-two adults were tested with the identical paradigm to validate its potential of revealing OM. Children (and adults) were readily able to solve the problems. We replicated previous findings of OM in the adults group. Using a Bayesian framework we observed an inverse OM effect in children, i.e., larger overestimations for subtraction compared to addition. A significant correlation between children’s level of attentional control and their propensity to exhibit OM was observed. The observed pattern of results, in particular the inverse OM in children is hard to reconcile with the previously proposed theoretical frameworks. The observed link between OM and the attentional system might be interpreted as evidence partially supporting the attentional shift hypothesis.
Highlights
Along with a variety of species humans possess an untrained and non-symbolic “number sense,” which yields representations of numerical magnitude that can be used productively in arithmetic operations such as addition and subtraction (Gallistel, 1990; Wynn, 1992; McCrink and Wynn, 2004; Barth et al, 2005; Cordes et al, 2007; Nieder and Dehaene, 2009)
We replicate the presence of proficient non-symbolic addition and subtraction in an adult population, along with a systematic overestimation of addition outcomes, and underestimation of subtraction outcomes (McCrink et al, 2007; Knops et al, 2009b)
The children tested here were capable of non-symbolic addition and subtraction, using only their “number sense”; they reliably altered their responses to the offered outcomes to correspond with a mental calculation of the estimated correct outcomes, and did so without the aid of confounding perceptual cues
Summary
Along with a variety of species humans possess an untrained and non-symbolic “number sense,” which yields representations of numerical magnitude that can be used productively in arithmetic operations such as addition and subtraction (Gallistel, 1990; Wynn, 1992; McCrink and Wynn, 2004; Barth et al, 2005; Cordes et al, 2007; Nieder and Dehaene, 2009). (McCrink et al, 2007; Knops et al, 2009b) the OM bias was explained by mechanisms which describe the underlying numerical magnitude representations as: (a) logarithmically compressed and (b) spatially oriented, with smaller numbers located left from larger numbers. The adult humans tested in these studies possess a cognitive system that enables them to perceive and process numerical magnitude information in an approximate, analog fashion – the aforementioned “number sense,” or approximate number system (ANS).
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