According to the internal/external frame of reference model, academic achievement has a strong impact on people’s self-concept, both within and between subjects. We conducted a series of meta-analyses of k = 505 data sets containing the six bivariate correlations between achievement and self-concept in two subjects. Negative paths from achievement to noncorresponding self-concept, indicating dimensional comparison effects, were strongest when the subjects were dissimilar with regard to the math-verbal continuum, reduced but still significantly negative when both subjects belonged to the verbal domain, and near-zero when both subjects belonged to the math/science domain. Additionally, we found stronger positive paths from achievements to corresponding self-concepts, indicating social comparison effects, and stronger dimensional comparison effects for grades than for standardized test scores, and for older rather than younger students. We extend dimensional comparison theory by discussing these results with particular regard to the nonexistence of assimilation effects, the effects of subject similarity on dimensional comparison effects, and other moderators of dimensional comparison effects.

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.

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