Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task) is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate.

Additional Information:• This paper was accepted for publication in the journal Acta twice to obtain a measure of immediate test-retest reliability. We found no significant correlation between participants' accuracy scores on trials created with the two protocols, suggesting that tasks employing these protocols may measure different cognitive constructs.Additionally, there were significant differences in the test-retest reliabilities for trials created with each protocol. Finally, strong congruency effects for convex hull size were found for both sets of protocol trials, which provides some clarification for conflicting results in the literature.

Dot comparison tasks are commonly used to index an individual's Approximate Number System (ANS) acuity, but the cognitive processes involved in completing these tasks are poorly understood. Here we investigated how factors including numerosity ratio, set size and visual cues influence task performance. Forty--four children aged 7--9 years completed a dot comparison task with a range of to--be--compared numerosities. We found that as the size of the numerosities increased, with ratios held constant, accuracy decreased due to the heightened salience of incongruent visual information.Furthermore, in trials with larger numerosities participants' accuracies were influenced more by the convex hull of the array than the average dot size. The numerosity ratio between the arrays in each trial was an important predictor for all set sizes. We argue that these findings are consistent with a 'competing processes' inhibition--based account, where accuracy scores are influenced by individual differences in both ANS acuity and inhibitory control skills.

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