Abstract
Prior research suggests that the acuity of the approximate number system (ANS) predicts future mathematical abilities. Modelling the development of the ANS might therefore allow monitoring of children's mathematical skills and instigate educational intervention if necessary. A major problem however, is that our knowledge of the development of the ANS is acquired using fundamentally different paradigms, namely detection in infants versus discrimination in children and adults. Here, we question whether such a comparison is justified, by testing the adult ANS with both a discrimination and a detection task. We show that adults perform markedly better in the discrimination compared to the detection task. Moreover, performance on discrimination but not detection, correlated with performance on mathematics. With a second similar experiment, in which the detection task was replaced by a same-different task, we show that the results of experiment 1 cannot be attributed to differences in chance level. As only task instruction differed, the discrimination and the detection task most likely reflect differences at the decisional level. Future studies intending to model the development of the ANS should therefore rely on data derived from a single paradigm for different age groups. The same-different task appears a viable candidate, due to its applicability across age groups.
Highlights
The approximate number system (ANS) has been put forth as the foundation for our acquired mathematical abilities [1,2]
Performance on the detection task was only significantly above chance level for the seven largest ratio conditions but not for the three smallest ratio conditions (ratio 1.09 (11 dots) [t(23) = -1.62, p = 0.12] / ratio 1.08 (13 dots) [t(23) = -2.53, p = 0.19] / ratio 1.17 (14 dots) [t(23) = -0.28, p = 0.78]). These results implicate that the discrimination task and the detection task are not comparable in difficulty
The results show that chance level cannot explain the differences in performance in the detection and discrimination task of experiment 1
Summary
The approximate number system (ANS) has been put forth as the foundation for our acquired mathematical abilities [1,2]. Researchers used fundamentally different paradigms to assess the ANS at different developmental stages It is unclear whether results from these different studies can be compared and incorporated into a single model, or whether a single paradigm for testing infants as well as children and adults might be more useful. The ANS has been extensively studied in infants using the socalled ‘looking-time’ paradigm In studies employing this method, a stimulus (e.g. a random dot array) with the same numerosity content (often called a ‘standard’) is presented repeatedly, which results in a decrease in time spent looking at the stimulus (a phenomenon called ‘habituation’). The presentation of a stimulus with a distinct numerosity subsequently results in a looking-time increase Such an increase in looking time can only be obtained if the infant is capable of detecting the number-deviant stimuli among the standards. That other studies failed to replicate this finding, and instead revealed a relation between comparing symbolic number stimuli and math ability [11,12]
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