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Symbolic and non-symbolic number processing, a developmental perspective

Final Report Summary - QUANTITY IN NUMBER (Symbolic and non-symbolic number processing, a developmental perspective)

The ability to perform simple mathematics is useful in everyday life. Unfortunately, around 10 % of the children have problems with mathematics. It is suggested that proficiency in non-symbolic number processes forms the basis for (future) more complex mathematical abilities. Several studies reported a relation between the performance in comparing or estimating different sets of items and mathematical procedures such as addition and multiplication. The approximate number system (ANS) is suggested the crucial mechanism that underlies the ability to compare or judge numerosities. The ANS is able to process numerosity independent of its confounding sensory cues (such as surface and density). If this is indeed the case, training children on numerosity tasks and thus improve the ANS could improve more complex mathematical abilities. Because of the potential importance of numerosity processes in the development of mathematical skills it is necessary to get a clear idea about the underlying (neural) mechanisms.

Numerosity processing is generally studied using the number comparison task. Here, two numerosities are presented and the participant has to judge which of the two numerosities is numerically larger. Often, the different visual cues of the stimuli are manipulated to control for the confounding sensory cues (e.g. surface increases with increasing number). The comparison task is however suggested to reflect decisional instead of numerosity processes. To exclude this possibility a priming paradigm was used to study the development of numerosity processes (Defever et al., 2011, JECP). Here, two numerosities are presented sequentially. An interaction between the first and the second numerosity occurs and this effect is larger when the two numerosities are closer to each other. We studied this so-called priming distance effect and its possible relation with mathematical abilities across different ages using symbolic and non-symbolic number stimuli. The results showed that a priming distance effect is already present in kindergartners and it remained stable across development. This suggests that formal schooling does not affect magnitude representation. The priming distance effect was also associated with performance on a standardised mathematics test confirming the hypotheses that the approximate number system is directly related to mathematical abilities.

The neural mechanisms involved in numerosity processing were studied using the priming paradigm and adult participants. Unfortunately, no significant difference between the different numerosity conditions or between symbolic and non-symbolic notation were found (Gebuis and Reynvoet, unpublished data). A possible explanation for the absence of an effect could be the sensory cues that comprise the numerosity stimuli. The different visual cues present in the numerosity stimuli were manipulated in such a way that they did not correlate with numerosity across trials. Although this manipulation should prevent participants to rely on the sensory cues, the visual cues can still influence performance. This hypothesis is consistent with studies investigating the role of sensory information in numerosity judgments in children (Szucs et al., under review). Children perform under chance level when they have to judge non-symbolic number stimuli when the sensory cues are inconsistent with numerosity. Similar results were also obtained using adults (Gebuis and van der Smagt, 2011, Plos One). To test whether sensory cues can explain the contradictory results we created a program that not only manipulated the sensory cues but also gave insight in its relation to the sensory cues (Gebuis and Reynvoet, 2011, BRM).

Using the programme, conditions where only a single or multiple visual cues were manipulated were created to study the interaction between numerosity and its sensory cues (Gebuis and Reynvoet, 2012, JEPg). In the four different visual cue conditions, an effect of visual cues was present. Interestingly, this effect was larger when multiple visual cues were manipulated compared to a single visual cue. Furthermore, if two sensory cues influenced the numerosity judgment in opposite directions, the combination of both sensory cues resulted in the cancellation of the sensory effect. The influence of different sensory cues on numerosity processes was not only visible in numerosity comparison but also in numerosity estimation (Gebuis and Reynvoet, 2012, Plos One). These results suggest that the current hypothesis of an ANS that supports numerosity processing is incorrect. Alternatively, it appears more likely that the different sensory cues are used to make the numerosity judgments.

To further investigate whether an ANS or sensory processes underlie the ability to judge numerosities the neural mechanisms supporting numerosity processing were studied using EEG (Gebuis and Reynvoet, 2012, Psychophysiology). Systematic manipulation of the sensory cues present in numerosity stimuli caused an increase in the ERP components often associated with numerosity. This implied that if the sensory cues are not properly controlled, neural responses to numerosity could falsely be identified as numerical instead of sensory. Indeed, when the sensory cues were controlled in such a manner that they did not linearly correlate with number, no numerosity related effect was present even though numerosity changed. This study was a passive viewing paradigm. A second study was conducted where participants had to passively as well as actively attend numerosity (Gebuis and Reynvoet, 2013, Neuroimage). In both the passive and active task, no significant effects of numerosity were present when the sensory cues were not correlated with numerosity. However, when the data was analysed according to the sise of the different visual cues, a strong effect of the visual cues appeared at the ERP components previously suggested to support numerosity processes. These results show that visual cues can explain earlier findings of numerosity and support the theory that not an ANS but visual cues support our numerosity processes.

It can then be questioned again what underlies the relation between proficiency in numerosity processing and (future) mathematical abilities. It should be noted that not all studies find this relation. Possibly the hypothesis that sensory cues underlie numerosity processes could explain these contradictory results. Researchers investigating numerosity processes often use their own methods to control the sensory stimuli present in numerosity data and sometimes also different tasks. To investigate the role of both visual cues and task, children from different age groups were studied using a numerosity comparison and a same different task. Also mathematical abilities were measured using standardised mathematics tests. The results showed that the reliance on the sensory cues changed with age. The visual cues also differently affected the results depending on the task instructions. In the comparison task children looked at the sise of the stimuli (smaller versus larger) while in the same different task the visual similarity of the stimuli was responded to (visual cues are more similar or dissimilar). That different processes play a role in these magnitude tasks was confirmed using EEG (Smets, Gebuis and Reynvoet, 2013, FHN). Unfortunately, in the behavioural study, no relationship between numerosity processing on either task or mathematical abilities was found. This prevented us from investigating the potential role visual cues could play in the relationship between proficiency in numerosity tasks and mathematical abilities. The different hypotheses regarding the relation between mathematical abilities and numerosity processing are summarised in a book chapter (Gebuis and Reynvoet, in press).