Previous studies investigating whether symbolic and non-symbolic numbers are processed by one representation system or whether two distinct number systems exist, have provided us with contradicting findings. Some researchers claim that there are separate systems, based on the presence of a cognitive switch cost when adults have to integrate symbolic and non-symbolic quantities 22. Others claim that non-symbolic and symbolic numbers are automatically integrated 21. Therefore, the aim of the present study was to use various experimental manipulations to investigate this issue again, while bridging some of the methodological differences between these previous studies.

We conducted three behavioral experiments with adults. In Experiment 1, we replicated experiments 2 and 3 of Lyons et al. 22, but instead of only using one instruction format, our participants performed the task with both comparison and matching instructions. In Experiment 2 of the current study, we examined the role of the presentation order of the trials (i.e., blocked vs. randomized presentation). At first sight, and contrary to our expectations based on the findings of Lyons et al. 22, Experiments 1 and 2 did not support the hypothesis of two distinct magnitude representation systems. However, by analyzing the data in more detail we showed that the presence of a cost when switching from symbolic to non-symbolic numbers can be masked by differences in processing times for the different notations. In order to circumvent this problem, we conducted Experiment 3, using an audio-visual paradigm. In this last experiment, as hypothesized, a clear switch cost for mixed trials was observed. Taken together, our results show that, when investigating the integration between symbolic and non-symbolic quantities with a paradigm well-suited for the purpose, i.e., one that is less affected by the RT differences between symbolic and non-symbolic numbers, an additional processing cost becomes apparent.

From a methodological point of view, our results show that, when comparing different types of sequentially presented trials, it is crucial to keep the second stimulus identical, in order to control for differences in processing time. The audiovisual paradigm is not affected by the above – it has been used before by Sasanguie et al. 14 and in our Experiment 3. In addition, this paradigm has several other advantages. The first one is that participants cannot base their decisions solely on the visual similarities between the stimuli properties – a problem that has been previously reported in studies using other paradigms (e.g., 38,26,28,39,40). Second, as we already pointed out above, a notation switch is always present in all types of trials. Consequently, a difference in performance between the pure and mixed trials is never confounded by the fact that participants have to switch between notations in mixed trials (e.g., digit – dot) but not in pure trials (e.g., dot – dot; see Experiment 1 – 2, Lyons et al.22), and is therefore most likely due to switching between underlying mental representations. Finally, the audio-visual paradigm is very well-suited to investigations of the developmental trajectory of the integration between symbolic and non-symbolic quantities, because it does not require that the participants can read (e.g., number words; for similar reasoning, see 41).

From a theoretical point of view, our overall results are compatible with the findings of Lyons et al. 22, suggesting that symbolic and non-symbolic quantities are processed by two distinct magnitude representation systems. The question now, however, is how do these two systems look like? One suggestion regarding the features of these systems comes for the study of Sasanguie et al. 14. There the authors argued that non-symbolic quantities are processed by the approximate system, whereas symbolic quantities are processed independently by a discrete and precise system (see also 19,42,5).

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