Research in numerical cognition has led to a widely accepted view of the existence of innate, domain-specific, core numerical knowledge that involves the intraparietal sulcus in the brain. Much of this research has revolved around the ability to perceive and manipulate discrete quantities (e.g., enumeration of dots). We question several aspects of this accepted view and suggest that continuous noncountable dimensions might play an important role in the development of numerical cognition. Accordingly, we propose that a relatively neglected aspect of performance—the ability to perceive and evaluate sizes or amounts—might be an important foundation of numerical processing. This ability might even constitute a more primitive system that has been used throughout evolutionary history as the basis for the development of the number sense and numerical abilities.

What is bigger, an elephant or a mouse? This question can be answered without seeing the two animals, since these objects elicit conceptual magnitude. How is an object’s conceptual magnitude processed? It was suggested that conceptual magnitude is automatically processed; namely, irrelevant conceptual magnitude can affect performance when comparing physical magnitudes. The current study further examined this question and aimed to expand the understanding of automaticity of conceptual magnitude. Two different objects were presented and participants were asked to decide which object was larger on the screen (physical magnitude) or in the real world (conceptual magnitude), in separate blocks. By creating congruent (the conceptually larger object was physically larger) and incongruent (the conceptually larger object was physically smaller) pairs of stimuli it was possible to examine the automatic processing of each magnitude. A significant congruity effect was found for both magnitudes. Furthermore, quartile analysis revealed that the congruity was affected similarly by processing time for both magnitudes. These results suggest that the processing of conceptual and physical magnitudes is automatic to the same extent. The results support recent theories suggested that different types of magnitude processing and representation share the same core system.

Enumeration of elements differs as a function of their range. Subitizing (quantities 1–4) is considered to be an accurate and quick process with reaction times minimally affected by the number of presented elements within its range. In contrast, small estimation (range of 5–9 elements exposed briefly) is a less precise linear process. Subitizing was consider to be a pre-attentive process for many years. However, recent studies found that when attentional resources were occupied elsewhere, the subitizing process was impaired. In the current study, we examined whether subitizing can be facilitated by improving engagement of attention. Specifically, brief alerting cues that increase attentional engagement were presented in half of the trials during enumeration tasks. In Experiment 1, participants were required to enumerate dots presented in random arrays within the subitizing or small estimation range. Alerting facilitated enumeration of quantities in the subitizing range, but not in the small estimation range. We suggested that the benefit of alerting on the subitizing process was achieved via enhancement of global processing, a process that was previously associated with both alerting and subitizing. In Experiment 2, we provided direct evidence for this hypothesis by demonstrating that when global processing was used for items in the small estimation range (i.e., presenting quantities in a canonical array), a subitizing-like pattern was revealed in quantities beyond the subitizing range.

Enumeration, the ability to report an amount of elements, differs as a function of range. Subitizing (quantities 1–4) is an accurate and quick process with reaction times (RTs) minimally affected by the number of presented elements within its range. In the counting range (range of 5–9 elements), RTs increase linearly. Subitizing was considered to be a pre-attentive process for many years. However, recently we found that subitizing could be facilitated by improving engagement of attention. Specifically, brief alerting cues increase attentional engagement and reduced RTs in the subitizing range. Moreover, previous studies found that students with developmental dyscalculia (DD) have a smaller than normal subitizing range (3 vs. 4) and their alerting attentional system is impaired. In the current study, we explored whether an alerting cue would increase the subitizing range of adults suffering from DD from 3 to 4. For controls, alerting increased accuracy rates and facilitated enumeration of quantities only in the subitizing range. Participants with DD presented a larger alerting effect; an alerting cue enhanced their RTs in all ranges, but did not increase their smaller than normal subitizing range or accuracy. Our results suggest that both domain-general and domain-specific abilities contribute to the mechanism of enumeration and related to developmental dyscalculia.

Our results fit with previous findings of weaker magnitude representation in those with DD, specifically regarding noncountable magnitudes, and support theories of a shared neurocognitive substrate for different types of magnitudes. (PsycINFO Database Record