Horses (Equus caballus) select the greater of two quantities in small numerical contrasts

The ability to select the greater numerosity over another in small sets seems to stem from the calculation of which set contains more, and has been taken as evidence of a primordial representation at the roots of the primate numerical system. We tested 56 horses (Equus caballus) in a paradigm previously used with human infants and nonhuman primates. Horses saw two quantities paired in contrasts—2 versus 1, 3 versus 2, 6 versus 4 and a control for volume, 2 versus 1 big—and had to make a choice by snout touching the container holding the numerosity selected. The horses spontaneously selected the greater of the two quantities when the numerosities were small. These results add to evidence showing spontaneous quantity assessment in a variety of species. To my brother Marcelo Uller (1964–2008), for whom the understanding of animals, through biomimetics, was the only way to understand man-made engineering.     

Children’s early mental number line: Logarithmic or decomposed linear?

Recently, the nature of children’s mental number line has received much investigation. In the number line task, children are required to mark a presented number on a physical number line with fixed endpoints. Typically, it was observed that the estimations of younger/inexperienced children were accounted for best by a logarithmic function, whereas those of older/more experienced children were reflected best by a linear function. This led to the conclusion that children’s mental number line transforms from logarithmic to linear with age and experience. In this study, we outline an alternative interpretation of children’s performance in a number line task. We suggest that two separate linear representations for one- and two-digit numbers may exist in young children and that initially the integration of these two representations into the place value structure of the Arabic number system is not fully mastered. When testing this assumption in a sample of more than 120 first graders, we observed that the two-linear model consistently provided better fit indexes. We conclude that instead of assuming a transition from logarithmic to linear coding, performance differences could also be accounted for by an improvement in integrating tens and units into the Arabic place value system.     

Number estimation relies on a set of segmented objects

How do we estimate the number of objects in a set? Two types of visual representations might underlie this ability - an unsegmented visual image or a segmented collection of discrete objects. We manipulated whether individual objects were isolated from each other or grouped into pairs by irrelevant lines. If number estimation operates over an unsegmented image, then this manipulation should not affect estimates. But if number estimation relies on a segmented image, then grouping pairs of objects into single units should lead to lower estimates. In Experiment 1 participants underestimated the number of grouped objects, relative to disconnected objects in which the connecting lines were ‘broken’. Experiment 2 presents evidence that this segmentation process occurred broadly across the entire set of objects. In Experiment 3, a staircase procedure provides a quantitative measure of the underestimation effect. Experiment 4 shows that the strength of the grouping effect was equally strong for a single thin line, and the effect can be eliminated by a small break in the line. These results provide direct evidence that number estimation relies on a segmented input.     

Re-visiting the competence/performance debate in the acquisition of the counting principles

Advocates of the "continuity hypothesis" have argued that innate non-verbal counting principles guide the acquisition of the verbal count list (Gelman & Galistel, 1978). Some studies have supported this hypothesis, but others have suggested that the counting principles must be constructed anew by each child. Defenders of the continuity hypothesis have argued that the studies that failed to support it obscured children's understanding of counting by making excessive demands on their fragile counting skills. We evaluated this claim by testing two-, three-, and four-year-olds both on "easy" tasks that have supported continuity and "hard" tasks that have argued against it. A few noteworthy exceptions notwithstanding, children who failed to show that they understood counting on the hard tasks also failed on the easy tasks. Therefore, our results are consistent with a growing body of evidence that shows that the count list as a representation of the positive integers transcends pre-verbal representations of number.     

How to trigger elaborate processing? A comment on Kunde, Kiesel, and Hoffmann (2003)

Recently, [Kunde, W., Kiesel, A., & Hoffmann, J. (2003). Conscious control over the content of unconscious cognition. Cognition, 88, 223-242] used a masked priming paradigm to argue that neither the 'elaborate processing' or the 'evolving automaticity' view can account for the processing of unconscious numerical stimuli. In our Experiment 1 we replicated [Kunde, W., Kiesel, A., & Hoffmann, J. (2003). Conscious control over the content of unconscious cognition. Cognition, 88, 223-242] Experiment 4 and show that with a less demanding mask than that used by Kunde et al., 'elaborate processing' can explain priming results given that there are side conditions to trigger elaborate processing of unconscious stimuli. The second experiment further explores this influence of the masks by increasing the relevance of the symbols by which the mask is composed. The results show that an increase in relevance of the mask is accompanied by a decrease in the priming effect, though there was no significant change in conscious awareness of the prime.     

Pseudoneglect for the bisection of mental number lines

Patients with unilateral neglect of the left side bisect physical lines to the right whereas individuals with an intact brain bisect lines slightly to the left (pseudoneglect). Similarly, for mental number lines, which are arranged in a left-to-right ascending sequence, neglect patients bisect to the right. This study determined whether individuals with an intact brain show pseudoneglect for mental number lines. In Experiment 1, participants were presented with visual number triplets (e.g., 16, 36, 55) and determined whether the numerical distance was greater on the left or right side of the inner number. Despite changing the spatial configuration of the stimuli, or their temporal order, the numerical length on the left was consistently overestimated. The fact that the bias was unaffected by physical stimulus changes demonstrates that the bias is based on a mental representation. The leftward bias was also observed for sets of negative numbers (Experiment 2)—demonstrating not only that the number line extends into negative space but also that the bias is not the result of an arithmetic distortion caused by logarithmic scaling. The leftward bias could be caused by a rounding-down effect. Using numbers that were prone to large or small rounding-down errors, Experiment 3 showed no effect of rounding down. The task demands were changed in Experiment 4 so that participants determined whether the inner number was the true arithmetic centre or not. Participants mistook inner numbers shifted to the left to be the true numerical centre—reflecting leftward overestimation. The task was applied to 3 patients with right parietal damage with severe, moderate, or no spatial neglect (Experiment 5). A rightward bias was observed, which depended on the severity of neglect symptoms. Together, the data demonstrate a reliable and robust leftward bias for mental number line bisection, which reverses in clinical neglect. The bias mirrors pseudoneglect for physical lines and most likely reflects an expansion of the space occupied by lower numbers on the left side of the line and a contraction of space for higher numbers located on the right.     

The approximate number system is not predictive for symbolic number processing in kindergarteners

The relation between the approximate number system (ANS) and symbolic number processing skills remains unclear. Some theories assume that children acquire the numerical meaning of symbols by mapping them onto the preexisting ANS. Others suggest that in addition to the ANS, children also develop a separate, exact representational system for symbolic number processing. In the current study, we contribute to this debate by investigating whether the nonsymbolic number processing of kindergarteners is predictive for symbolic number processing. Results revealed no association between the accuracy of the kindergarteners on a nonsymbolic number comparison task and their performance on the symbolic comparison task six months later, suggesting that there are two distinct representational systems for the ANS and numerical symbols.     

Numerical and physical magnitudes are mapped into time

In two experiments we investigated mapping of numerical and physical magnitudes with temporal order. Pairs of digits were presented sequentially for a size comparison task. An advantage for numbers presented in ascending order was found when participants were comparing the numbers' physical and numerical magnitudes. The effect was more robust for comparisons of physical size, as it was found using both select larger and select smaller instructions, while for numerical comparisons it was found only for select larger instructions. Varying both the digits' numerical and physical sizes resulted in a size congruity effect, indicating automatic processing of the irrelevant magnitude dimension. Temporal order and the congruency between numerical and physical magnitudes affected comparisons in an additive manner, thus suggesting that they affect different stages of the comparison process.     

Task instructions determine the visuospatial and verbal–spatial nature of number–space associations

Evidence for number–space associations comes from the spatial–numerical association of response codes (SNARC) effect, consisting in faster reaction times to small/large digits with the left/right hand, respectively. Two different proposals are commonly discussed concerning the cognitive origin of the SNARC effect: the visuospatial account and the verbal–spatial account. Recent studies have provided evidence for the relative dominance of verbal–spatial over visuospatial coding mechanisms, when both mechanisms were directly contrasted in a magnitude comparison task. However, in these studies, participants were potentially biased towards verbal–spatial number processing by task instructions based on verbal–spatial labels. To overcome this confound and to investigate whether verbal–spatial coding mechanisms are predominantly activated irrespective of task instructions, we completed the previously used paradigm by adding a spatial instruction condition. In line with earlier findings, we could confirm the predominance of verbal–spatial number coding under verbal task instructions. However, in the spatial instruction condition, both verbal–spatial and visuospatial mechanisms were activated to an equal extent. Hence, these findings clearly indicate that the cognitive origin of number–space associations does not always predominantly rely on verbal–spatial processing mechanisms, but that the spatial code associated with numbers is context dependent.