Does the number sense represent number?

On a now orthodox view, humans and many other animals are endowed with a “number sense”, or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques, with critics maintaining either that numerical content is absent altogether, or else that some primitive analog of number (‘numerosity’) is represented as opposed to number itself. We distinguish three arguments for these claims – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then highlight positive reasons for thinking that the ANS genuinely represents numbers. The upshot is that proponents of the orthodox view should not feel troubled by recent critiques of their position

Incongruence in number–luminance congruency effects

Congruency tasks have provided support for an amodal magnitude system for magnitudes that have a “spatial” character, but conflicting results have been obtained for magnitudes that do not (e.g., luminance). In this study, we extricated the factors that underlie these number–luminance congruency effects and tested alternative explanations: (unsigned) luminance contrast and saliency. When luminance had to be compared under specific task conditions, we revealed, for the first time, a true influence of number on luminance judgments: Darker stimuli were consistently associated with numerically larger stimuli. However, when number had to be compared, luminance contrast, not luminance, influenced number judgments. Apparently, associations exist between number and luminance, as well as luminance contrast, of which the latter is probably stronger. Therefore, similar tasks, comprising exactly the same stimuli, can lead to distinct interference effects

Developmental differences in approaches to nonsymbolic comparison tasks

Nonsymbolic comparison tasks are widely used to measure children’s and adults’ Approximate Number System (ANS) acuity. Recent evidence has demonstrated that task performance can be influenced by changes to the visual characteristics of the stimuli, leading some researchers to suggest it is unlikely that an ANS exists that can extract number information independently of the visual characteristics of the arrays. Here we analysed 124 children’s and 120 adults’ dot comparison accuracy scores from three separate studies to investigate individual and developmental differences in how numerical and visual information contribute to nonsymbolic numerosity judgements. We found that, in contrast to adults, the majority of children did not use numerical information over and above visual cue information to compare quantities. This finding was consistent across different studies. The results have implications for research on the relationship between dot comparison performance and formal mathematics achievement. Specifically, if most children’s performance on dot comparison tasks can be accounted for without the involvement of numerical information, it seems unlikely that observed correlations with mathematics achievement stem from ANS acuity alone

Inhibition in dot comparison tasks

Dot comparison tasks are commonly used to index an individual’s Approximate Number System (ANS) acuity, but the cognitive processes involved in completing these tasks are poorly understood. Here we investigated how factors including numerosity ratio, set size and visual cues influence task performance. Forty-­four children aged 7-­9 years completed a dot comparison task with a range of to-­be-­compared numerosities. We found that as the size of the numerosities increased, with ratios held constant, accuracy decreased due to the heightened salience of incongruent visual information. Furthermore, in trials with larger numerosities participants’ accuracies were influenced more by the convex hull of the array than the average dot size. The numerosity ratio between the arrays in each trial was an important predictor for all set sizes. We argue that these findings are consistent with a ‘competing processes’ inhibition-­based account, where accuracy scores are influenced by individual differences in both ANS acuity and inhibitory control skills

Arithmetic word problem solving: evidence for a magnitude-based mental representation

[EN] Previous findings have suggested that number processing involves a mental representation of numerical magnitude. Other research has shown that sensory experiences are part and parcel of the mental representation (or “simulation”) that individuals construct during reading.We aimed at exploring whether arithmetic word-problem solving entails the construction of a mental simulation based on a representation of numerical magnitude. Participants were required to solve word problems and to perform an intermediate figure discrimination task that matched or mismatched, in terms of magnitude comparison, the mental representations that individuals constructed during problem solving. Our results showed that participants were faster in the discrimination task and performed better in the solving task hen the figures matched the mental representations. These findings provide evidence that an analog magnitude-based mental representation is routinely activated during word-problem solving, and they add to a growing body of literature that emphasizes the experiential view of language comprehension

Indexing the approximate number system

Much recent research attention has focused on understanding individual differences in the Approximate Number System, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the Numerical Ratio Effect has poor testretest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or Numerical Ratio Effects

Implicit response-irrelevant number information triggers the SNARC effect : Evidence using a neural overlap paradigm

Peer reviewedPostprin

Correlation Between Automatic Processing of Symbolic and Non-symbolic Magnitudes in Children

Does the automatic activation of number influence children’s decision-making on physical size judgments? Previous work dealing with how children process symbolic and non-symbolic numbers typically involves making direct judgments about numerical values. In this study, instead of asking for judgments about numerical magnitude, we assessed the automatic activation of number by asking children to make physical size judgments. This will allow us to further learn how children use their understanding of numbers to help them make decisions that do not directly involve numbers. In addition to this, by looking at how the processing of symbolic and non-symbolic numbers relate, we will get a closer look at when children acquire an understanding of both symbolic and non-symbolic numbers. In the symbolic task, children were asked to indicate which number was physically larger; and in the non-symbolic task, children were asked to indicate which dot array took up a larger area. Through these tasks we hope to address two questions. First, if the automatic activation of numbers will facilitate or interfere with the required size judgments; and second, the extent to which responses on the symbolic and non-symbolic tasks relate. Fifty-two children between the ages of 6 and 9 completed the study on a laptop computer. Response time and accuracy were recorded for each participant on each task. Results indicate that in the non-symbolic task, the automatic activation of number facilitates and interferes with size judgments, but in the symbolic task, automatic activation of number only interferes with size judgments. To assess the relationship between the two tasks, we correlated interference and facilitation effects; however, no significant correlations were found. The findings from this study will help further our understanding of how children learn numbers, and the mechanisms involved in number processing

Are bilingual children better at ignoring perceptually misleading information? A novel test

Does speaking more than one language help a child perform better on certain types of cognitive tasks? One possibility is that bilingualism confers either specific or general cognitive advantages on tasks that require selective attention to one dimension over another (e.g., Bialystok, 2001; Hilchey & Klein, 2011). Other studies have looked for such an advantage but found none (e.g., Morton & Harper, 2007; Paap & Greenberg, 2013). The present study compared monolingual and bilingual children's performance on a numerical discrimination task, which required children to ignore area and attend to number. Ninety-two children, ages 3 to 6 years, were asked which of two arrays of dots had “more dots.” Half of the trials were congruent, where the numerically greater array was also larger in total area, and half were incongruent, where the numerically greater array was smaller in total area. All children performed better on congruent than on incongruent trials. Older children were more successful than younger children at ignoring area in favor of number. Bilingual children did not perform differently from monolingual children either in number discrimination itself (i.e., identifying which array had more dots) or at selectively attending to number. The present study thus finds no evidence of a bilingual advantage on this task for children of this age

The role of short-term memory and visuo-spatial skills in numerical magnitude processing: evidence from Turner syndrome

Peer reviewe