Numerical order and quantity processing in number comparison

We investigated processing of numerical order information and its relation to mechanisms of numerical quantity processing. In two experiments, performance on a quantity-comparison task (e.g. 2 5; which is larger?) was compared with performance on a relative-order judgment task (e.g. 2 5; ascending or descending order?). The comparison task consistently produced the standard distance effect (faster judgments for far relative to close number pairs), but the distance effect was smaller for ascending (e.g. 2 5) compared to descending pairs (e.g. 5 2). The order task produced a pair-order effect (faster judgments for ascending pairs) and a reverse distance effect for consecutive pairs in ascending order. The reverse effect implies an order-specific process, such as serial search or direct recognition of order for successive numbers. Thus, numerical quantity and order judgments recruited different cognitive mechanisms. Nonetheless, the reduced distance effect for ascending pairs in the quantity task implies involvement of order-related processes in magnitude comparison. Accordingly, distance effects in the quantity-comparison task are not necessarily a process-pure measure of magnitude representation.     

The Early Numeracy Test in Finnish: children's norms

This article concerns psychometric aspects of the Finnish Early Numeracy Test, which has been translated from the original Dutch Early Numeracy Test. The advantage of the test is that young children's numerical skills can be assessed systematically, which was not possible previously in Finland. A norm study was conducted in which the test was administered to a representative sample of 1,029 Finnish children. The reliability and validity results justify the use of the test as an early-childhood screening test and in research on number sense. The indicative effects of gender, parental professional education, domicile and number of siblings are discussed.     

Language effects in magnitude comparison: small, but not irrelevant

It is assumed that number magnitude comparison is performed by assessing magnitude representation on a single analog mental number line. However, we have observed a unit-decade-compatibility effect in German which is inconsistent with this assumption (Nuerk, Weger, & Willmes, 2001). Incompatible magnitude comparisons in which decade and unit comparisons lead to different responses (e.g., 37_52 for which 3<5, but 7>2) are slower and less accurately responded to than compatible trials in which decade and unit comparisons lead to the same response (e.g., 42_57, for which 4<5 and 2<7). As overall distance was held constant, a single holistic magnitude representation could not account for this compatibility effect. However, because of the inversion property of the corresponding German two-digit number words ("einundzwanzig" ), the language-generality of the effect is questionable. We have therefore examined the compatibility effect with native English speakers. We were able to replicate the compatibility effect using Arabic notation. Thus, the compatibility effect is not language-specific. However, in cross-linguistic analyses language-specific modulations were observed not only for number words but also for Arabic numbers. The constraints imposed on current models by the verbal mediation of Arabic number comparison are discussed.     

Atypical trajectories of number development: a neuroconstructivist perspective

Despite the fact that number deficits are as prevalent as literacy deficits, research on basic numerical skills lags seriously behind the successful studies identifying low-level deficits in dyslexia. We review current debates on number, discussing how the competing theories pertain to mathematical disabilities in normal children and numeracy deficits in genetic disorders. We stress the need to consider these issues within the framework of a developing system rather than from the neuropsychological perspective of focal damage. The earlier the exploration of atypical trajectories in very basic numerical skills, the better we will be able to chart their developmental impact on subsequent, higher-level arithmetic abilities.     

Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking

While reaction time data have shown that decomposed processing of two-digit numbers occurs, there is little evidence about how decomposed processing functions. Poltrock and Schwartz (1984) argued that multi-digit numbers are compared in a sequential digit-by-digit fashion starting at the leftmost digit pair. In contrast, Nuerk and Willmes (2005) favoured parallel processing of the digits constituting a number. These models (i.e., sequential decomposition, parallel decomposition) make different predictions regarding the fixation pattern in a two-digit number magnitude comparison task and can therefore be differentiated by eye fixation data. We tested these models by evaluating participants' eye fixation behaviour while selecting the larger of two numbers. The stimulus set consisted of within-decade comparisons (e.g., 53_57) and between-decade comparisons (e.g., 42_57). The between-decade comparisons were further divided into compatible and incompatible trials (cf. Nuerk, Weger, & Willmes, 2001) and trials with different decade and unit distances. The observed fixation pattern implies that the comparison of two-digit numbers is not executed by sequentially comparing decade and unit digits as proposed by Poltrock and Schwartz (1984) but rather in a decomposed but parallel fashion. Moreover, the present fixation data provide first evidence that digit processing in multi-digit numbers is not a pure bottom-up effect, but is also influenced by top-down factors. Finally, implications for multi-digit number processing beyond the range of two-digit numbers are discussed.     

Judgement of discrete and continuous quantity in adults: Number counts!

Three experiments involving a Stroop-like paradigm were conducted. In Experiment 1, adults received a number comparison task in which large sets of dots, orthogonally varying along a discrete dimension (number of dots) and a continuous dimension (cumulative area), were presented. Incongruent trials were processed more slowly and with less accuracy than congruent trials, suggesting that continuous dimensions such as cumulative area are automatically processed and integrated during a discrete quantity judgement task. Experiment 2, in which adults were asked to perform area comparison on the same stimuli, revealed the reciprocal interference from number on the continuous quantity judgements. Experiment 3, in which participants received both the number and area comparison tasks, confirmed the results of Experiments 1 and 2. Contrasting with earlier statements, the results support the view that number acts as a more salient cue than continuous dimensions in adults. Furthermore, the individual predisposition to automatically access approximate number representations was found to correlate significantly with adults' exact arithmetical skills.     

The role of numerical and non-numerical cues in nonsymbolic number processing: Evidence from the line bisection task

In line bisection tasks, adults and children bisect towards the numerically larger of two nonsymbolic numerosities [de Hevia, M. D., & Spelke, E. S. (2009 de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110, 198–207. doi:10.1016/j.cognition.2008.11.003[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Spontaneous mapping of number and space in adults and young children. Cognition, 110, 198–207. doi:10.1016/j.cognition.2008.11.003]. However, it is not clear whether this effect is driven by number itself or rather by visual cues such as subtended area [Gebuis, T., & Gevers, W. (2011 Gebuis, T., & Gevers, W. (2011). Numerosities and space: Indeed a cognitive illusion! A reply to de Hevia and Spelke (2009). Cognition, 121, 248–252. doi:10.1016/j.cognition.2010.09.008[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Numbers and space: Indeed a cognitive illusion! A reply to de Hevia and Spelke (2009 de Hevia, M. D., & Spelke, E. S. (2009). Spontaneous mapping of number and space in adults and young children. Cognition, 110, 198–207. doi:10.1016/j.cognition.2008.11.003[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Cognition, 121, 248–252. doi:10.1016/j.cognition.2010.09.008]. Furthermore, this effect has only been demonstrated with flanking displays of two and nine items. Here, we report three studies that examined whether this “spatial bias” effect occurs across a range of absolute and ratio numerosity differences; in particular, we examined whether the bias would occur when both flankers were outside the subitizing range. Additionally, we manipulated the subtended area of the stimulus and the aggregate surface area to assess the influence of visual cues. We found that the spatial bias effect occurred for a range of flanking numerosities and for ratios of 3:5 and 5:6 when subtended area was not controlled (Experiment 1). However, when subtended area and aggregate surface area were held constant, the biasing effect was reversed such that participants bisected towards the flanker with fewer items (Experiment 2). Moreover, when flankers were identical, participants bisected towards the flanker with larger subtended area or larger aggregate surface area (Experiments 2 and 3). On the basis of these studies, we conclude that the spatial bias effect for nonsymbolic numerosities is primarily driven by visual cues.     

Eye movements when reading words with $YMβOL$ and NUM83R5: There is a cost

Recent evidence from masked priming experiments has revealed that readers regularize letter-like symbols and letter-like numbers into their corresponding base letters with minimal processing cost. However, one open question is whether the same pattern occurs when these items are presented during normal silent reading. In the present study, we respond to this question in an eye-movement experiment that included sentences with words that had symbols and numbers as letters, as in “YESTERDAY I SAW THE SECRE74RY WORKING VERY HARD”. Results revealed that there is a greater reading cost associated with letter-by-number replacements than with letter-by-symbol replacements, especially when the replaced letters occur at the beginning of the word. We examine the implications of these findings for models of visual word recognition and reading.     

Laypeople do use sample variance: The effect of embedding data in a variance-implying story

When using sample data to decide whether two populations differ, laypeople attend to the difference between group means, but largely overlook within-group variability (Obrecht, Chapman, & Gelman, 2007 Obrecht, N. A., Chapman, G. B. and Gelman, R. 2007. Intuitive t-tests: Lay use of statistical information. Psychonomic Bulletin & Review, 14: 1147–1152.  [Google Scholar]). We show, first, that laypeople know about and use story-implied variability when making pairwise comparisons. Then we demonstrate that participants’ sensitivity to variance in a dataset is boosted when presented in a context that implies consistent variance information. Statistical data were couched in stories about electrical conductivity measurements obtained from element samples (low-variability category) or body weight measurements from samples of peoples (high-variability category). We manipulated, between participants, whether the data variance matched or mismatched the story-implied variability. Participants who received data in a matching context showed high sensitivity to variance, while those in the mismatching condition did not. Laypeople use statistical data to make reasonable inferences when those data are provided in a context that makes sense.     

Competitor effects in naming objects and famous faces

The prior production of an alternative name increases the time taken to name a famous face. For example, naming a picture of the comedy actor “John Cleese” by the name of the character he played in the TV series Fawlty Towers (Basil Fawlty) increases the time required to subsequently produce the name “John Cleese”. This effect has been termed the “nominal competitor effect”. In contrast prior production of a property associated with a famous person has no effect on naming speed. For example, prior production of the name of the TV series Fawlty Towers does not slow subsequent production of “John Cleese”. The experiments reported explored analogous effects in object naming. Experiment 1 examined the effects of prior production of an alternative name (e.g., from American English or British English) and a semantic associate on the time taken to name line drawings of objects. It was found that prior production of an alternative name slowed object naming, but prior production of the name of a semantic associate did not. Experiment 2 demonstrated that cueing a specific name (e.g., the British English name) was not a necessary condition for the nominal competitor effect on object naming. Experiment 3 demonstrated that the nominal competitor effect on naming famous faces was also observed under both cued and uncued naming instructions. The data from both object and face naming are interpreted within the terms of current models of speech production.