Children's comparison of different-length numbers: Managing different attributes in multidigit number processing

In everyday life the comparison of numbers usually occurs between numbers with different numbers of digits. However, experimental research here is scarce. Recent research has shown that adults respond faster to congruent pairs (the initial digit in the number with more digits is larger, e.g., 2384 vs. 107) than to incongruent pairs (the initial digit is larger in the number with fewer digits, e.g., 2675 vs. 398). This has been interpreted as support for the processing of multiple attributes in parallel and against serial accounts. The current research asked whether there is a change in the relevance of these attributes as school grades increase. School-age children from the second to sixth grades (N = 206) were presented with pairs of numbers that had either the same number of digits (3 vs. 3 or 4 vs. 4) or a different number of digits (3 vs. 4). In this latter condition, the stimuli, matched by distance, could be either length/digit congruent (e.g., 2384 vs. 107) or length/digit incongruent (e.g., 2675 vs. 398). Linear mixed models showed a length/digit congruity effect from second graders. Interestingly, in the response time measure, congruity interacted with school grade and the side in which the larger number of the pair was presented. Whereas these results support a model that considers number comparison as a process that weighs different attributes in parallel, it is also argued that developmental changes are associated with differences in the level of automatization of the componential skills involved in the comparison.

Place-value and physical size converge in automatic processing of multi-digit numbers

Previous research has shown that multi-digit number processing is modulated by both place-value and physical size of the digits. By pitting place-value against physical size, the present study examined whether one of the attributes had a greater impact on the automatic processing of multi-digit numbers. In three experiments, participants were presented with two-digit number pairs that appeared in frames. They were instructed to select the larger frame while ignoring the numbers within the frames. Importantly, we manipulated the physical size of the digits (i.e., both decade/unit digits were physically larger) within the frames, the unit-decade compatibility (i.e., the relationship between the numerical values of both decade and unit digits was consistent or inconsistent), and the congruity between the numerical values of the decade digits and the frames' physical size (i.e., decade-value-frame-size congruity). In Experiment 1, where all pairs were unit-decade compatible, a decade-value-frame-size congruity effect emerged for pairs with physically larger decade, but not unit, digits. However, when adding unit-decade incompatible pairs (Experiments 2-3), in unit-decade compatible pairs, there was a decade-value-frame-size congruity effect regardless of the digits' physical size. In contrast, in unit-decade incompatible pairs, there was no decade-value-frame-size congruity effect, even when the physically larger digit (i.e., unit) contradicted the place-value information, presumably due to the cancellation of the opposing influences of the digits' physical sizes their place-values. Overall, these findings suggest that place-value and physical size are intertwined in the Hindu-Arabic numerical system and are processed as one.

Length is not all that matters: testing the role of number identity and the ratio of fillers in comparisons of multi-digits with different digit length

Research in multi-digit number comparison usually considers stimuli with the same number of digits (e.g., 3452 vs. 7831). Surprisingly, there is almost no research on the comparison of numbers that differ in length (e.g., 995 vs. 1000), which demands a focus on the number of digits in each multi-digit, despite the fact that the role of number length has been explicitly acknowledged in componential models of multi-digit processing. Our study explores whether the comparison of pairs of natural numbers that differ in length is affected by the identity of the leftmost digit of each multi-digit, and asks what is the effect of having variable proportions of trials with pairs of numbers of the same-length in the task. Across three studies participants compared numbers in blocks with different proportions of same-length multi-digit pairs (Experiment 1 and 2: 25% vs. 50% vs. 75%; Experiment 3: 0% vs. 50%). Stimuli in the different-length condition were length-digit congruent (the number with more digits starting with a larger digit: 2384 vs. 107) or length-digit incongruent (the number with more digits starting with a smaller number: 2675 vs. 398). Response times were shorter in length-digit congruent pairs than in the incongruent pairs. Unexpectedly, this effect was only slightly modulated by the proportion of same-/different-length multi-digit pairs in the experimental set. Despite its perceptual saliency, length is not the only information considered when comparing different-length numbers. The leftmost-digit is also taken into account, with variable relevance here, depending on the characteristics of the stimuli set.

Syntactic priming reveals an explicit syntactic representation of multi-digit verbal numbers

When we say or understand verbal numbers, a major challenge to the cognitive system is the need to process the number's syntactic structure. Several studies showed that number syntax is handled by dedicated processes, however, it is still unclear how precisely these processes operate, whether the number's syntactic structure is represented explicitly, and if it is - what this representation looks like. Here, we used a novel experimental paradigm, syntactic priming of numbers, which can examine in detail the syntactic representation of multi-digit verbal numbers. In each trial, the participants - Arabic-Hebrew bilinguals and Hebrew monolinguals - heard a multi-digit number and responded orally with a random number. The syntactic structure of their responses was similar to that of the targets, showing that they represented the verbal number's syntax. This priming effect was genuinely syntactic, and could not be explained as lexical - repeating words from the target; as phonological - responding with words phonologically-similar to the target; or as a numerical distance effect - producing responses numerically close to the target. The syntactic priming effect was stronger for earlier words in the verbal number and weaker for later words, suggesting that the syntactic representation is capped by working-memory limits. We propose that syntactic priming could become a useful method to examine various aspects of the syntactic representation of numbers.

Is place-value processing in four-digit numbers fully automatic? Yes, but not always

Knowing the place-value of digits in multi-digit numbers allows us to identify, understand and distinguish between numbers with the same digits (e.g., 1492 vs. 1942). Research using the size congruency task has shown that the place-value in a string of three zeros and a non-zero digit (e.g., 0090) is processed automatically. In the present study, we explored whether place-value is also automatically activated when more complex numbers (e.g., 2795) are presented. Twenty-five participants were exposed to pairs of four-digit numbers that differed regarding the position of some digits and their physical size. Participants had to decide which of the two numbers was presented in a larger font size. In the congruent condition, the number shown in a bigger font size was numerically larger. In the incongruent condition, the number shown in a smaller font size was numerically larger. Two types of numbers were employed: numbers composed of three zeros and one non-zero digit (e.g., 0040-0400) and numbers composed of four non-zero digits (e.g., 2795-2759). Results showed larger congruency effects in more distant pairs in both type of numbers. Interestingly, this effect was considerably stronger in the strings composed of zeros. These results indicate that place-value coding is partially automatic, as it depends on the perceptual and numerical properties of the numbers to be processed.

Position coding effects in a 2D scenario: the case of musical notation

How does the cognitive system encode the location of objects in a visual scene? In the past decade, this question has attracted much attention in the field of visual-word recognition (e.g., "jugde" is perceptually very close to "judge"). Letter transposition effects have been explained in terms of perceptual uncertainty or shared "open bigrams". In the present study, we focus on note position coding in music reading (i.e., a 2D scenario). The usual way to display music is the staff (i.e., a set of 5 horizontal lines and their resultant 4 spaces). When reading musical notation, it is critical to identify not only each note (temporal duration), but also its pitch (y-axis) and its temporal sequence (x-axis). To examine note position coding, we employed a same-different task in which two briefly and consecutively presented staves contained four notes. The experiment was conducted with experts (musicians) and non-experts (non-musicians). For the "different" trials, the critical conditions involved staves in which two internal notes that were switched vertically, horizontally, or fully transposed--as well as the appropriate control conditions. Results revealed that note position coding was only approximate at the early stages of processing and that this encoding process was modulated by expertise. We examine the implications of these findings for models of object position encoding.

Multi-digit number processing beyond the two-digit number range: a combination of sequential and parallel processes

Investigations of multi-digit number processing typically focus on two-digit numbers. Here, we aim to investigate the generality of results from two-digit numbers for four- and six-digit numbers. Previous studies on two-digit numbers mostly suggested a parallel processing of tens and units. In contrast, the few studies examining the processing of larger numbers suggest sequential processing of the individual constituting digits. In this study, we combined the methodological approaches of studies implying either parallel or sequential processing. Participants completed a number magnitude comparison task on two-, four-, and six-digit numbers including unit-decade compatible and incompatible differing digit pairs (e.g., 32_47, 3<4 and 2<7 vs. 37_52, 3<5 but 7>2, respectively) at all possible digit positions. Response latencies and fixation behavior indicated that sequential and parallel decomposition is not exclusive in multi-digit number processing. Instead, our results clearly suggested that sequential and parallel processing strategies seem to be combined when processing multi-digit numbers beyond the two-digit number range. To account for the results, we propose a chunking hypothesis claiming that multi-digit numbers are separated into chunks of shorter digit strings. While the different chunks are processed sequentially digits within these chunks are processed in parallel.

Facilitation versus Inhibition in the Masked Priming Same–Different Matching Task

In the past years, growing attention has been devoted to the masked priming same–different task introduced by Norris and Kinoshita (2008, Journal of Experimental Psychology: General). However, a number of researchers have raised concerns on the nature of the cognitive processes underlying this task—in particular the suspicion that masked priming effects in this task are mostly inhibitory in nature and may be affected by probe–prime contingency. To examine the pattern of facilitative/inhibitory priming effects in this task, we conducted two experiments with an incremental priming paradigm using four stimulus–onset asynchronies (13, 27, 40, and 53 ms). Experiment 1 was conducted under a predictive-contingency scenario (probe–prime–target; i.e., “same” trials: HOUSE– house– HOUSE vs. house– water– HOUSE; “different” trials: field– house– HOUSE vs. field– water– HOUSE), while Experiment 2 employed a zero-contingency scenario (i.e., “same” trials: HOUSE– house– HOUSE vs. house– water– HOUSE; “different” trials: field– field– HOUSE vs. field– water– HOUSE). Results revealed that, for “same” responses, both facilitation and inhibition increased linearly with prime duration in the two scenarios, whereas the pattern of data varied for “different” responses, as predicted by the Bayesian Reader model.

Sequential Processing of Two-Digit Numbers

Two experiments using a number matching task (NMT) explored whether two-digit numbers are processed holistically or in a compositional fashion. In the NMT participants are required to decide whether one of the two numbers initially provided (cues) is presented some milliseconds later or not (probe). Probes which have some arithmetic relationship to the cues (e.g., cues: 2 3, probe: 6) are rejected more slowy than probes unrelated to their cues (e.g., cues: 2 3, probe: 7) – interference effect –, and this is considered as evidence of the automatic activation of that arithmetic relationship. Participants were presented with two-digit cues and probes which had an arithmetic progression relationship only detectable once the numbers were decomposed (Experiment 1: cues: 56 7, probe: 89; Experiment 2: cues: 45 67, probe: 89). Results showed longer response times in these conditions compared to unrelated conditions. Data support componential processing even when the numbers to be matched are presented serially.