Chronometric studies of numerical cognition in five-month-old infants

Developmental research suggests that some of the mechanisms that underlie numerical cognition are present and functional in human infancy. To investigate these mechanisms and their developmental course, psychologists have turned to behavioral and electrophysiological methods using briefly presented displays. These methods, however, depend on the assumption that young infants can extract numerical information rapidly. Here we test this assumption and begin to investigate the speed of numerical processing in five-month-old infants. Infants successfully discriminated between arrays of 4 vs. 8 dots on the basis of number when a new array appeared every 2 s, but not when a new array appeared every 1.0 or 1.5 s. These results suggest alternative interpretations of past findings, provide constraints on the design of future experiments, and introduce a new method for probing infants' enumeration process. Further experiments using this method provide initial evidence that infants' enumeration mechanism operates in parallel and yields increasingly accurate numerical representations over time, as does the enumeration mechanism used by adults in symbolic and non-symbolic tasks.     

Do domestic dogs show any evidence of being able to count?

Numerical competence has been demonstrated in a wide range of animal species. The level of numerical abilities shown ranges from simple relative numerousness judgements to true counting. In this study we used the preferential looking technique to test whether 11 pet dogs could count. The dogs were presented with three simple calculations: "1+1=2"; "1+1=1"; and "1+1=3". These calculations were performed by presenting the dogs with treats that were placed behind a screen that allowed manipulation of the outcome of the calculation. When the dogs expected the outcome they spent the same amount of time looking at the result of the calculation as they did on the initial presentation. However, when the result was unexpected dogs spent significantly longer looking at the outcome of the calculation. The results suggest that the dogs were anticipating the outcome of the calculations they observed, thus suggesting that dogs may have a rudimentary ability to count. Electronic Publication     

Early and late mismatch negativity elicited by words and speech-like stimuli in children

In auditory perception the brain's attentional and preattentional mechanisms select certain stimuli for preferential processing and filter out irrelevant input. This study investigated nonattentive auditory processing in children. Event-related potentials (ERPs) provide a means to study neural correlates related to language and speech-sound processing. Mismatch negativity (MMN) is an ERP wave that indicates attention-independent perceptual change detection. In this study cortical ERPs were elicited by complex tones, naturally spoken words, and pseudowords, with each stimulus type containing equal acoustical elements. Tones elicited a bifurcated mismatch negativity (MMN), with early MMN (peaking at 150-200 ms) being more dominant. On the other hand, words elicited a strong late MMN, peaking at about 400-450 ms after stimulus onset. The MMN wave form was significantly weaker for pseudowords than for words. The late MMN wave, especially for word differences, was found to reflect summating MMN generators and memory trace formation on gestalt bases. Results suggest that the auditory processing, even nonattended, is highly associated with the cognitive meaning of the stimuli.     

The Declarative/Procedural Model of Lexicon and Grammar

Our use of language depends upon two capacities: a mental lexicon of memorized words and a mental grammar of rules that underlie the sequential and hierarchical composition of lexical forms into predictably structured larger words, phrases, and sentences. The declarative/procedural model posits that the lexicon/grammar distinction in language is tied to the distinction between two well-studied brain memory systems. On this view, the memorization and use of at least simple words (those with noncompositional, that is, arbitrary form-meaning pairings) depends upon an associative memory of distributed representations that is subserved by temporal-lobe circuits previously implicated in the learning and use of fact and event knowledge. This declarative memory system appears to be specialized for learning arbitrarily related information (i.e., for associative binding). In contrast, the acquisition and use of grammatical rules that underlie symbol manipulation is subserved by frontal/basal-ganglia circuits previously implicated in the implicit (nonconscious) learning and expression of motor and cognitive skills and habits (e.g., from simple motor acts to skilled game playing). This procedural system may be specialized for computing sequences. This novel view of lexicon and grammar offers an alternative to the two main competing theoretical frameworks. It shares the perspective of traditional dual-mechanism theories in positing that the mental lexicon and a symbol-manipulating mental grammar are subserved by distinct computational components that may be linked to distinct brain structures. However, it diverges from these theories where they assume components dedicated to each of the two language capacities (that is, domain-specific) and in their common assumption that lexical memory is a rote list of items. Conversely, while it shares with single-mechanism theories the perspective that the two capacities are subserved by domain-independent computational mechanisms, it diverges from them where they link both capacities to a single associative memory system with broad anatomic distribution. The declarative/procedural model, but neither traditional dual- nor single-mechanism models, predicts double dissociations between lexicon and grammar, with associations among associative memory properties, memorized words and facts, and temporal-lobe structures, and among symbol-manipulation properties, grammatical rule products, motor skills, and frontal/basal-ganglia structures. In order to contrast lexicon and grammar while holding other factors constant, we have focused our investigations of the declarative/procedural model on morphologically complex word forms. Morphological transformations that are (largely) unproductive (e.g., in go—went, solemn—solemnity) are hypothesized to depend upon declarative memory. These have been contrasted with morphological transformations that are fully productive (e.g., in walk—walked, happy—happiness), whose computation is posited to be solely dependent upon grammatical rules subserved by the procedural system. Here evidence is presented from studies that use a range of psycholinguistic and neurolinguistic approaches with children and adults. It is argued that converging evidence from these studies supports the declarative/procedural model of lexicon and grammar.     

The role of derivational morphology in vocabulary acquisition: get by with a little help from my morpheme friends

This study explores the role of morphology in vocabulary knowledge of 3rd and 6th grade Finnish elementary school children. In a word definition task, children from both grades performed overall better on derived words than on monomorphemic words. However, the results were modified by the factors Frequency and Productivity. Most strikingly, performance on monomorphemic words was disproportionately weaker than on derived words at the low frequency range. At the high-frequency range, derived words with low-productive suffixes yielded poorest performance. We partly make an appeal to the lexical-statistical properties of the Finnish language to explain the interaction of Frequency and Word Structure. At any rate, the results suggest that Finnish elementary school children benefit significantly from utilizing morphology in determining word meanings.     

Age differences in working memory updating: The role of interference,focus switching and substituting information

Working memory updating (WMU) tasks require different elements in working memory (WM) to be maintained simultaneously, accessing one of these elements, and substituting its content. This study examined possible developmental changes from childhood to adulthood both in focus switching and substituting information in WM. In addition, possible age-related changes in interference due to representational overlap between the different elements simultaneously held in these tasks were examined. Children (8- and 11-year-olds), adolescents (14-year-olds) and younger adults (mean age = 22 years) were administered a numerical updating memory task, in which updating and focus switching were manipulated. As expected, response times decreased and recall performance increased with age. More importantly, the time needed for focus switching was longer in children than in adolescents and younger adults. On the other hand, substitution of information and interference due to representational overlap were not affected by age. These results suggest that age-related changes in focus switching might mediate developmental changes in WMU performance.     

SNARC (spatial–numerical association of response codes) meets SPARC (spatial–pitch association of response codes): Automaticity and interdependency in compatibility effects

Concepts, including the mental number line, or addressing pitch as high and low, suggest that the spatial–numerical and spatial–pitch association of response codes (SNARC and SPARC) effects are domain-specific and thus independent. Alternatively, there may be dependencies between these effects, because they share common automatic or controlled decision mechanisms. In two experiments, participants were presented with spoken numbers in different pitches; their numerical value, pitch, and response compatibility were varied systematically. This allowed us to study SNARC and SPARC effects in a factorial design (see also Fischer, Riello, Giordano, &; Rusconi, 2013 Fischer, M. H., Riello, M., Giordano, B. L., &; Rusconi, E. (2013). Singing numbers?…?in cognitive space--a dual-task study of the link between pitch, space, and numbers. Topics in Cognitive Science, 5(2), 354–366. Retrieved from http://doi.org/10.1111/tops.12017[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Participants judged the stimuli on numerical magnitude, pitch, or parity (odd–even). In all tasks, the SNARC and SPARC effects had superadditive interactions. These were interpreted as both effects sharing a common mechanism. The task variation probes the mechanism: In the magnitude judgement task, numerical magnitude was explicit, whereas pitch was implicit; in the pitch judgement task, it was vice versa. In the parity judgement task, both dimensions were implicit. Regardless of whether they were implicit or explicit, both SNARC and SPARC effects occurred in all tasks. We concluded that by not requiring focal attention the common mechanism operates automatically.     

Numerical discrimination is mediated by neural coding variation

One foundation of numerical cognition is that discrimination accuracy depends on the proportional difference between compared values, closely following the Weber–Fechner discrimination law. Performance in non-symbolic numerical discrimination is used to calculate individual Weber fraction, a measure of relative acuity of the approximate number system (ANS). Individual Weber fraction is linked to symbolic arithmetic skills and long-term educational and economic outcomes. The present findings suggest that numerical discrimination performance depends on both the proportional difference and absolute value, deviating from the Weber–Fechner law. The effect of absolute value is predicted via computational model based on the neural correlates of numerical perception. Specifically, that the neural coding “noise” varies across corresponding numerosities. A computational model using firing rate variation based on neural data demonstrates a significant interaction between ratio difference and absolute value in predicting numerical discriminability. We find that both behavioral and computational data show an interaction between ratio difference and absolute value on numerical discrimination accuracy. These results further suggest a reexamination of the mechanisms involved in non-symbolic numerical discrimination, how researchers may measure individual performance, and what outcomes performance may predict.     

Flexible and unique representations of two-digit decimals

We examined the representation of two-digit decimals through studying distance and compatibility effects in magnitude comparison tasks in four experiments. Using number pairs with different leftmost digits, we found both the second digit distance effect and compatibility effect with two-digit integers but only the second digit distance effect with two-digit pure decimals. This suggests that both integers and pure decimals are processed in a compositional manner. In contrast, neither the second digit distance effect nor the compatibility effect was observed in two-digit mixed decimals, thereby showing no evidence for compositional processing of two-digit mixed decimals. However, when the relevance of the rightmost digit processing was increased by adding some decimals pairs with the same leftmost digits, both pure and mixed decimals produced the compatibility effect. Overall, results suggest that the processing of decimals is flexible and depends on the relevance of unique digit positions. This processing mode is different from integer analysis in that two-digit mixed decimals demonstrate parallel compositional processing only when the rightmost digit is relevant. Findings suggest that people probably do not represent decimals by simply ignoring the decimal point and converting them to natural numbers.     

Working Memory in Nonsymbolic Approximate Arithmetic Processing: A Dual‐Task Study With Preschoolers

Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an important predictor of children's math development and achievement. The aim of our study was to uncover the specific role of WM in nonsymbolic approximate math. For this purpose, we conducted a dual‐task study with preschoolers with active phonological, visual, spatial, and central executive interference during the completion of a nonsymbolic approximate addition dot task. With regard to the role of WM, we found a clear performance breakdown in the central executive interference condition. Our findings provide insight into the underlying cognitive processes involved in storing and manipulating nonsymbolic approximate numerosities during early arithmetic.