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Several psychophysical and neuropsychological investigations suggest that the processing of number and spatial information is strongly associated. A popular account for this bulk of evidence argues that this association has its origin in the underlying mental representation of numbers taking the form of a horizontally oriented mental number line, which is isomorphic to the representation of physical lines. Recently however, several alternative explanations have been put forward. We describe those theories and argue that no single current framework is on itself able to explain the full range of observations. To do this, a hybrid account is proposed which takes into account the underlying representation but emphasizes the processing mechanisms required by the task at hand.

The existence of an association between numbers and space is widely supported by cumulative data from behavioral, neuropsychological and neuroanatomical studies in adult subjects (de Hevia, Vallar and Girelli, 2006; 2008), but little is known about its ontogenetic origin. Recent evidence suggests that spatial-numeric association develops long before children begin formal reading-writing instruction (Opfer, Thompson and Furlong, 2010). The present study explores, in preschoolers, the presence of early directional indexes in processing of magnitude information and the association between these indexes and a mature numerical representation by means of a numerical estimation task (Siegler and Opfer, 2003). Results indicate that only a limited number of children expects magnitude increase (i.e., symbolic and non-symbolic) to occur from left to right and that this preference does not correlate with age. However, regardless of the directionality preferred (i.e., from left to right vs. from right to left), children who presented a stable number-space mapping performed more accurately a numerical estimation task.

Recent studies have suggested that numerical and physical magnitudes are similarly processed by a generalized magnitude system. The present study investigates the number-luminance interaction, taking advantage of illusory effects in a cued line bisection task with numerical or nonnumerical flankers and varying levels of luminance. The results showed that both dimensions influenced bisection performance. Whereas numbers (Experiment 1) induced a systematic shift of the subjective midpoint toward the larger digit, luminance (Experiment 2) modulated the bisection performance toward the darker flanker. By combining these two illusions (Experiments 3 and 4), the two dimensions interfered with each other. This pattern of results suggests overlapping representations for physical and numerical magnitudes and highlights the value of illusory effects in cognitive research.

Mapping numbers onto an oriented space is a widely known and replicable finding in human adults. Critically, this phenomenon appears to be modulated by culture and, therefore, it has been long believed to be the result of education and human invention. Recent developmental and comparative studies are challenging, however, this assumption by shedding light on the origins of this phenomenon. We will review evidence for the presence of basic number-space mappings in human infants, humans in isolated cultures, as well as in other non-human species such as monkeys and the domestic chick. These populations lack the symbolic tools that have been so far considered determinants for the presence of number-space mappings, thus offering a unique opportunity to explore the origins, evolution and development of numerical representations. Finally, we will describe a testable working hypothesis on the factors that contribute to the emergence of a ‘mental number line’ in a mind without language.

While infants’ ability to discriminate quantities has been extensively studied, showing that this competence is present even in neonates, the ability to compute ordinal relations between magnitudes has received much less attention. Here we show that the ability to represent ordinal information embedded in size-based sequences is apparent at 4 months of age, provided that magnitude changes involve increasing relations. Infants in Experiments 1A and 1B discriminated changes in ordinal relations after habituation to ascending sequences, but did not show evidence of discrimination after habituation to descending sequences. In Experiment 2 we replicated this asymmetry in magnitude discrimination even when additional cues known to boost ordinal competence were provided. The presence of an asymmetry between ascending vs. descending order during infancy suggests a developmental continuity in the underlying code used to represent magnitude, whereby the reported addition advantage in children and adults’ arithmetic performance emerges.

The spontaneous use of finger counting has been for long recognized as critical to the acquisition of number skills. Recently, the great interest on space–number associations shifted attention to the practice of finger counting itself, and specifically, to its spatial components. Besides general cross-cultural differences in mapping numbers onto fingers, contrasting results have been reported with regard to the directional features of this mapping. The key issue we address is to what extent directionality is culturally mediated, i.e., linked to the conventional reading–writing system direction, and/or biologically determined, i.e., linked to hand dominance. Although the preferred starting-hand for counting seems to depend on the surveyed population, even within the same population high inter-individual variability minimizes the role of cultural factors. Even if so far largely overlooked, handedness represents a sound candidate for shaping finger counting direction. Here we discuss adults and developmental evidence in support of this view and we reconsider the plausibility of multiple and coexistent number–space mapping in physical and representational space.

English and German readers have been shown to mark a position to the left of the true centre as the subjective midpoint in word bisection. This effect resembles a well-known phenomenon observed with the bisection of solid lines (pseudoneglect), although this behavioural similarity does not imply a common origin. The purpose of the present study was twofold: on the one hand, to investigate the perceptual and lexical features that influence the bisection of Italian orthographic strings and, on the other hand, to investigate whether identical or partially independent processing mediate bisection of line and orthographic stimuli. Five experiments were carried out to explore to what extent stimulus type (lines, words, pseudowords, consonant strings, symbols), stimulus length (from 3 to 13 characters), list context (pure and mixed), and written word frequency (high and low) affected the bisection performance. The results showed that list context modulated the processing similarities across different materials and that word frequency failed to influence the magnitude of the bisection bias.More critically, across all five experiments, the results showed different effects for solid lines versus orthographic material. Lines were always bisected to the left, independent of length and list context. By contrast, a crossover effect emerged with orthographic material; for long stimuli (above five letters) the bias was consistently to the left, while short stimuli showed a consistent rightward bias. The results indicate that manual bisection involved partly different cognitive mechanisms during word and line perception and that this may depend on the characteristics of the stimuli (words/discrete vs. lines/continuous). © 2010 Elsevier Ltd.

Previous evidence has shown that 11-month-olds represent ordinal relations between purely numerical values, whereas younger infants require a confluence of numerical and non-numerical cues. In this study, we show that when multiple featural cues (i.e., color and shape) are provided, 7-month-olds detect reversals in the ordinal direction of numerical sequences relying solely on number when non-numerical quantitative cues are controlled. These results provide evidence for the influence of featural information and multiple cue integration on infants' proneness to detect ordinal numerical information.

Different sources of evidence point to the strict interaction between finger counting and number processing. However, the influence of handedness on finger counting direction (Sato, & Lalain, 2008) as well as on the mapping of numbers in the representational space (Fischer, 2008) is still debated. The present study aims to explore the reciprocal interaction between handedness, finger counting habits, and orientation of the numerical spatial representation. To this aim, we contrasted Italian left-handed and right-handed participants in a counting task, a parity judgments task, and several computerized tasks requiring the bisection of digit (i.e. 11111) and counting (i.e. 123456789) strings. Results showed that handedness fully predicts finger counting direction, i.e., right-handed are “right-starters” and left-handed are “left-starters”. However, both groups showed comparable S-R compatibility effect (SNARC) and visuo-perceptual effects in the bisection tasks. These results favour the hypothesis according to which visual scanning direction rather than finger counting direction is the dominant factor in mapping numbers in the representational space.

Numerose evidenze convergono nel supportare l’ipotesi che i numeri siano rappresentati mentalmente lungo una linea numerica orientata compatibilmente alla direzione di lettura-scrittura. Recentemente è stato suggerito che le strategie di conteggio sulle dita, determinate culturalmente secondo alcuni e dipendenti dalla dominanza manuale secondo altri, siano un fattore influente sull’organizzazione spaziale della rappresentazione numerica. In particolare è stato osservato che la direzione di conteggio sembra interagire con l’elaborazione e la rappresentazione dell’informazione numerica, poichè il mapping dei numeri nello spazio rappresentazionale appare in alcuni casi congruente alla strategia di conteggio adottata invece che alla direzione dello scanning visivo nella letto-scrittura. Obiettivo di questo studio è quello di indagare l’interazione reciproca tra la dominanza manuale, le strategie di conteggio e l’orientamento della rappresentazione numerica spaziale. Soggetti destrimani (ad oggi 13) e soggetti mancini (ad oggi 9) hanno svolto un compito di conteggio con le dita, uno di giudizi di parità e 5 di bisezione computerizzata di stringhe costituite da un’unica cifra (11111) o da cifre ordinate (12345), in cui sono stati manipolati la lunghezza (5 o 9 cifre), la grandezza numerica (minore o maggiore di 5), l’ordine (crescente o decrescente) e l’orientamento (orizzontale, verticale o mirror). Nei risultati preliminari la dominanza manuale appare essere un buon predittore della direzione del conteggio, poiché i soggetti destrimani iniziano a contare con la mano destra e quelli mancini con la sinistra. Nonostante ciò, effetti di compatibilità S-R (SNARC) nel giudizio di parità ed effetti visuo-percettivi nella bisezione appaiano simili nei due gruppi di dominanza manuale. Questi risultati favoriscono l’ipotesi che sia la direzione dello scanning visivo e non quella del conteggio sulle dita il fattore dominante del mapping numerico nello spazio rappresentazionale.

To detect an ordered sequence of quantities refers to the ability to appreciate ‘greater than’ and ‘less than’ relations and it represents one essential component of numerical knowledge that develops early in infancy. Brannon (2002) argued that by 11 months infants possess this ability for numerical values, and that it follows a sudden onset between 9 and 11 months. In fact, by 9 months infants succeed at discriminating the ordinal direction of a single square varying in size, but fail for numerical sequences, suggesting that the ability to represent the ordinal information embedded in non-numerical quantities develops earlier than for numerical values. Our study aims to track the emergence of the ability to encode ordinal relations between continuous, non-numerical quantities. We tested 4-month-old infants in their ability to discriminate ascending vs. descending sequences of the size of a single square. In Exp. 1, infants saw increasing (N=10) or decreasing (N=10) sequences of a single square that varied in size across 3 steps following a 1:2 ratio. After habituation, all infants saw six new trials, alternating between increasing vs. decreasing sequences of the single square varying in size in a 1:2 ratio. The direction of the first sequence was counterbalanced across participants. We found that 4-month-old infants successfully discriminated the ordinal direction, Familiar vs. Novel, p=.001, but this ability was present only for infants habituated to the increasing sequence, who displayed a preference for the novel vs. the familiar sequence (M=9.3 s vs. 5.3 s; p=.002 ). In contrast, infants habituated to the decreasing sequence did not discriminate the familiar vs. novel sequence (M=4.6 s vs. 5.3 s; p=.20). These results suggest that by 4 months infants are sensitive to the ordinal information contained in a sequence that varies along a continuous dimension, i.e., the area of a single element. However, this ability seems to apply only to sequences that vary in an ascending order, i.e., ‘greater than’ relations, in line with studies showing that after being trained to respond to an ascending order, monkeys generalize the rule to new numerical values, but they fail for the descending order (Brannon and Terrace, 2000). However, because all squares in the sequences were located at the center of the screen, ascending sequences may generate the perceptual appearance of an approaching (looming) object, and descending sequences a retracting percept (zooming), suggesting that infants did not detect the ordinal information of the sequence. To test for this hypothesis, two additional experiments manipulated the spatial disposition of the elements within the ascending sequence. In Exp. 2, the position varied randomly within a region defined around the centre of the screen, and a masking was introduced in between changes of magnitude. Data collection is still in progress. In Exp. 3, the position of the element varied along the horizontal axis following a contiguous path, thus providing a spatial cue. Preliminary results indicate that infants fail to discriminate the ordinal direction of ascending sequences when spatial cues, in addition to temporal cues, are introduced.

The study of neuronal specialisation in different cognitive and perceptual domains is important for our understanding of the human brain, its typical and atypical development, and the evolutionary precursors of cognition. Central to this understanding is the issue of numerical representation, and the question of whether numbers are represented in an abstract fashion. Here we discuss and challenge the claim that numerical representation is abstract. We discuss the principles of cortical organisation with special reference to number and also discuss methodological and theoretical limitations that apply to numerical cognition and also to the field of cognitive neuroscience in general. We argue that numerical representation is primarily non-abstract and is supported by different neuronal populations residing in the parietal cortex. © 2009 Cambridge University Press.

The SNARC effect, consisting of a systematic association between numbers and lateralized response, reflects the mental representation of magnitude along a left-to-right mental number line (Dehaene et al. in J Exp Psychol 122:371-396, 1993). Critically, this effect has been reported in the classification of overlearned non-numerical sequences such as letters, days and months (Gevers et al. in Cognition 87:B87-B95, 2003 and Cortex 40:171-172, 2004) suggesting that ordinal, rather than magnitude information, is critical for spatial coding. This study tests the hypothesis of an oriented spatial representation as the privileged way of mentally organizing serial information, by looking for stimulus-response compatibility effects in the processing of a newly acquired arbitrary sequence. Here we report an association between ordinal position of the items and spatial response preference for both order-relevant and order-irrelevant tasks. These results suggest that any ordered information, even when order is not intrinsically relevant to it, is spontaneously mapped in the representational space. This spatial representation is likely to acquire a left-to-right orientation, at least in western cultures. © 2009 Springer-Verlag.

There is evidence that the spatial extent of written words is misperceived in normal reading. The left bias frequently founded in the bisection of orthographic material has been interpreted as resulting from an attentional bias towards the beginning of the word and the lexical or visuo-spatial nature (pseudoneglect) of this bias is still debated. Besides eye movements studies reported an opposite asymmetry in visual exploration of continuous (lines) and discrete (ortographical) material in left and right emispace. In order to investigate to what extent lexical access is responsible for this distortion and the impact of visuo-perceptual factors (i.e. length) on different material (stimulus continuity), five experiments required Italian readers to identify the centre of lines, words, pseudowords, consonant strings and graphic strings. The stimulus length was confirmed as a critical factor in the bisection performance across the five experiments that showed a left bias for lines, while discrete strings induced a left bias only when they were long and a right error if short. Moreover, essentially in discrete strings length proportionally modulates bias size. Overall, these findings suggest that different visuo-perceptual effects on bisection of continuous and discrete material reflect a different visual exploration that they require.

In recent years, a growing amount of evidence concerning the relationships between numerical and spatial representations has been interpreted, by and large, in favour of the mental number line hypothesis—namely, the analogue continuum where numbers are spatially represented (Dehaene, 1992; Dehaene, Piazza, Pinel, & Cohen, 2003). This numerical representation is considered the core of number meaning and, accordingly, needs to be accessed whenever numbers are semantically processed. The present study explored, by means of a length reproduction task, whether besides the activation of lateralized spatial codes, numerical processing modulates the mental representation of a horizontal spatial extension. Mis-estimations of length induced by Arabic numbers are interpreted in terms of a cognitive illusion, according to which the elaboration of magnitude information brings about an expansion or compression of the mental representation of spatial extension. These results support the hypothesis that visuo-spatial resources are involved in the representation of numerical magnitude.

In the study of numerical and arithmetical abilities, there is compelling evidence demonstrating that number and space representations are connected to one another. Historically the first source of support came more than a century ago, when Galton's investigations on mental imagery suggested that the internal representation of numbers may evoke a stable, linear space. In the past few decades, empirical evidence lent further support to the hypothesis that numerical representation is spatially coded into a non-verbal 'mental number line', which in turn lead to considering this representation as the core of number meaning. Visuo-spatial processing is intuitively involved in various aspects of number processing and calculation: For instance, the meaning of a digit in a multi-digit number is coded following spatial information, given its association to its relative position within the number; similarly, to solve a complex written multiplication one has to know the correct location of the intermediate results. In this review behavioral, neuropsychological, and neuroimaging data concerning the close relationship between numerical abilities and visuo-spatial processes are considered. © 2008 Elsevier Ltd. All rights reserved.

Primary mediastinal nonseminomatous germ cell tumors comprise a heterogeneous series of neoplasms characterized by limited chemosensitivity and a poor prognosis. We analyzed a large series of patients from our tertiary cancer center, including pre- and postsurgical variables, with the aim to provide a prognostic model that might be suitable for clinical use. The variables identified in the prognostic model were surgical removal of residuals after first-line chemotherapy, histological response, and the presence of lung metastases. Their joint analysis defined distinct overall survival (OS) curves. Background: Primary mediastinal germ cell tumors (PMGCTs) poorly benefit from chemotherapy and half of patients die because of disease progression. Enhancing the risk stratification might result in tailoring a more personalized treatment strategy from the time of diagnosis. Patients and Methods: Between the years 1985 and 2012, 86 patients with PMGCT were treated at our center. Cox proportional hazards regression analysis was conducted in the population of nonseminomas to examine the prognostic effect of candidate factors on progression-free and OS. OS curves were compared using the Kaplan-Meier method and the log-rank test. Results: Mean age was 29.8 years (range, 15-63 years). Twenty-five patients (29.1%) had lung and 8 (9.3%) liver, bone, or brain metastases. Twelve patients (13.9%) received upfront high-dose chemotherapy and 45 patients (52.3%) underwent surgery after chemotherapy. Cox analyses included 61 evaluable primary mediastinal nonseminomatous germ cell tumors (PMNSGCTs). The final model of factors indicating a poor prognosis included the combination of surgery and histological response (overall P = .011) and lung metastases (hazard ratio, 3.03; 95% confidence interval, 1.12-8.15; P = .028). The model showed a bootstrap-corrected Harrel c-statistic for OS of 0.66. A risk stratification model based on the combination of these factors and accounting for a 50% 5-year survival cutoff identified 2 groups (poor prognosis, n = 33 vs. good prognosis, n = 28) with distinct OS curves (P < .001). Preoperative serum tumor marker level was not associated with the final histology (P = .853, chi(2) test). Results were limited by small numbers. Conclusion: Patients with PMNSGCT included 2 subpopulations with distinct prognosis, and therapeutic improvements are needed for patients with poor-risk features.

Background: Several theorists maintain that exact number abilities rely on language-relevant processes whereas approximate number calls on visuo-spatial skills. We chose two genetic disorders, Williams syndrome and Down’s syndrome, which differ in their relative abilities in verbal versus spatial skills, to examine this hypothesis. Five experiments assessed number skills in these two genetic syndromes and in their mental age (MA) and chronological age (CA) matched controls. Methods: Experiment 1 used a preferential looking paradigm with infants and toddlers to measure sensitivity to changes in numerosity. Experiment 2 measured reaction times in older children and adults in anumerosity comparison task with dots in a random pattern. Experiment 3 comprised a number battery that measured various forms of countingandsimplearithmetic. Results: TheWSinfantsdisplayedalevelofperformanceequaltothatof their CA-controls, whereas the DS infants failed to reach even the level of their MA-controls. By contrast, the older DS children and adults outstripped the older WS group in their numerosity abilities, with different patterns of errors in the two clinical groups. Conclusions: Differences in the infant and adult number phenotypes between these two genetic disorders are discussed with reference to the processing styles used by each group and how these might impact on their developmental trajectories. Theoretically, wehighlightourcontentionthatonecannotinfertheinfantstartingstatefromtheadultendstate.Rather, the development process itself must be taken into account. Keywords: Williams syndrome, Down’s syndrome, number development, adults, infants. Abbreviations: WS: Williams syndrome; DS: Down’s syndrome; SDE: symbolic distance effect.

Background: Zero has a special role in calculation: indeed it is not obvious which representation may be invoked in multiplication or division by zero. In particular, zero as an operand, unlike any other operand, makes any quantity disappear. Aims: The study is intended to shed light on the mechanisms mediating the manipulation of zero. Methods & Procedures: Three neuropsychological patients, AF, FV, and FS, are described, whose specific pattern of preserved/ impaired performance with single-and multi-digit multiplication shows selective problems with the use of zero (Nx0 and 0xN). Outcome & Results: AF's performance in single-and multi-digit multiplication showed a clear dissociation between spared fact-based problems and impaired 0 rule-based problems. FV was totally unable, in multi-digit multiplication, to apply adequately the 0 rule that he could master in simple calculation. Finally, FS showed, within the rule-based problems, a clear-cut dissociation between a preserved performance on Nx0 problems and an impaired performance on 0xN problems, a difficulty that almost disappeared in multi-digit multiplications. Conclusions: Overall the reported dissociations indicate that a full grasp of the concept of zero may not be used in routine calculation, and that processing of zero rather appears to rely on a collection of independent, shallow representations.

This study investigated the relationships between numerical and spatial representations by means of a bisection task, exploring the view that the core representation of number meaning is spatially organized as a mental number line. In Experiment nos. 1 (bisection of digit strings) and 2 (bisection of flanked lines) spatial biases towards the larger digit were found to be related only to processing of relative magnitude. Experiment nos. 3 (bisection of an unfilled space) and 4 (bisection of flanked lines/unfilled spaces) aimed at disclosing perceptual, attentional, and numerical constraints on the bias induced by the position of the larger digit. This effect is interpreted in terms of a cognitive illusion of length, whereby a spatial bias compensates for the numerical disparity. This seems to operate in a categorical fashion ("small/ large"), and to be congruent with the assumption that relatively large numbers are associated with the right side of a mental representational space. © Springer-Verlag 2005.

Objectives This paper investigates mathematical skills in Prader–Willi Syndrome (PWS), a pathological condition because of congenital alterations of chromosome pair 15. The following questions were addressed: (1) Are mathematical skills in PWS relatively more impaired with respect to other cognitive functions (as has been repeatedly but anecdotally reported)?; and (2) What is the nature of the mathematical impairment? Methods The first study employed the Wechsler Adult Intelligence Scale (WAIS) and an extensive battery of cognitive tasks for which norms are known. Both batteries include a mathematical section. The second study used a theoretically motivated series of mathematical tasks specifically designed to individually assess the different cognitive components underlying mathematical skills. Results Mathematical skills were found to be the most impaired cognitive abilities together with short-term memory capacity. No specific mathematical domain was seen to be unaffected in PWS participants. The clearest deficits observed concern ‘syntactic’ processes in number transcoding, multiplication, number facts retrieval and calculation procedures. Conclusion Failure of mathematical skills is the most distinctive feature in the cognitive profile of PWS. However, to determine whether this is indeed a specific pattern of performance related to PWS, results must be compared with those obtained with patients manifesting other genetic disorders.

A progressively dysgraphic patient is described, whose deficit involved, at different stages, the post-allographic, the allographic and the orthographic representation of words. The patient's roughly comparable difficulties in oral and written spelling and in dictation by composition, as the disease progressed, showed that the damage was no longer limited to output mechanisms but also involved more central processes. The nature of the errors (phonologically based), their identical distributions for words and non-words, the inability to write under articulatory suppression, the normal repetition and the impairment in reading and lexical decision suggest that the patient cannot rely on the orthographic representation of words and instead makes use of a phonological representation by spelling through the phonological buffer. © 2005 Elsevier Ltd. All rights reserved.

Despite the high incidence of numerical deficits in neurological patients, little attention has been paid to the development of diagnostic tools. In fact, most of the published reports on acquired numerical disorders, whether single case or group studies, do not refer to standardised measures of performance providing little, if any, control data specifically collected for the examination. In this study we present data of 282 healthy controls of different age groups and educational levels in a new battery of Number Processing and Calculation (NPC). The NPC battery includes a total of 35 tasks, assessing different counting abilities, various aspects of number comprehension (such as parity and magnitude judgements), numerical transcoding, calculation, arithmetic reasoning and conceptual knowledge. Special attention is paid to the assessment of different calculation abilities, including simple fact retrieval, rule based processing, mental calculation and written calculation in all four operations. Moreover, text problem solving is assessed as well as the understanding of arithmetic principles. Thus, the NPC battery differs from the EC 301 battery proposed by Deloche et al., 1994 (Dellatolas, Deloche, Basso, & Claros-Salinas, 2001) and allows a more fine grained diagnosis which is relevant for planning targeted interventions. The battery is easy to administer and does not require special materials or equipment.

The present paper describes two patients, AB and FS, whose deficit in transcoding verbal to Arabic numerals was greatly affected by the format of the input. Despite intact comprehension of written verbal numerals and otherwise intact production of Arabic numerals they both transcode inefficiently the former into the latter. Yet, their ability to write the same Arabic numerals on dictation was fully preserved. Moreover, in both patients’ performance, a systematic error pattern emerged reflecting the influence of the lexico-syntactic structure of the input numerals in the transcoding processes. Current models of number transcoding may not easily account for this pattern of dissociation without postulating different code-dependent pathways for verbal to Arabic transcoding. Within a more parsimonious approach, it is tentatively suggested that spoken and written verbal codes activate with different efficiency the same transcoding algorithm.

This paper describes a patient (LD) showing a selective syntactic deficit in the production of Arabic numerals. Unlike in previously reported cases, LD's syntactic difficulties result in deletions rather than insertions of zeros, with a reduction of the number magnitude. The pattern of errors highlighted a distinction between "lexical zeros", i.e. the zeros in tens, that are semantically derived, and "syntactic zeros" that are syntactically produced as the result of specific production rules. In LD, only syntactic zeros were affected. Furthermore, the processing of numerals with final zeros was found to be easier than the processing of numerals with internal zeros. This pattern of errors is compatible with the lexical-semantic model of Power and Dal Martello. In this model, in fact, lexical zeros originate from a numerical concept, while syntactic zeros originate from a concatenation operation, plus an overwriting operation leaving one or more intermediary zeros. Thus, lexical zeros may be easier to manipulate than syntactic zeros that merely represent a null quantity associated to a specific power of 10. (C) 2003 Published by Elsevier Ltd.

In this study, we modified a classic problem solving task, number series completion, in order to explore the contribution of implicit memory to inductive reasoning. Participants were required to complete number series sharing the same underlying algorithm (e.g., +2),differing in both constituent elements (e.g., 2 4 6 8 versus 5 7 9 11) and correct answers (e.g., 10 versus 13). In Experiment 1, reliable priming effects emerged, whether primes and targets were separated by four or ten fillers. Experiment 2 provided direct evidence that the observed facilitation arises at central stages of problem solving, namely the identification of the algorithm and its subsequent extrapolation. The observation of analogous priming effects in a severely amnesic patient strongly supports the hypothesis that the facilitation in number series completionwas largely determined by implicit memory processes. These findings demonstrate that the influence of implicit processes extends to higher level cognitive domain such as induction reasoning.

The present study is concerned with two Slovenian-speaking patients who were asked to produce, in various tasks, verbs, nouns, and adjectives derived by prefixation with prepositions. Despite differences due to their specific linguistic difficulties, both patients' performance was characterized by the differential processing of prefixes and remaining components of complex words. Prepositions in prefixation were mostly preserved, and less frequently substituted, regardless of the numerous errors produced in the remaining portion of the words. These errors seem clearly determined by the morphological structure of the words and therefore appear to be authentic morphological errors. These findings contribute to the theoretical debate on mental lexical representation, speaking in favor of a morphological decomposition in processing of prefixed complex words at different processing levels.

The aim of the present study was to evaluate the efficacy of a reorganisation approach in the rehabilitation of simple arithmetic deficits as an instance of disturbed semantic knowledge. We report the case of FS, who underwent targeted training to overcome specific difficulties with multiplication facts. The programme was based on the strategic use of his residual knowledge and explicit reference to the principles underlying simple arithmetic. The purpose of this approach was to facilitate the reacquisition process by reducing the number of facts to be memorised and inducing a meaningful organisation of this knowledge in memory. The positive outcome of the intervention speaks in favour of a reorganisation rationale in the rehabilitation of arithmetic skills, where the integration of declarative, procedural, and conceptual knowledge critically mediate the re-acquisition process.