Impaired parietal magnitude processing in developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability affecting the acquisition of school-level mathematical abilities in the context of otherwise normal academic achievement, with prevalence estimates in the order of 3-6%. Behavioural studies show deficits in elementary numerical processing among individuals with pure DD, indicating that deficits in higher-level mathematical skills may stem from impaired representation and processing of basic numerical magnitude. Adult neuropsychological and neuroimaging research points to the intraparietal sulcus as a key region for the representation and processing of numerical magnitude. This raises the possibility of a parietal dysfunction as a root cause of DD. We show that, in children with pure DD, the right intraparietal sulcus is not modulated in response to numerical processing demands to the same degree as in typically developing children. This finding provides the first direct evidence for a specific impairment of parietal magnitude systems in DD during non-symbolic numerosity processing.     

Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin

Cognitive theories of numerical representation suggest that understanding of numerical quantities is driven by a magnitude representation associated with the intraparietal sulcus and possibly under genetic control. The aim of this study was to investigate, using fMRI and structural imaging, the interaction between the abnormal development of numerical representation in an X-linked condition, Turner syndrome (TS), and the development of the intraparietal sulcus. fMRI during exact and approximate calculation in TS showed an abnormal modulation of intraparietal activations as a function of number size. Morphological analysis revealed an abnormal length, depth, and sulcal geometry of the right intraparietal sulcus, suggesting an important disorganization of this region in TS. Thus, a genetic form of developmental dyscalculia can be related to both functional and structural anomalies of the right intraparietal sulcus, suggesting a crucial role of this region in the development of arithmetic abilities.     

Does the Parietal Cortex Distinguish between “10,” “Ten,” and Ten Dots?

It is well established that the intraparietal sulcus (IPS) plays an important role in the processing and representation of numerical magnitude. Two recent studies by Piazza et al. and Cohen Kadosh et al. published in this issue of Neuron used fMRI adaptation to explore the extent to which parietal number processing is dependent upon or independent of a numbers' surface format. Their results, while slightly different, converge to suggest that the answer may be neither, but rather that it depends on the hemisphere.     

Bilateral Bi-Cephalic Tdcs with Two Active Electrodes of the Same Polarity Modulates Bilateral Cognitive Processes Differentially

Transcranial direct current stimulation (tDCS) is an innovative method to explore the causal structure-function relationship of brain areas. We investigated the specificity of bilateral bi-cephalic tDCS with two active electrodes of the same polarity (e.g., cathodal on both hemispheres) applied to intraparietal cortices bilaterally using a combined between- and within-task approach. Regarding between-task specificity, we observed that bilateral bi-cephalic tDCS affected a numerical (mental addition) but not a control task (colour word Stroop), indicating a specific influence of tDCS on numerical but not on domain general cognitive processes associated with the bilateral IPS. In particular, the numerical effect of distractor distance was more pronounced under cathodal than under anodal stimulation. Moreover, with respect to within-task specificity we only found the numerical distractor distance effect in mental addition to be modulated by direct current stimulation, whereas the effect of target identity was not affected. This implies a differential influence of bilateral bi-cephalic tDCS on the recruitment of different processing components within the same task (number magnitude processing vs. recognition of familiarity). In sum, this first successful application of bilateral bi-cephalic tDCS with two active electrodes of the same polarity in numerical cognition research corroborates the specific proposition of the Triple Code Model that number magnitude information is represented bilaterally in the intraparietal cortices.     

Assessment of the Hemispheric Lateralization of Grapheme-Color Synesthesia with Stroop-Type Tests

Grapheme-color synesthesia, the idiosyncratic, arbitrary association of colors to letters or numbers, develops in childhood once reading is mastered. Because language processing is strongly left-lateralized in most individuals, we hypothesized that grapheme-color synesthesia could be left-lateralized as well. We used synesthetic versions of the Stroop test with colored letters and numbers presented either in the right or the left visual field of thirty-four synesthetes. Interference by synesthetic colors was stronger for stimuli in the right hemifield (first experiment, color naming task). Synesthetes were also faster in the right hemifield when naming the synesthetic color of graphemes (second experiment). Overall, the lateralization effect was 7 ms (the 95% confidence interval was [1.5 12] ms), a delay compatible with an additional callosal transfer for stimuli presented in the left hemifield. Though weak, this effect suggests that the association of synesthetic colors to graphemes may be preferentially processed in the left hemisphere. We speculate that this left-lateralization could be a landmark of synesthetic grapheme-color associations, if not found for color associations learnt by non-synesthete adults.     

Unconscious letter discrimination is enhanced by association with conscious color perception in visual form agnosia

Adaptive behavior guided by unconscious visual cues occurs in patients with various kinds of brain damage as well as in normal observers, all of whom can process visual information of which they are fully unaware [1] [2] [3] [4] [5] [6] [7] [8]. Little is known on the possibility that unconscious vision is influenced by visual cues that have access to consciousness [9]. Here we report a 'blind' letter discrimination induced through a semantic interaction with conscious color processing in a patient who is agnosic for visual shapes, but has normal color vision and visual imagery. In seeing the initial letters of color names printed in different colors, it is normally easier to name the print color when it is congruent with the initial letter of the color name than when it is not [10]. The patient could discriminate the initial letters of the words 'red' and 'green' printed in the corresponding colors significantly above chance but without any conscious accompaniment, whereas he performed at chance with the reverse color-letter mapping as well as in standard tests of letter reading. We suggest that the consciously perceived colors activated a representation of the corresponding word names and their component letters, which in turn brought out a partially successful, unconscious processing of visual inputs corresponding to the activated letter representations.     

A magnitude code common to numerosities and number symbols in human intraparietal cortex

Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in various number-processing tasks, whether numbers were conveyed by symbolic numerals (digits, number words) or by nonsymbolic displays (dot patterns). This suggests an abstract coding of numerical magnitude. Here, we critically tested this hypothesis using fMRI adaptation to demonstrate notation-independent coding of numerical quantity in the hIPS. Once subjects were adapted either to dot patterns or to Arabic digits, activation in the hIPS and in frontal regions recovered in a distance-dependent fashion whenever a new number was presented, irrespective of notation changes. This remained unchanged when analyzing the hIPS peaks from an independent localizer scan of mental calculation. These results suggest an abstract coding of approximate number common to dots, digits, and number words. They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities.     

Numerical magnitude in the human parietal lobe; tests of representational generality and domain specificity

Behavioral evidence suggests that human adults have a single system for representing the numerical magnitude of both symbolic numbers (e.g., Arabic digits) and nonsymbolic number stimuli (e.g., dot arrays). Brain imaging studies have implicated a specific parietal region in symbolic number processing, leading to the influential hypothesis that this region is the locus of a dedicated, domain-specific number system. Here we evaluated a prediction of this hypothesis, that this region should be activated not only by symbolic but also nonsymbolic number processing. Using nonsymbolic stimuli, we tested for higher parietal activations for number than for nonnumber comparison tasks (experiment 1), fMRI adaptation for numerosity repetition (experiment 2), and greater fMRI increases with increasing task difficulty for number than nonnumber tasks (experiment 3). None of these predictions were supported by the data, posing a serious challenge to the hypothesis that a single, domain-specific parietal region underlies both symbolic and nonsymbolic number representation.     

Oscillatory Brain Activity Reveals Linguistic Prints in the Quantity Code

Number representations change through education, although it is currently unclear whether and how language could impact the magnitude representation that we share with other species. The most prominent view is that language does not play any role in modulating the core numeric representation involved in the contrast of quantities. Nevertheless, possible cultural hints on the numerical magnitude representation are currently on discussion focus. In fact, the acquisition of number words provides linguistic input that the quantity system may not ignore. Bilingualism offers a window to the study of this question, especially in bilinguals where the two number wording systems imply also two different numerical systems, such as in Basque-Spanish bilinguals. The present study evidences linguistic prints in the core number representational system through the analysis of EEG oscillatory activity during a simple number comparison task. Gamma band synchronization appears when Basque-Spanish bilinguals compare pairs of Arabic numbers linked through the Basque base-20 wording system, but it does not if the pairs are related through the base-10 system. Crucially, this gamma activity, originated in a left fronto-parietal network, only appears in bilinguals who learned math in Basque and not in equivalent proficiency bilinguals who learned math in Spanish. Thus, this neural index reflected in gamma band synchrony appears to be triggered by early learning experience with the base-20 numerical associations in Basque number words.     

Thinking big; many modules or much cortex?

Is there a neural system dedicated to generic magnitude judgments? In this issue of Neuron, Pinel et al. report qualitative spatial overlap of fMRI responses during judgments of luminance, size, and numerical magnitude but also quantitative response differences in intraparietal cortex that mirror behavioral interference between perceptual and symbolic magnitude.     

The number domain- can we count on parietal cortex?

Does the primate brain contain a dedicated and localized neural circuitry for processing generic numerical information? The human parietal cortex, particularly the intraparietal sulcus (IPS), has long been implicated in processing symbolic (verbal) number information. If the IPS is indeed the site of generic numerical processing, however, its neurons should also encode nonsymbolic numerosity information. Two recent studies by Shuman and Kanwisher and by Piazza et al. published in this issue of Neuron tested this assumption...with quite different results.     

Size matters: non-numerical magnitude affects the spatial coding of response

It is known that small and large numbers facilitate left/right respectively (the SNARC effect). Recently, it has been proposed that numerical magnitude is just one example of a range of quantities, which have a common cognitive/neural representation. To investigate this proposition, response congruency effects were explored for stimuli which differed according to their: (a) numerical size, (b) physical size, (c) luminance, (d) conceptual size and (e) auditory intensity. In a series of experiments, groups of undergraduate participants made two-alternative forced choice discriminations with their left or right hands. There were clear interactions between magnitude and responding hand whereby right hand responses were faster for stimuli with (a) large numbers, (b) large physical size, (c) low luminance, and (d) a reference to large objects. There was no congruency effect for the auditory stimuli. The data demonstrate that the response congruency effect observed for numbers also occurs for a variety of other non-numerical visual quantities. These results support models of general magnitude representation and suggest that the association between magnitude and the left/right sides of space may not be related to culture and/or directional reading habits.     

THE EFFECT OF 40 HOURS OF CONSTANT WAKEFULNESS ON NUMBER COMPARISON PERFORMANCE

We investigated the effects of sleep loss and circadian rhythm on number comparison performance. Magnitude comparison of single-digits is robustly characterized by a distance effect: Close numbers (e.g., 5 versus 6) produce longer reaction times than numbers further apart (e.g., 2 versus 8). This distance effect is assumed to reflect the difficulty of a comparison process based on an analogous representation of general magnitude. Twelve male participants were required to stay awake for 40?h in a quasi-constant-routine protocol. Response speed and accuracy deteriorated between 00:00 and 06:00?h but recovered afterwards during the next day, indicating a circadian rhythm of elementary cognitive function (i.e., attention and speed of mental processing). The symbolic distance effect, however, did not increase during the nighttime, indicating that neither cumulative sleep loss nor the circadian clock prolongs numerical comparison processes. The present findings provide first evidence for a relative insensitivity of symbolic magnitude processing against the temporal variation in energy state. (Author correspondence: michael.steinborn@uni-tuebingen.de)     

Virtual dyscalculia induced by parietal-lobe TMS impairs automatic magnitude processing

People suffering from developmental dyscalculia encounter difficulties in automatically accessing numerical magnitudes [1-3]. For example, when instructed to attend to the physical size of a number while ignoring its numerical value, dyscalculic subjects, unlike healthy participants, fail to process the irrelevant dimension automatically and subsequently show a smaller size-congruity effect (difference in reaction time between incongruent [e.g., a physically large 2 and a physically small 4] and congruent [e.g., a physically small 2 and a physically large 4] conditions), and no facilitation (neutral [e.g., a physically small 2 and a physically large 2] versus congruent) [3]. Previous imaging studies determined the intraparietal sulcus (IPS) as a central area for numerical processing [4-11]. A few studies tried to identify the brain dysfunction underlying developmental dyscalculia but yielded mixed results regarding the involvement of the left [12] or the right [13] IPS. Here we applied fMRI-guided TMS neuronavigation to disrupt left- or right-IPS activation clusters in order to induce dyscalculic-like behavioral deficits in healthy volunteers. Automatic magnitude processing was impaired only during disruption of right-IPS activity. When using the identical paradigm with dyscalculic participants, we reproduced a result pattern similar to that obtained with nondyscalculic volunteers during right-IPS disruption. These findings provide direct evidence for the functional role of right IPS in automatic magnitude processing.     

Symbolic Numerical Magnitude Processing Is as Important to Arithmetic as Phonological Awareness Is to Reading

In this article, we tested, using a 1-year longitudinal design, whether symbolic numerical magnitude processing or children’s numerical representation of Arabic digits, is as important to arithmetic as phonological awareness is to reading. Children completed measures of symbolic comparison, phonological awareness, arithmetic, reading at the start of third grade and the latter two were retested at the start of fourth grade. Cross-sectional and longitudinal correlations indicated that symbolic comparison was a powerful domain-specific predictor of arithmetic and that phonological awareness was a unique predictor of reading. Crucially, the strength of these independent associations was not significantly different. This indicates that symbolic numerical magnitude processing is as important to arithmetic development as phonological awareness is to reading and suggests that symbolic numerical magnitude processing is a good candidate for screening children at risk for developing mathematical difficulties.     

Training Synesthetic Letter-color Associations by Reading in Color

Synesthesia is a rare condition in which a stimulus from one modality automatically and consistently triggers unusual sensations in the same and/or other modalities. A relatively common and well-studied type is grapheme-color synesthesia, defined as the consistent experience of color when viewing, hearing and thinking about letters, words and numbers. We describe our method for investigating to what extent synesthetic associations between letters and colors can be learned by reading in color in nonsynesthetes. Reading in color is a special method for training associations in the sense that the associations are learned implicitly while the reader reads text as he or she normally would and it does not require explicit computer-directed training methods. In this protocol, participants are given specially prepared books to read in which four high-frequency letters are paired with four high-frequency colors. Participants receive unique sets of letter-color pairs based on their pre-existing preferences for colored letters. A modified Stroop task is administered before and after reading in order to test for learned letter-color associations and changes in brain activation. In addition to objective testing, a reading experience questionnaire is administered that is designed to probe for differences in subjective experience. A subset of questions may predict how well an individual learned the associations from reading in color. Importantly, we are not claiming that this method will cause each individual to develop grapheme-color synesthesia, only that it is possible for certain individuals to form letter-color associations by reading in color and these associations are similar in some aspects to those seen in developmental grapheme-color synesthetes. The method is quite flexible and can be used to investigate different aspects and outcomes of training synesthetic associations, including learning-induced changes in brain function and structure.     

An ERP Study of the Processing of Common and Decimal Fractions: How Different They Are

This study explored event-related potential (ERP) correlates of common fractions (1/5) and decimal fractions (0.2). Thirteen subjects performed a numerical magnitude matching task under two conditions. In the common fraction condition, a nonsymbolic fraction was asked to be judged whether its magnitude matched the magnitude of a common fraction; in the decimal fraction condition, a nonsymbolic fraction was asked to be matched with a decimal fraction. Behavioral results showed significant main effects of condition and numerical distance, but no significant interaction of condition and numerical distance. Electrophysiological data showed that when nonsymbolic fractions were compared to common fractions, they displayed larger N1 and P3 amplitudes than when they were compared to decimal fractions. This finding suggested that the visual identification for nonsymbolic fractions was different under the two conditions, which was not due to perceptual differences but to task demands. For symbolic fractions, the condition effect was observed in the N1 and P3 components, revealing stimulus-specific visual identification processing. The effect of numerical distance as an index of numerical magnitude representation was observed in the P2, N3 and P3 components under the two conditions. However, the topography of the distance effect was different under the two conditions, suggesting stimulus specific semantic processing of common fractions and decimal fractions.     

Effects of development and enculturation on number representation in the brain

A striking way in which humans differ from non-human primates is in their ability to represent numerical quantity using abstract symbols and to use these 'mental tools' to perform skills such as exact calculations. How do functional brain circuits for the symbolic representation of numerical magnitude emerge? Do neural representations of numerical magnitude change as a function of development and the learning of mental arithmetic? Current theories suggest that cultural number symbols acquire their meaning by being mapped onto non-symbolic representations of numerical magnitude. This Review provides an evaluation of this contention and proposes hypotheses to guide investigations into the neural mechanisms that constrain the acquisition of cultural representations of numerical magnitude.     

Multi-representation of symbolic and nonsymbolic numerical magnitude in Chinese number processing

Numerical information can be conveyed by either symbolic or nonsymbolic representation. Some symbolic numerals can also be identified as nonsymbolic quantities defined by the number of lines (e.g., I, II, III in Roman and -, =, ≡ in Japanese Kanji and Chinese). Here we report that such multi-representation of magnitude can facilitate the processing of these numerals under certain circumstances. In a magnitude comparison task judging 1 to 9 (except 5) Chinese and Arabic numerals presented at the foveal (at the center) or parafoveal (3° left or right of the center) location, multi-representational small-value Chinese numerals showed a processing advantage over single-representational Arabic numerals and large-value Chinese numerals only in the parafoveal condition, demonstrated by lower error rates and faster reaction times. Further event-related potential (ERP) analysis showed that such a processing advantage was not reflected by traditional ERP components identified in previous studies of number processing, such as N1 or P2p. Instead, the difference was found much later in a N400 component between 300-550 msec over parietal regions, suggesting that those behavioral differences may not be due to early processing of visual identification, but later processing of subitizing or accessing mental number line when lacking attentional resources. These results suggest that there could be three stages of number processing represented separately by the N1, P2p and N400 ERP components. In addition, numerical information can be represented simultaneously by both symbolic and nonsymbolic systems, which will facilitate number processing in certain situations.     

Neurocognitive mechanisms of synesthesia

Synesthesia is a condition in which stimulation of one sensory modality causes unusual experiences in a second, unstimulated modality. Although long treated as a curiosity, recent research with a combination of phenomenological, behavioral, and neuroimaging methods has begun to identify the cognitive and neural basis of synesthesia. Here, we review this literature with an emphasis on grapheme-color synesthesia, in which viewing letters and numbers induces the perception of colors. We discuss both the substantial progress that has been made in the past fifteen years and some open questions. In particular, we focus on debates in the field relating to the neural basis of synesthesia, including the relationship between synesthesia and attention and the role of meaning in synesthetic colors. We propose that some, but probably not all, of these differences can be accounted for by differences in the synesthetes studied and discuss some methodological implications of these individual differences.