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How do bilinguals solve arithmetic problems in each of their languages? We investigated this question by exploring the neural substrates of mental arithmetic in bilinguals. Critically, our population was composed of a homogeneous group of adults who were fluent in both of their instruction languages (i.e., German as first instruction language and French as second instruction language). Twenty bilinguals were scanned with fMRI (3 T) while performing mental arithmetic. Both simple and complex problems were presented to disentangle memory retrieval occuring in very simple problems from arithmetic computation occuring in more complex problems. In simple additions, the left temporal regions were more activated in German than in French, whereas no brain regions showed additional activity in the reverse constrast. Complex additions revealed the reverse pattern, since the activations of regions for French surpassed the same computations in German and the extra regions were located predominantly in occipital regions. Our results thus highlight that highly proficient bilinguals rely on differential activation patterns to solve simple and complex additions in each of their languages, suggesting different solving procedures. The present study confirms the critical role of language in arithmetic problem solving and provides novel insights into how highly proficient bilinguals solve arithmetic problems.

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... In a second screening, from the total of 89 articles that measured mathematical performance in or between bilingual subjects, 18 articles were excluded due to not meeting one or several of the inclusion criteria, namely, (1) studies comparing mathematics performance in multilingual (more than two languages) versus monolingual learners (e.g., [70,71]); (2) studies using lexical decision task comparing regular words and number words (e.g., [72]), the translation of numbers from L1 to L2 or L2 to L1 (e.g., [73][74][75]), or number memory span (e.g., [76][77][78][79][80]); (3) studies that assessed mathematics performance in bilinguals in only one of their languages (e.g., [81][82][83][84][85]); or (4) studies providing incomplete data for the current purposes (e.g., measuring the compatibility effect with Arabic digits providing only the mean difference between compatible and incompatible trials in each language (e.g., [86][87][88])). Figure 1 presents a simplified diagram of the study selection process. ...

... For these 52 studies, the measures considered were accuracy (12) or both reaction time and accuracy (40). A total of 14 studies used neuroimaging and scanning techniques (functional magnetic resonance imaging, fMRI; event-related potential, ERP; magnetoencephalography, MEG) that measured brain activity when exposed to arithmetical operations using language and/or response times when judging the correctness of number word operations in their language of instruction and non-instructional language [63,[66][67][68][69][70][71][72][73][74][75][76][77]. ...

... For these 52 studies, the measures considered were accuracy (12) or both reaction time and accuracy (40). A total of 14 studies used neuroimaging and scanning techniques (functional magnetic resonance imaging, fMRI; event-related potential, ERP; magnetoencephalography, MEG) that measured brain activity when exposed to arithmetical operations using language and/or response times when judging the correctness of number word operations in their language of instruction and noninstructional language [63,[66][67][68][69][70][71][72][73][74][75][76][77]. ...

As part of the demands of a globalized and interconnected world, studying second languages has become a major priority. Bilingual programs implemented in recent decades have motivated an educational strategy in which content area courses are taught through L2. The potential costs of this strategy in academic performance are debated, especially in challenging areas such as mathematics. The present work systematically reviewed 71 papers based on experiments measuring mathematics performance in bilinguals in order to establish if bilinguals show a (dis)advantage in mathematics compared to monolinguals. The results of a total of 305,136 participants (57,703 bilinguals and 247,503 monolinguals) show that bilingualism does not seem to affect mathematical performance, but this is dependent on whether subjects are highly proficient bilinguals. This type of bilingual may only be affected by lower reaction times depending on the testing language. On the other hand, low language proficiency negatively impacts mathematical performance. Lastly, bilingualism enhances mathematical encoding and processes in non-language-related tasks.

... This task was adapted from previous tasks using Arabic Digits to study arithmetic processing (see Berteletti et al., 2014;Demir-Lira et al., 2020;Prado et al., 2011Prado et al., , 2013Prado et al., , 2014Suárez-Pellicioni & Booth, 2022;Suárez-Pellicioni et al., 2020 to allow for auditory presentation of the problems. Only two other fMRI studies on bilingual arithmetic have used auditory presentation of arithmetic problems ( Van Rinsveld et al., 2017;Wang et al., 2007). Van Rinsveld et al. (2017) presented bilinguals with simple and complex addition problems, and Wang et al. (2007) presented second language learners with complex multiplication problems involving two-digit numbers. ...

... Only two other fMRI studies on bilingual arithmetic have used auditory presentation of arithmetic problems ( Van Rinsveld et al., 2017;Wang et al., 2007). Van Rinsveld et al. (2017) presented bilinguals with simple and complex addition problems, and Wang et al. (2007) presented second language learners with complex multiplication problems involving two-digit numbers. However, the current study is the first to use auditory presentation of simple multiplication problems across a bilingual's languages while acquiring images with fMRI. ...

... Thus, we hypothesized that an increase in STG/MTG for LA+ relative to LA-would be most prominent for small problems. In contrast, given that operating in a weaker language for arithmetic has been linked with the activation of a more extensive language network ( Van Rinsveld et al., 2017), we hypothesized that LA-would recruit IFG to a greater extent than LA+, and that this would be most prominent when verifying larger (more difficult to retrieve) problems. Additionally, we predicted that LA-would recruit the IPS, reflecting reliance on quantity processes for a weaker arithmetic language. ...

Verbally memorized multiplication tables are thought to create language-specific memories. Supporting this idea, bilinguals are typically faster and more accurate in the language in which they learned math (LA+) than in their other language (LA-). No study has yet revealed the underlying neurocognitive mechanisms explaining this effect, or the role of problem size in explaining the recruitment of different brain regions in LA+ and LA-. To fill this gap in the literature, 29 Spanish-English early bilingual adults, proficient in both languages, verified simple multiplication problems in each language while functional magnetic resonance imaging (fMRI) was acquired. More specifically, this study aimed to answer two questions: 1) Does LA+ recruit STG/MTG to a greater extent than LA-, reflecting more robust verbal representations of multiplication facts in LA+. In contrast, does LA- recruit the IFG, reflecting more effortful retrieval, or the IPS, reflecting reliance on quantity processes? 2) Is there an interaction between language and problem size, where language differences are more pronounced for less practiced, large multiplication problems (e.g. 8x9) in comparison to more familiar, small problems (e.g. 2x3). Functional localizer tasks were used to identify hypothesis-driven regions of interest in verbal areas associated with verbal representations of arithmetic facts (left STG/MTG) and with the effortful retrieval of these facts (left IFG) and quantity areas engaged when calculation-based strategies are used (bilateral IPS). In planned analyses, no cluster reached significance for the direct comparison of languages (question 1) or for the interaction between language and problem size (question 2). An exploratory analysis found a main effect of problem size, where small problems recruited left STG/MTG and left IFG to a greater extent than large problems, suggesting greater verbal involvement for these problems in both languages. Additionally, large problems recruited right IPS to a greater extent than small problems, suggesting reliance on quantity processes. Our results suggest that proficient early bilingual adults engage similar brain regions in both languages, even for more difficult, large problems.

... Therefore, bilinguals might show different strengths of association between number words of the different languages, Indo-Arabic digits and their semantic representations. The strength of association possibly depends on the language of mathematical education and might in turn influence mathematical performances (Van Rinsveld et al., 2017). The present study aims to investigate how the language of learning mathematics shapes lexical and semantic representations of number words of proficient bilinguals, which is of particular interest for bilingual school curricula. ...

... This finding suggests the existence of late plasticity for arithmetic memory networks in specific cases, which might also exist for numbers. On the other side, weaker LM2 lexico-semantic associations fit with fMRI studies indicating more brain areas for solving arithmetics in the LM2 (Lin et al., 2019;Van Rinsveld et al., 2017;Wang et al., 2007). More extensive brain activation patterns are hence interpreted as more effortful and less efficient processes. ...

... From a neuroscientific perspective, these differences are reflected in the recruitment of more brain regions when solving arithmetic in the L2 than the L1 (Martinez-Lincoln et al., 2015;Wang et al., 2007). Specifically, in a comparable sample more extensive brain activations for LM2 than LM1 arithmetic were also found (Van Rinsveld et al., 2017). A larger brain activation pattern could reflect less optimised cognitive networks when solving arithmetic in L2 or LM2. ...

Bilinguals’ exact number representations result from associations between language-independent Indo-Arabic digits (“5”), two verbal codes (“fünf” and “cinq”) and a common, largely overlapping semantic representation. To compare the lexical and semantic access to number representations between two languages, we recruited a sample of balanced highly proficient German–French adult bilinguals. At school, those bilinguals learned mathematics in German for 6 years (LM1) and then switched to French (LM2) in 7th grade (12 years old) until 13th grade. After the brief presentation of primes (51 ms) consisting of Indo-Arabic digits or number words in German or French, an Indo-Arabic digits target had to be read in either German or French in an online study. Stimuli were numbers from 1 to 9, and we varied the absolute distance between primes and targets from 0 (i.e., 1–1) to 3 (1–4; as in Reynvoet et al., 2002). The priming distance effect (PDE) was used to measure the strength of numerical semantic association. We find comparable PDEs with Indo-Arabic digits and German number word primes, independently from the target naming language. However, we did not find a clear PDE with French number word primes, neither when naming targets in German, nor in French. The weaker PDE from LM2 compared to LM1 primes is interpreted as a weaker lexico-semantic association of LM2 number words. These results indicate a critical role of the LM1 and further emphasize the role of language in processing numbers. They might have important implications for designing bilingual school curricula.

... Often, the language bilinguals used when learning math, herein LA+, is preferred over their other language, or LA−, and this preference can persist into adulthood [3][4][5]. In line with this self-reported preference, multiple studies have reported that bilinguals perform or verify arithmetic faster and/or more accurately in LA+ than LA− [1,2,4,[6][7][8][9][10][11][12]. This suggests that the memory for arithmetic facts might be accessible more efficiently (or directly only) in LA+. ...

... Similarly, the teacher study discussed above revealed that language use can override the LA+ advantage [14], and a recent metaanalysis investigation strongly suggests that language differences in processing arithmetic can be explained by these language use factors [13]. Still, these critical factors are not always considered in studies of bilingual arithmetic [1,2,[7][8][9]11,19,51]. ...

... Our sample includes early Spanish-English bilinguals who learned both languages before learning early arithmetic facts, similar to the children included in Cerda et al. [6]. In this way, we could dissociate the role of the language of learning from the age of acquisition of that language, which other studies did not control [1,2,7,8,11,[51][52][53]. In addition, all participants had equivalent fluency in both languages and frequently used both languages in daily life, yet learned multiplication primarily or solely in one language. ...

Many studies of bilingual arithmetic report better performance when verifying arithmetic facts in the language of learning (LA+) over the other language (LA−). This could be due to language-specific memory representations, processes established during learning, or to language and task factors not related to math. The current study builds on a small number of event-related potential (ERP) studies to test this question while controlling language proficiency and eliminating potential task confounds. Adults proficient in two languages verified single-digit multiplications presented as spoken number words in LA+ and LA−, separately. ERPs and correctness judgments were measured from solution onset. Equivalent P300 effects, with larger positive amplitude for correct than incorrect solutions, were observed in both languages (Experiment 1A), even when stimuli presentation rate was shortened to increase difficulty (Experiment 1B). This effect paralleled the arithmetic correctness effect for trials presented as all digits (e.g., 2 4 8 versus 2 4 10), reflecting efficient categorization of the solutions, and was distinct from an N400 generated in a word–picture matching task, reflecting meaning processing (Experiment 2). The findings reveal that the language effects on arithmetic are likely driven by language and task factors rather than differences in memory representation in each language.

... There is evidence that the language used for early learning shapes the representation of these facts in memory, persisting even into adulthood (Salillas & Wicha, 2012). Supporting this idea, bilinguals typically report having a preference for performing arithmetic in one language (Dewaele, 2007;Vaid & Menon, 2000) and are typically faster and more accurate at solving arithmetic in LA+, than in the language that was not used for learning arithmetic, or LA− (Cerda et al., 2019;Dehaene et al., 1999;Frenck-Mestre & Vaid, 1993;Lotus Lin et al., 2019;Marsh & Maki, 1976;Salillas & Wicha, 2012;Spelke & Tsivkin, 2001;Tamamaki, 1993;van Rinsveld et al., 2016van Rinsveld et al., , 2017. ...

... They suggested this difference was driven by the unfamiliarity of arithmetic facts presented as written words. Similarly, previous work in bilinguals also reported interactions between a bilingual's two languages and problem complexity, where more pronounced language differences are observed for addition problems that require more complex operations (e.g., carrying) compared to memorized, simple additions (Lotus Lin et al., 2019;Mondt et al., 2011;van Rinsveld et al., 2016van Rinsveld et al., , 2017. ...

The problem size effect (PSE) is defined by better performance solving small problems (e.g., 2 × 4) than large problems (e.g., 8 × 9). For monolinguals, the PSE is larger when problems are presented in unfamiliar formats (e.g., written words), reflecting increased processing difficulty. Bilinguals are typically faster and more accurate at retrieving multiplication facts in the language of learning (LA+) than in their other language (LA−). We hypothesized that the less familiar arithmetic language (i.e., LA−) would elicit larger PSEs than LA+. Here, fluent Spanish–English bilingual adults verified spoken multiplication problems presented in LA+ and LA− while event-related potentials (ERPs) were recorded (Experiment 1A). To further promote language differences, we increased task difficulty by presenting problems at a faster pace (Experiment 1B) and requiring bilinguals to verbally produce solutions (Experiment 2). Language differences in performance were only observed for Experiment 2, where solutions were produced more slowly in LA− than LA+. In the ERPs, a PSE was driven by larger P300s for small than large solutions. A language effect was only observed under time pressure where LA− elicited a PSE at the second operand. Additionally, the PSE was smaller for LA− at the solution. This suggests that categorizing multiplication facts is more effortful in LA−. In sum, very subtle language differences arise in fluent bilinguals when problems are more difficult, such as larger problems presented under time pressure in a weaker language. Critically, the effect of LA+ is at the level of response production and not access to the facts from memory.

... The CLA assembles substantial cognitive-relevant cells such as Von Economo neurons (VEN) and position-responsive cells apart from multitudinous claustral neurons (see Figure 1; Smythies et al., 2014;Jankowski and O'Mara, 2015;Smith et al., 2020). Consequently, the CLA and its related circuitries get involved in several cognitive functions, including attention, executive function (White et al., 2018), visuospatial ability (Gould et al., 2006), language (Van Rinsveld et al., 2017), and memory (Seo et al., 2016), and these cognitive functions achieved by varies brain networks in AD tend to denigrate over the course of the disease. ...

... A series of neuroimaging investigations prove that CLA occupies an essential linguistic role. Combined with fMRI on the brains of proficient bilingual subjects doing simple and complex addition mental arithmetic tasks, the CLA has different levels of evocation in people with different language dominance (Van Rinsveld et al., 2017). The MRI scans of all aphasia patients emerge ischemic lesions in the left hemisphere, and the largest areas of overlapping foci are localized in the CLA and other brain structures (Marangolo et al., 2014). ...

Alzheimer's disease (AD) is one of the most common neurodegenerative diseases characterized by cognitive deficits and dementia. AD entails predominant pathological characteristics including amyloid beta (Aβ) plaque formation, neurofibrillary entanglements, and brain atrophy, which gradually result in cognitive dysfunctions. Studies showed that these pathological changes are found in a myriad of brain structures, including the claustrum (CLA), a nucleus that penetrates deeply into the brain and is extensively interconnected to various brain structures. The CLA modulates many aspects of cognitive functions, with attention, executive function, visuospatial ability, language, and memory in particular. It is also implicated in multiple neuropsychiatric disorders, of which one worthy of particular attention is AD-related cognitive impairments. To inspire novel AD treatment strategies, this review has summarized the CLA functionality in discriminative cognitive dysfunctions in AD. And then propose an array of potential mechanisms that might contribute to the cognitive impairments caused by an abnormal CLA physiology. We advocate that the CLA might be a new promising therapeutic target in combination with existing anti-AD drugs and brain stimulation approaches for future AD treatment.

... Functional magnetic resonance imaging studies revealed that the LM1 recruited more temporal regions, supposedly related to direct semantic retrieval, than the LM2 for simple additions. In turn, the LM2 recruited a network of regions indicating the need for more generic cognitive resources [60]. On the contrary, Cerda et al., [61] recently investigated Spanish-English bilingual children's performance in a multiplication verification task and observed similar ERP responses in both of their languages. ...

... directly retrieved from long-term memory), while the LM2 (French), could rely on slower procedural rules, even for numbers under 60. In line with this view, weaker fMRI temporal lobe activation was observed when solving simple additions in LM2, proposedly reflecting less verbal retrieval than for LM1 additions [60]. Furthermore, since in ADAPT algorithmic rules are enacted by the short-term memory, it could potentially impact its capacity by using more resources [84,85] and in turn explain parts of the LM2 costs observed in the same bilingual population for exact arithmetic [57]. ...

Number transcoding is the cognitive task of converting between different numerical codes (i.e. visual “42”, verbal “forty-two”). Visual symbolic to verbal transcoding and vice versa strongly relies on language proficiency. We evaluated transcoding of German-French bilinguals from Luxembourg in 5th, 8th, 11th graders and adults. In the Luxembourgish educational system, children acquire mathematics in German (LM1) until the 7th grade, and then the language of learning mathematic switches to French (LM2). French `70s `80s `90s are less transparent than `30s `40s `50s numbers, since they have a base-20 structure, which is not the case in German. Transcoding was evaluated with a reading aloud and a verbal-visual number matching task. Results of both tasks show a cognitive cost for transcoding numbers having a base-20 structure (i.e. `70s, `80s and `90s), such that response times were slower in all age groups. Furthermore, considering only base-10 numbers (i.e. `30s `40s `50s), it appeared that transcoding in LM2 (French) also entailed a cost. While participants across age groups tended to read numbers slower in LM2, this effect was limited to the youngest age group in the matching task. In addition, participants made more errors when reading LM2 numbers. In conclusion, we observed an age-independent language effect with numbers having a base-20 structure in French, reflecting their reduced transparency with respect to the decimal system. Moreover, we find an effect of language of math acquisition such that transcoding is less well mastered in LM2. This effect tended to persist until adulthood in the reading aloud task, while in the matching task performance both languages become similar in older adolescents and young adults. This study supports the link between numbers and language, especially highlighting the impact of language on reading numbers aloud from childhood to adulthood.

... C'est le cas pour les 2 études précédentes qui avaient pour population des bilingues plus tardifs avec des âges moyens d'acquisition de L2 se situant en moyenne entre 10 et 12 ans. Une nouvelle étude s'est donc intéressée aux mêmes questions de recherche mais en utilisant un échantillon de bilingues plus homogènes et plus balancés en choisissant une population de bilingues luxembourgeois (Van Rinsveld, Dricot, Guillaume, Rossion & Schiltz, 2017). En effet, le système scolaire national luxembourgeois impose une éducation multilingue. ...

... De même, la mémoire de travail verbal pourrait être plus facilement mobilisée en LA+, car l'utilisation de cette dernière pourrait faire partie d'une procédure plus automatisée en LA+ qu'en LA-. Alors que des arguments existent en faveur d'un meilleur accès en mémoire à long terme pour les problèmes arithmétiques simples appris en LA+ (Van Rinsveld et al., 2017), des études futures devront explorer plus en détail les mécanismes cognitifs et neuronaux qui sont affectés par la langue de l'apprentissage de l'arithmétique. ...

Educational policies tend to encourage bilingualism from an early age. Learning one or more foreign languages is undoubtedly beneficial but requires considering how bilingualism influences learning in other disciplines, such as mathematics. Language influences certain aspects of mathematical cognition, including arithmetic. In particular fields, it appears that the mastery of several languages can have cognitive benefits or, on the other hand generate costs related to the stimulation of the executive functions. This chapter aims to describe the influence of language on arithmetic, as well as current controversies regarding bilingualism and arithmetic learning in school.

... Furthermore, the match between math learners' language profiles and the linguistic context in which mathematical learning takes place plays a critical role in the acquisition and use of basic number knowledge. Matching language contexts improve bilinguals' arithmetic performance in their second language (Van Rinsveld et al., 2016), and neural activation patterns of bilinguals solving additions differ depending on the language they used, suggesting different problem-solving processes (Van Rinsveld et al., 2017). ...

... Other studies have highlighted that proficiency in the language of instruction (Abedi and Lord, 2001;Hickendorff, 2013;Paetsch et al., 2016;Saalbach et al., 2016) and, more specifically, the mastery of mathematical language are essential predictors of mathematics performance (Purpura and Reid, 2016). It also becomes increasingly clear that test language modulates the neuronal substrate of mathematical cognition (Salillas and Carreiras, 2014;Salillas et al., 2015;Van Rinsveld et al., 2017). On the other hand, we do claim that a testee's access to the assessment tools should not be limited by proficiency in a certain language. ...

While numerical skills are fundamental in modern societies, some estimated 5–7% of children suffer from mathematical learning difficulties (MLD) that need to be assessed early to ensure successful remediation. Universally employable diagnostic tools are yet lacking, as current test batteries for basic mathematics assessment are based on verbal instructions. However, prior research has shown that performance in mathematics assessment is often dependent on the testee's proficiency in the language of instruction which might lead to unfair bias in test scores. Furthermore, language-dependent assessment tools produce results that are not easily comparable across countries. Here we present results of a study that aims to develop tasks allowing to test for basic math competence without relying on verbal instructions or task content. We implemented video and animation-based task instructions on touchscreen devices that require no verbal explanation. We administered these experimental tasks to two samples of children attending the first grade of primary school. One group completed the tasks with verbal instructions while another group received video instructions showing a person successfully completing the task. We assessed task comprehension and usability aspects both directly and indirectly. Our results suggest that the non-verbal instructions were generally well understood as the absence of explicit verbal instructions did not influence task performance. Thus we found that it is possible to assess basic math competence without verbal instructions. It also appeared that in some cases a single word in a verbal instruction can lead to the failure of a task that is successfully completed with non-verbal instruction. However, special care must be taken during task design because on rare occasions non-verbal video instructions fail to convey task instructions as clearly as spoken language and thus the latter do not provide a panacea to non-verbal assessment. Nevertheless, our findings provide an encouraging proof of concept for the further development of non-verbal assessment tools for basic math competence.

... Accordingly, neurocognitive studies suggest that solving arithmetic problems in LM2 requires more effort and recruits additional brain areas compared to LM1 (Salillas & Wicha, 2012;Van Rinsveld et al., 2017;Wang et al., 2007). ...

In an increasingly multilingual and multicultural world, understanding the interactions between language and mathematics is critical, especially when individuals must acquire and exercise their mathematical competencies in multiple languages. Indeed, research shows that, overall, L2 language learners are at an academic disadvantage compared to their L1 peers. The current article briefly overviews how multilingualism influences basic and advanced mathematical skills and interacts with mathematical learning difficulties. We first outline the traditional cognitive models of number learning and language processing. We then discuss the particularities of multilingualism and how it impacts numerical skills such as counting and building lexical-semantic associations, transcoding and arithmetic, mathematical word problems and mathematical performance tests, and dyscalculia diagnosis. We end this review by outlining challenges, recommendations, and solutions for multilingual educational settings. The article is intended as a guide for numerical cognition researchers who work with diverse populations and for mathematics educators and educational policy-makers facing the challenges of a multilingual classroom.

... However, the effect of multilingualism on mathematical abilities depends on the language that is being used (native or non-native) and the type of mathematical problem being solved (simple arithmetic or mathematical word problems). When multilingual adults solved complex arithmetic problems presented auditorily in their non-native language, they were slower to respond and recruited additional brain regions associated with visuo-spatial thinking (Van Rinsveld et al., 2017). Multilinguals may need to visualize the symbolic form of the numbers when performing arithmetic in their second language. ...

The chapter considers how language sparks discovery and innovation by examining creativity and problem-solving through the unique vantage point of multilingualism. The chapter begins with an overview of how creativity and problem-solving are operationalized and measured, followed by a review of how multilingualism impacts the ability to innovate and solve problems. The relationship between multilingualism and creativity is modulated by proficiency and age of second language acquisition. Similarly, performance on problem-solving tasks depends on which language multilinguals use and on their proficiency level in each language. The final section discusses multilingualism, creativity, and problem-solving in real-world settings, as well as potential future directions, concluding with the suggestion that knowing multiple languages can lead to more creative outcomes and better problem-solving skills.

... For instance, inner speech is typically used in mental multiplication because the execution of common calculation algorithms, like LM, involves utilizing multiplication tables, which are normally acquired through rote verbal memorization (Lee & Kang 2002). In addition, bilinguals tend to be more reliable and quicker when performing mental arithmetic with the aid of the language in which they were taught basic arithmetic facts and decision procedures (Shanon 1984;Van Rinsveld, Dricot, Guillaume, Rossion, & Schiltz 2017). Despite being fluent with a second language (and being able to use that second language in inner speech, De Guerrero 2005) bilinguals translate into the language in which they received their mathematical education in order to solve arithmetic problems presented in other languages with which they are competent. ...

In updating our beliefs on the basis of our background attitudes and evidence we frequently employ objects in our environment to represent pertinent information. For example, we may write our premises and lemmas on a whiteboard to aid in a proof or move the beads of an abacus to assist in a calculation. In both cases, we generate extramental (that is, occurring outside of the mind) representational states, and, at least in the case of the abacus, we operate over these states in light of their contents (e.g., the integers represented by the beads) to generate new representations. In this paper, I argue that our belief updating processes and the grounds of their rational evaluation are partly constituted by extramental representations and operations. In other words, we don’t merely update our attitudes through an internal process of reasoning on the basis of available evidence. If we are to accurately understand and rationally evaluate our belief updating processes and resultant attitudes, we need to examine how we representationally appropriate our extramental environment in the updating process.

... However, these studies suggest that language differences may arise for complex problems because of other factors. For example, a second language may recruit additional resources for number manipulation, including activating visual representations of numbers (Van Rinsveld et al., 2017) or translating less familiar two-digit operands into a stronger language (Lotus Lin et al., 2019). Critically, these processes are secondary to accessing the arithmetic facts from memory, which seems to be equivalent across languages in balanced bilinguals (Cerda et al., 2022). ...

In 2020, 21.5% of US preschoolers spoke a language other than English at home. These children transition into English‐speaking classrooms in different ways, often handling foundational concepts in two languages. Critically, some knowledge may be dependent on the language of learning. For instance, both bilingual children and adults typically prefer, and exhibit higher performance on arithmetic in the language in which they learned math (LA+) compared with their other language (LA−). The typical interpretation is that arithmetic facts are accessed from memory more efficiently or solely in LA+. However, recent research suggests that bilingual arithmetic is not restricted to one language in memory, and that language experience plays an important role in performance. Moreover, evidence suggests children and adults process arithmetic fundamentally differently. Thus, bilingual arithmetic memory may manifest differently across the life span. This review outlines evidence to date at the intersection between the brain basis of bilingualism, arithmetic processing, and development.

... Although the relationship between mathematics and language has been investigated for a long time, it needs to be noted that almost all studies have focused on language's contribution to the development of mathematical skills. Even second language (L2) contributes to the development of mathematical thinking (Van Rinsveld et al., 2017). None of them studied the reverse, mathematical thinking's influence on language acquisition, especially learners' L2 acquisition. ...

... PATHWAYS TO LEARNING MATHEMATICS language as well as instructional experiences (Frenck-Mestre & Vaid, 1993;Salillas & Wicha, 2012;Van Rinsveld et al., 2017). ...

Canadian students enrolled in either French-immersion or English-instruction programs were followed from Grades 2 to 3 (Mage = 7.8 years to 8.9 years; N = 244; 55% girls). In each grade, students completed two mathematical tasks that required oral language processing (i.e., word-problem solving and number transcoding from dictation) and two that did not (i.e., arithmetic fluency and number line estimation). Students in both English-instruction (n = 92) and French-immersion programs (n = 152) completed tasks in English. Students in French-immersion programs also completed word-problem solving and transcoding tasks in French. The models were framed within the Pathways to Mathematics model, with a focus on the linguistic pathways for students in English-instruction and French-immersion programs. For tasks with oral language processing, performance in Grade 3 was predicted by students’ English receptive vocabulary for both English-instruction and French-immersion students, even when French-immersion students were tested in French, controlling for performance in Grade 2. In contrast, for tasks without oral language processing, receptive vocabulary in either English or French did not predict performance in Grade 3, controlling for performance in Grade 2. These results have implications for teaching mathematics within the context of immersion education.

... Given their somewhat lower understanding of verbal information in the language of instruction, children speaking a Roman language might for instance rely more on visuo-spatial input and processes in an attempt to compensate their verbal difficulties. Such a mechanism would be in line with the finding that highly skilled bilingual adults display activation in the visual cortex when solving orally presented complex additions in their second, but not their first language of mathematics acquisition (Van Rinsveld et al., 2017). Future studies will need to address this speculation by assessing the cognitive strategies used by children of different language groups directly. ...

Achievement in mathematics has been shown to partially depend on verbal skills. In multilingual educational settings, varying language proficiencies might therefore contribute to differences in mathematics achievement. We explored the relationship between mathematics achievement and language competency in terms of home language and instruction language proficiency in the highly multilingual society of Luxembourg. We focussed on third graders' linguistic and mathematical achievement and used data from the national school monitoring program from two consecutive years to assess the influence of children's language profiles on reading comprehension in German (the instruction language) and mathematics performance. Results were similar for both co-horts. Regression analysis indicated that German reading comprehension was a significant predictor of mathematics achievement when accounting for both home language group and socioeconomic status. Moreover, mediation analysis showed that lower mathematics achievement of students with a home language that is very different from the instruction language relative to the Luxembourgish reference group were significantly mediated by achievement in German reading comprehension. These findings show that differences in mathematics achievement between speakers of a home language that is similar to the instruction language and speakers of distant home languages can be explained by their underachievement in reading comprehension in the instruction language. Possible explanations for varying performance patterns between language groups and solutions are being discussed.

... These include differences in outcome variables across genders and levels of social deprivation (OECD, 2012). Moreover, Van Rinsveld et al. (2017) provided evidence to suggest that bilingual individuals rely on differential activation patterns in the brain to solve simple and complex arithmetic questions in their different languages. As such, we also conducted a series of moderation analyses to investigate the effects of these variables (refer to supplementary material). ...

The Say-All-Fast-Minute-Every-Day-Shuffled (SAFMEDS) strategy promotes fast and accurate recall. The existing literature suggests that the strategy can help learners improve academic outcomes. Through a cluster randomized controlled trial, we assessed the impact of implementation support on children’s mathematics outcomes during a teacher-led SAFMEDS intervention. Following training and prior to baseline assessments, we randomly allocated schools to receive either no (n = 31) or ongoing (n = 33) support from a researcher. Support consisted of three in-situ visits and email contact. Assessors remained blind to the condition of the schools throughout. We analyzed the outcomes of children (nSupport = 294, nNoSupport = 281) using a multi-level mixed-effects model; accounting for the children nested within schools. The results suggest that implementation support has a small effect on children’s fluency of arithmetic facts (Mathematics Fluency and Calculation Tests (MFaCTs): Grades 1–2, d = 0.23, 95% CI: 0.06–0.40; MFaCTs: Grades 3–5, d = 0.25, 95% CI: 0.08–0.42). These results are larger than the average effect sizes reported within professional development literature that apply coaching elements to mathematics programs.

... However, when exposed to previously learned but language-dependent math learning content such as multiplication facts, knowledge does not simply generalize to another language but rather needs to be newly established in a second language. Crucially, as shown for highly balanced bilingual learners with math learning exposure in both L1 and L2 (Van Rinsveld et al. 2017), it is possible that fact retrieval becomes equally efficient in different verbal codes and does no longer require an inefficient translation of problems from one language to the other. However, gaining highly proficient fact retrieval in more than one language, does seem to entail different learning and proficiency stages. ...

The importance of language in mathematics education becomes increasingly obvious, as multilingual learners are not an exception nowadays. But how can language dominance and the language of first or later instruction affect arithmetic training in adults? 101 bilingual adults whose first and dominant language was German (LM+ and L1) and who spoke English as their second language (L2) were tested. Participants were assigned to three different training groups and either practiced basic multiplications in German, English or both languages. In a verification paradigm, reaction times on solving multiplication problems in German and English respectively were recorded before and after the training. Results showed a strong influence of the language adult bilinguals initially acquired arithmetic knowledge in (German). German items were overall solved more quickly than English counterparts, irrespective of the language items were specifically trained in. English were affected by differing training conditions with respect to training effects. This leads to the consideration of various factors including language proficiency levels, the language of first mathematics instruction in early school years as well as the language of mathematics instruction in later learning contexts, in understanding bilingual arithmetic learning.

... Another study led to the same conclusions because the unbalanced Chinese-English bilinguals participants had higher activation in the left frontal areas when they performed mental additions using their L2 (Lin, Imada, & Kuhl, 2012). In contrast, a more recent fMRI study (Van Rinsveld, Dricot, Guillaume, Rossion, & Schiltz, 2017) did not find any support for the existence of translation mechanisms in a population of much more balanced bilinguals. It rather pointed towards the activation of partly different neuronal substrates when calculating in different languages without evidence of translations processes. ...

We investigated the influence of language on transcoding in bilinguals and monolinguals. Bilingual adults who learned math in German (LM+) during primary school and in French during secondary school (LM-) were compared to German and French monolinguals. Participants had to listen to two-digit numbers and had to identify the heard number amongst four visually presented Arabic numbers. To mimic the German vs. the French number word systems, the order of visual appearance of the units and tens of the two-digit numbers was manipulated. Participants also performed a classical transcoding task with simultaneous appearance of the tens and units. Bilinguals were faster to transcode in LM+ than in LM-. Furthermore, they were slower and made more errors when transcoding in LM- compared to monolingual French-speaking participants. We conclude that math acquisition’s language influences simple numerical tasks such as transcoding in adulthood, confirming the critical role of language in numerical cognition.

... This implies that there can be no other mental code for the second language. He and others have inferred from this that bilinguals might use qualitatively different cognitive processes, for example, direct retrieval from LA+ versus translation from LA− to LA+, and, by inference engage qualitatively different brain processes for arithmetic facts in each language (see Dehaene, Piazza, Pinel, & Cohen, 2005, p. 442 andalso Dehaene et al., 1999;Spelke & Tsivkin, 2001;Van Rinsveld, Dricot, Guillaume, Rossion, & Schiltz, 2017). ...

English learners (ELs) are a rapidly growing population in schools in the United States with limited experience and proficiency in English. To better understand the path for EL’s academic success in school, it is important to understand how EL’s brain systems are used for academic learning in English. We studied, in a cohort of Hispanic middle-schoolers (n = 45, 22F) with limited English proficiency and a wide range of reading and math abilities, brain network properties related to academic abilities. We applied a method for localizing brain regions of interest (ROIs) that are group-constrained, yet individually specific, to test how resting state functional connectivity between regions that are important for academic learning (reading, math, and cognitive control regions) are related to academic abilities. ROIs were selected from task localizers probing reading and math skills in the same participants. We found that connectivity across all ROIs, as well as connectivity of just the cognitive control ROIs, were positively related to measures of reading skills but not math skills. This work suggests that cognitive control brain systems have a central role for reading in ELs. Our results also indicate that an individualized approach for localizing brain function may clarify brain-behavior relationships.

Research has demonstrated that learning two or more languages during development (i.e., becoming bilingual) shapes children's cognition in myriad ways. However, because such studies have largely been conducted using laboratory experiments, it is unclear how bilingualism may modulate more naturalistic cognitive skills such as arithmetic fluency. Moreover, how the relationship between speaking two (or more) languages and arithmetic varies with language fluency-specifically, the degree of bilingualism-has been understudied. Therefore, this study examined third- to fifth-grade monolingual (n = 70) and bilingual (n = 51) children's performance on an arithmetic fluency task. Monolinguals' and bilinguals' performance on the arithmetic fluency task did not differ. However, individual differences in the relation between children's arithmetic fluency and their language fluency were found, suggesting that bilingual children's skill in their nondominant language was associated with arithmetic fluency. These findings point to the importance of examining individual differences in language fluency among bilinguals to understand how bilingualism may shape cognitive skills.

It has been consistently reported that deaf individuals experience mathematical difficulties compared to their hearing peers. However, the idea that deafness and early language deprivation might differently affect verbal (i.e., multiplication) vs. visuospatial (i.e., subtraction) arithmetic performances is still under debate. In the present paper, three groups of 21 adults (i.e., deaf signers, hearing signers, and hearing controls) were therefore asked to perform, as fast and as accurately as possible, subtraction and multiplication operations. No significant group effect was found for accuracy performances. However, reaction time results demonstrated that the deaf group performed both arithmetic operations slower than the hearing groups. This group difference was even more pronounced for multiplication problems than for subtraction problems. Weaker language-based phonological representations for retrieving multiplication facts, and sensitivity to interference are two hypotheses discussed to explain the observed dissociation.

Our conscious thought, at least at times, seems suffused with language. We may experience thinking as if we were ‘talking in our head’, thus using inner speech to verbalize, e.g., our premises, lemmas, and conclusions. I take inner speech to be part of a larger phenomenon I call inner semiotics, where inner semiotics involves the subjective experience of expressions in a semiotic (or symbol) system absent the overt articulation of the expressions. In this paper, I argue that inner semiotics allows us to bootstrap our way into entertaining thoughts about exact numbers and quantities that we couldn't prior to our competence with a numeric code. I establish that our arithmetic thoughts literally occur as (internal ‘articulations’ of) expressions in a numeric code. However, a problem arises for my view: just as we can slip in overt speech, producing an utterance that deviates from what we mean to say, there is very good evidence that we can slip in inner speech as well. If our arithmetic thought occurs in a numeric code, it's far from clear how we determine when a covert utterance constitutes a slip. In closing, I provide an account of what makes an inner speech utterance a slip.

Are bilinguals faster and/or better at performing numerical judgments in one language than in their other language? What factors moderate language differences in number processing ease? To address these issues, we conducted a meta-analysis of 38 studies (based on 1861 participants) in which bilinguals’ speeded performance and accuracy on number tasks was compared across languages within subjects. Analysis of 63 independent effect sizes for reaction time data and 28 for accuracy data showed an overall language difference favoring the first language. This effect was particularly observed in reaction time studies for number tasks involving arithmetic judgments or number naming. The L1 effect was characteristic of bilinguals with low or medium proficiency in the second language, those who were schooled in the first language, and those whose stated preference for arithmetic was the first language. Further, a first language advantage was most characteristic of late bilinguals (for reaction time). For accuracy, additional moderators of a first language advantage included differences between the languages in decade unit counting system. No other effects were significant. The findings lend support to models of number cognition that posit format-sensitive codes. They further clarify that a privileging of the first language is not uniform but varies by bilingualism onset, proficiency, language of early schooling, and language specific characteristics.

The psycholinguistic literature suggests that the length of a to-be-spoken phrase impacts the scope of speech planning, as reflected by different patterns of speech onset latencies. However, it is unclear whether such findings extend to first and second language (L1, L2) speech planning. Here, the same bilingual adults produced multi-phrase numerical equations (i.e., with natural break points) and single-phrase numbers (without natural break points) in their L1 and L2. For single-phrase utterances, both L1 and L2 were affected by L2 exposure. For multi-phrase utterances, L1 scope of planning was similar to what has been previously reported for monolinguals; however, L2 scope of planning exhibited variable patterns as a function of individual differences in L2 exposure. Thus, the scope of planning among bilinguals varies as a function of the complexity of their utterances: specifically, by whether people are speaking in their L1 or L2, and bilingual language experience.

Bilingual experience alters brain structure and enhances certain cognitive functions. Bilingualism can also affect mathematical processing. Reduced accuracy is commonly reported when arithmetic problems are presented in bilinguals’ second (L2) vs. first (L1) language. We used MEG brain imaging during mental addition to characterize spatiotemporal dynamics during mental addition in bilingual adults. Numbers were presented auditorally and sequentially in bilinguals’ L1 and L2, and brain and behavioral data were collected simultaneously. Behaviorally, bilinguals showed lower accuracy for two-digit addition in L2 compared to L1. Brain data showed stronger response magnitude in L2 versus L1 prior to calculation, especially when two-digit numbers were involved. Brain and behavioral data were significantly correlated. Taken together, our results suggest that differences between languages emerge prior to mathematical calculation, with implications for the role of language in mathematics.

How does the human brain conceptualize abstract ideas? In particular, what is the origin of mathematical activity, especially when it is associated with high-level of abstraction? Is mathematical thought independent of language? Cognitive science has now started to investigate this question that has been of great interest to philosophers, mathematicians and educators for a long time. While studies have so far focused on basic arithmetic processing, my PhD thesis aims at further investigating the cerebral processes involved in the manipulation and learning of more advanced mathematical ideas. I have shown that (1) advanced mathematical reflection on concepts mastered for many years does not recruit the brain circuits for language; (2) mathematical activity systematically involves number- and space-related brain regions, regardless of mathematical domain, problem difficulty, and participants' visual experience; (3) non-verbal acquisition of geometrical rules relies on a language of thought that is independent of natural spoken language. Finally, altogether these results raise new questions and pave the way to further investigations in neuroscience: - is the human ability for language also irrelevant to advanced mathematical acquisition in schools where knowledge is taught verbally? - What is the operational definition of the fields of “mathematics” and “language” at the brain level?

In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of arithmetic facts, and outline an attentional account of the role of the AG in arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp, 2016. © 2016 Wiley Periodicals, Inc.

Solving arithmetic problems is a cognitive task that heavily relies on language processing. One might thus wonder whether this language-reliance leads to qualitative differences (e.g., greater difficulties, error types, etc.) in arithmetic for bilingual individuals who frequently have to solve arithmetic problems in more than one language. The present study investigated how proficiency in two languages interacts with arithmetic problem solving throughout language acquisition in adolescents and young adults. Additionally, we examined whether the number word structure that is specific to a given language plays a role in number processing over and above bilingual proficiency. We addressed these issues in a German–French educational bilingual setting, where there is a progressive transition from German to French as teaching language. Importantly, German and French number naming structures differ clearly, as two-digit number names follow a unit-ten order in German, but a ten-unit order in French. We implemented a transversal developmental design in which bilingual pupils from grades 7, 8, 10, 11, and young adults were asked to solve simple and complex additions in both languages. The results confirmed that language proficiency is crucial especially for complex addition computation. Simple additions in contrast can be retrieved equally well in both languages after extended language practice. Additional analyses revealed that over and above language proficiency, language-specific number word structures (e.g., unit-ten vs. ten-unit) also induced significant modulations of bilinguals' arithmetic performances. Taken together, these findings support the view of a strong relation between language and arithmetic in bilinguals.

The current study provides a generalizable account of the anatomo-functional associations as well as the connectivity of representational codes underlying numerical processing as suggested by the triple code model (TCM) of numerical cognition. By evaluating the neural networks subserving numerical cognition in two specific and substantially different numerical tasks with regard to both grey matter localizations as well as white matter tracts we (1) considered the possibility of additional memory-related cortex areas crucial for arithmetic fact retrieval (e.g., the hippocampus); (2) specified the functional involvement of prefrontal areas in number magnitude processing, and, finally; (3) identified the connections between these anatomo-functional instantiations of the representations involved in number magnitude processing and arithmetic fact retrieval employing probabilistic fiber tracking. The resulting amendments to the TCM are summarized in a schematic update, and ideas concerning the possible functional interplay between number magnitude processing and arithmetic fact retrieval are discussed.

We examined the effects of learning a second language (L2) on brain structure. Cortical thickness was measured in the MRI datasets of 22 monolinguals and 66 bilinguals. Some bilingual subjects had learned both languages simultaneously (0-3years) while some had learned their L2 after achieving proficiency in their first language during either early (4-7years) or late childhood (8-13years). Later acquisition of L2 was associated with significantly thicker cortex in the left inferior frontal gyrus (IFG) and thinner cortex in the right IFG. These effects were seen in the group comparisons of monolinguals, simultaneous bilinguals and early and late bilinguals. Within the bilingual group, significant correlations between age of acquisition of L2 and cortical thickness were seen in the same regions: cortical thickness correlated with age of acquisition positively in the left IFG and negatively in the right IFG. Interestingly, the monolinguals and simultaneous bilinguals did not differ in cortical thickness in any region. Our results show that learning a second language after gaining proficiency in the first language modifies brain structure in an age-dependent manner whereas simultaneous acquisition of two languages has no additional effect on brain development.

Numerical cognition is a case of multi-modular and distributed cerebral processing. So far neither the anatomo-functional connections between the cortex areas involved nor their integration into established frameworks such as the differentiation between dorsal and ventral processing streams have been specified. The current study addressed this issue combining a re-analysis of previously published fMRI data with probabilistic fiber tracking data from an independent sample. We aimed at differentiating neural correlates and connectivity for relatively easy and more difficult addition problems in healthy adults and their association with either rather verbally mediated fact retrieval or magnitude manipulations, respectively. The present data suggest that magnitude- and fact retrieval-related processing seem to be subserved by two largely separate networks, both of them comprising dorsal and ventral connections. Importantly, these networks not only differ in localization of activation but also in the connections between the cortical areas involved. However, it has to be noted that even though seemingly distinct anatomically, these networks operate as a functionally integrated circuit for mental calculation as revealed by a parametric analysis of brain activation.

Language and math are intertwined during children's learning of arithmetic concepts, but the importance of language in adult arithmetic processing is less clear. To determine whether early learning plays a critical role in the math-language connection in adults, we tested retrieval of simple multiplication in adult bilinguals who learned arithmetic in only one language. We measured electrophysiological and behavioral responses during correctness judgments for problems presented as digits or as number words in Spanish or English. Problems presented in the language in which participants learned arithmetic elicited larger, more graded, and qualitatively different brain responses than did problems presented in participants' other language, and these responses more closely resembled responses for digits, even when participants' other language was more dominant. These findings suggest that the memory networks for simple multiplication are established when arithmetic concepts are first learned and are independent of language dominance in adulthood.

The unusual preservation of calculation skills in a patient with severe global aphasia is described. The implications for the relationship between numerical and language abilities are discussed.

This study investigates the neuro-mechanisms underlying mathematical processing in native (L1) and nonnative (L2) languages.
Using functional magnetic resonance imaging (fMRI), Mandarin Chinese learners of English were imaged while performing calculations,
parity judgments and linguistic tasks in their L1 (Chinese) and L2 (English). Results show that compared to L1, (1) calculation
in L2 involves additional neural activation, especially in the left hemisphere, including the inferior frontal gyrus (Broca’s
area); (2) parity judgment engages similar regions for both languages, and (3) phonetic discrimination in L2 does not involve
the perisylvian language (Broca’s and Wernicke’s) areas. These findings indicate that, calculation in L2, but not parity,
can be processed through the L1 system, suggesting that the interaction between language and mathematics involves a specific
neurocircuitry when associated with L2.

Positron emission tomography was used to examine the cerebral networks underlying number comparison and multiplication in eight normal volunteers. Cerebral blood flow was measured within anatomical regions of interest defined in each subject using magnetic resonance imaging. Three conditions were used: rest with eyes closed, mental multiplication of pairs of arabic digits and larger-smaller comparison of the same pairs. Both multiplication and comparison activated the left and right lateral occipital cortices, the left precentral gyrus, and the supplementary motor area. Beyond these common activations, multiplication activated also the left and right inferior parietal gyri, the left fusiform and lingual gyri, and the right cuneus. Relative to comparison, multiplication also yielded superior activity in the left lenticular nucleus and in Brodmann's area 8, and induced a hemispheric asymmetry in the activation of the precentral and inferior frontal gyri. Conversely, relative to multiplication, comparison yielded superior activity in the right superior temporal gyrus, the left and right middle temporal gyri, the right superior frontal gyrus, and the right inferior frontal gyrus. These results underline the role of bilateral inferior parietal regions in number processing and suggest that multiplication and comparison may rest on partially distinct networks.

The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing. I then review three current models of simple arithmetic processing and the empirical reports that support or challenge their explanations. The third section of the review discusses the relationship between basic fact retrieval and a rule-based component or system, and considers current evidence and proposals on the overall architecture of the cognitive arithmetic system. The review concludes with a final set of speculations about the all-pervasive problem difficulty effect, still a central puzzle in the field.

Behavioral studies show that bilinguals are slower and less accurate when performing mental calculation in their nondominant
(second; L2) language than in their dominant (first; L1) language. However, little is known about the neural correlates associated
with the performance differences observed between bilinguals' 2 languages during arithmetic processing. To address the cortical
activation differences between languages, the current study examined task-related and performance-related brain activation
during mental addition when problems were presented auditorily in participants' L1 and L2. Eleven Chinese–English bilinguals
heard 2-digit addition problems that required exact or approximate calculations. Functional magnetic resonance imaging results
showed that auditorily presented multidigit addition in bilinguals activates bilateral inferior parietal and inferior frontal
regions in both L1 and L2. Language differences were observed in the form of greater activation for L2 exact addition in the
left inferior frontal area. A negative correlation between brain activation and behavioral performance during mental addition
in L2 was observed in the left inferior parietal area. Current results provide further evidence for the effects of language-specific
experience on arithmetic processing in bilinguals at the cortical level.

How do the two languages of bilingual individuals interact in everyday communication? Numerous behavioral- and event-related brain potential studies have suggested that information from the non-target language is spontaneously accessed when bilinguals read, listen, or speak in a given language. While this finding is consistent with predictions of current models of bilingual processing, most paradigms used so far have mixed the two languages by using language ambiguous stimuli (e.g., cognates or interlingual homographs) or explicitly engaging the two languages because of experimental task requirements (e.g., word translation or language selection). These paradigms will have yielded different language processing contexts, the effect of which has seldom been taken into consideration. We propose that future studies should test the effect of language context on cross-language interactions in a systematic way, by controlling and manipulating the extent to which the experiment implicitly or explicitly prompts activation of the two languages.

Recently it was suggested that the carry effect observed in addition involves both categorical and continuous processing characteristics.
In the present study, we aimed at identifying the specific neural correlates associated with processing either categorical or continuous aspects of the carry effect in an fMRI study on multi-digit addition.
In line with our expectations, we observed two distinct parts of the fronto-parietal network subserving numerical cognition to be associated with either one of these two characteristics. On the one hand, the categorical aspect of the carry effect was associated with left-hemispheric language areas and the basal ganglia probably reflecting increased demands on procedural and problem solving processes. Complementarily, the continuous aspect of the carry effect was associated with increased intraparietal activation indicating increasing demands on magnitude processing as well as place-value integration with increasing unit sum.
In summary, the findings suggest representations and processes underlying the carry effect in multi-digit addition to be more complex and interactive than assumed previously.

Did evolution endow the human brain with a predisposition to represent and acquire knowledge about numbers? Although the parietal lobe has been suggested as a potential substrate for a domain-specific representation of quantities, it is also engaged in verbal, spatial, and attentional functions that may contribute to calculation. To clarify the organisation of number-related processes in the parietal lobe, we examine the three-dimensional intersection of fMRI activations during various numerical tasks, and also review the corresponding neuropsychological evidence. On this basis, we propose a tentative tripartite organisation. The horizontal segment of the intraparietal sulcus (HIPS) appears as a plausible candidate for domain specificity: It is systematically activated whenever numbers are manipulated, independently of number notation, and with increasing activation as the task puts greater emphasis on quantity processing. Depending on task demands, we speculate that this core quantity system, analogous to an internal "number line," can be supplemented by two other circuits. A left angular gyrus area, in connection with other left-hemispheric perisylvian areas, supports the manipulation of numbers in verbal form. Finally, a bilateral posterior superior parietal system supports attentional orientation on the mental number line, just like on any other spatial dimension.

Two experiments were conducted to test cultural differences in the role of phonological and visual working memory in complex arithmetic. Canadian- and Chinese-educated students solved complex subtraction problems (e.g., 85 - 27; Experiment 1) and complex multiplication problems (e.g., 6 x 13; Experiment 2) under phonological and visual working memory loads. Problem complexity (i.e., borrow or carry operations) and presentation format (i.e., horizontal vs. vertical) were also manipulated. The results showed that both Chinese- and Canadian-educated participants relied on both phonological and visual working memory resources when solving complex subtraction and multiplication problems. Selective involvement of phonological and visual working memory as a function of operation (Lee & Kang, 2002) or presentation format (Trbovich & LeFevre, 2003) was found only for Chinese-educated participants and not for Canadian-educated participants, calling into question the generalizability of these findings across arithmetic operations and cultural groups.

There is growing interest regarding the role of the right inferior frontal gyrus (RIFG) during a particular form of executive control referred to as response inhibition. However, tasks used to examine neural activity at the point of response inhibition have rarely controlled for the potentially confounding effects of attentional demand. In particular, it is unclear whether the RIFG is specifically involved in inhibitory control, or is involved more generally in the detection of salient or task relevant cues. The current fMRI study sought to clarify the role of the RIFG in executive control by holding the stimulus conditions of one of the most popular response inhibition tasks-the Stop Signal Task-constant, whilst varying the response that was required on reception of the stop signal cue. Our results reveal that the RIFG is recruited when important cues are detected, regardless of whether that detection is followed by the inhibition of a motor response, the generation of a motor response, or no external response at all.

Neuroimaging studies have revealed a strong link between mental calculation and the angular gyrus (AG) which has been interpreted to reflect arithmetic fact retrieval. Moreover, a stronger AG activation in individuals with higher mathematical competence has been reported. The present fMRI study investigates the specificity of the AG for arithmetic fact learning and the interplay between training and mathematical competence on brain activation. Adults of lower and higher mathematical competence underwent a five-day training on sets of complex multiplication and figural-spatial problems. In the following fMRI test session, trained and untrained problems were presented. Similar training effects were observed in both problem types, consisting of AG activation increases bilaterally and wide-spread activation decreases in frontal and parietal regions. This finding indicates that the AG is not specifically involved in the learning of arithmetic facts. Competence-related differences in the AG only emerged in untrained but not in trained multiplication problems. The relation between AG activation and mathematical competence in arithmetic problem solving therefore seems to be due to differences in arithmetic fact retrieval which can be attenuated through training.

While there is consistent evidence from neuropsychological and brain imaging studies for an association between the left angular gyrus and mental arithmetic, its specific role in calculation has remained poorly understood. It has been speculated that the angular gyrus mediates the retrieval of arithmetic facts during problem solving, but this hypothesis has not been directly tested. In the present functional Magnetic Resonance Imaging study comprising 28 adults, we used trial-by-trial strategy self-reports to identify brain regions underpinning different strategies in arithmetic problem solving. Analyses revealed stronger activation of the left angular gyrus while solving arithmetic problems for which participants reported fact retrieval whereas the application of procedural strategies was accompanied by widespread activation in a fronto-parietal network. These data directly link the left angular gyrus with arithmetic fact retrieval and show that strategy self-reports can be used to predict differential patterns of brain activation.

Human infants can discriminate between different small numbers of items, and can determine numerical equivalence across perceptual modalities. This may indicate the possession of true numerical concepts. Alternatively, purely perceptual discriminations may underlie these abilities. This debate addresses the nature of subitization, the ability to quantify small numbers of items without conscious counting. Subitization may involve the holistic recognition of canonical perceptual patterns that do not reveal ordinal relationships between the numbers, or may instead be an iterative or 'counting' process that specifies these numerical relationships. Here I show that 5-month-old infants can calculate the results of simple arithmetical operations on small numbers of items. This indicates that infants possess true numerical concepts, and suggests that humans are innately endowed with arithmetical abilities. It also suggests that subitization is a process that encodes ordinal information, not a pattern-recognition process yielding non-numerical percepts.

Mental calculation is an important everyday skill involving access to well-learned procedures, problem solving, and working memory. Although there is an active literature on acquiring concepts and procedures for mental arithmetic, relatively little is known about the role of working memory in this task. This paper reports two experiments in which dual-task methodology is used to study the role of components of working memory in mental addition. In Experiment 1, mental addition of auditorily presented two-digit numbers was significantly disrupted by concurrent random letter generation and, to a lesser extent, by concurrent articulatory suppression, but was unimpaired by concurrent hand movement or by presentation of irrelevant pictures. Although the number of errors increased with two of the dual tasks, the incorrect responses tended to be quite close to the correct answer. In Experiment 2, the numbers for addition were presented visually. Here again, random generation produced the largest disruption of mental arithmetic performance, while a smaller amount of disruption was observed for articulatory suppression, hand movement, and unattended auditorily presented two-digit numbers. The overall levels of performance were better and the absolute size of the disruptive effects shown with visual presentation was very small compared with those found for auditory presentation. This pattern of results is consistent with a role for a central executive component of working memory in performing the calculations required for mental addition and in producing approximately correct answers. Visuospatial resources in working memory may also be involved in approximations. The data support the view that the subvocal rehearsal component of working memory provides a means of maintaining accuracy in mental arithmetic, and this matches a similar conclusion derived from previous work on counting. The general implications for the role of working memory in arithmetic problem solving will be discussed.

Two experiments examined the effect of the presentation format of numbers--digits versus word format in the first and in the second languages of bilinguals--on mental arithmetic. Speed of number-fact retrieval and the presence of interference produced by numbers that were either numerically close to or associatively related to the correct answers of stored arithmetic problems (e.g., 2+5 and 7x8) were compared across formats. The verification of true problems was increasingly slower and less accurate from the digit condition to the second-language condition. Interference was produced by both types of incorrect answers in the digit and first-language conditions, whereas in the second-language condition, it was constrained to answers that were numerically close to correct answers. Together, the results suggest that the retrieval of arithmetic facts and the automatic spreading of activation within the network of numerical facts are not only language-sensitive, but format-sensitive in general.

The relationship between the semantic processing of words and of pictures is a matter of debate among cognitive scientists. We studied the functional anatomy of such processing by using positron-emission tomography (PET). We contrasted activity during two semantic tasks (probing knowledge of associations between concepts, and knowledge of the visual attributes of these concepts) and a baseline task (discrimination of physical stimulus size), performed either with words or with pictures. Modality-specific activations unrelated to semantic processing occurred in the left inferior parietal lobule for words, and the right middle occipital gyrus for pictures. A semantic network common to both words and pictures extended from the left superior occipital gyrus through the middle and inferior temporal cortex to the inferior frontal gyrus. A picture-specific activation related to semantic tasks occurred in the left posterior inferior temporal sulcus, and word-specific activations related to semantic tasks were localized to the left superior temporal sulcus, left anterior middle temporal gyrus, and left inferior frontal sulcus. Thus semantic tasks activate a distributed semantic processing system shared by both words and pictures, with a few specific areas differentially active for either words or pictures.

Differences between languages in terms of number naming systems may lead to performance differences in number processing. The current study focused on differences concerning the order of decades and units in two-digit number words (i.e., unit-decade order in German but decade-unit order in French) and how they affect number magnitude judgments. Participants performed basic numerical tasks, namely two-digit number magnitude judgments, and we used the compatibility effect (Nuerk et al. in Cognition 82(1):B25-B33, 2001) as a hallmark of language influence on numbers. In the first part we aimed to understand the influence of language on compatibility effects in adults coming from German or French monolingual and German-French bilingual groups (Experiment 1). The second part examined how this language influence develops at different stages of language acquisition in individuals with increasing bilingual proficiency (Experiment 2). Language systematically influenced magnitude judgments such that: (a) The spoken language(s) modulated magnitude judgments presented as Arabic digits, and (b) bilinguals' progressive language mastery impacted magnitude judgments presented as number words. Taken together, the current results suggest that the order of decades and units in verbal numbers may qualitatively influence magnitude judgments in bilinguals and monolinguals, providing new insights into how number processing can be influenced by language(s).

In our TICS Review in 2004, we proposed that a sector of the right inferior frontal cortex (rIFC) in humans is critical for inhibiting response tendencies. Here we survey new evidence, discuss ongoing controversies, and provide an updated theory. We propose that the rIFC (along with one or more fronto-basal-ganglia networks) is best characterized as a brake. This brake can be turned on in different modes (totally, to outright suppress a response; or partially, to pause), and in different contexts (externally, by stop or salient signals; or internally, by goals). We affirm inhibition as a central component of executive control that relies upon the rIFC and associated networks, and explain why rIFC disruption could generally underpin response control disorders.

Reading/writing direction or number word formation influence performance even in basic numerical tasks such as magnitude comparison. However, so far the interaction of these language properties has not been evaluated systematically. In this study we tested English, German, Hebrew, and Arab participants realizing a natural 2×2 design of reading/writing direction (left-to-right vs. right-to-left) and number word formation (non-inverted vs. inverted, i.e., forty-seven vs. seven-and-forty). Symbolic number magnitude comparison was specifically influenced by the interaction of reading/writing direction and number word formation: participants from cultures where reading direction and the order of tens and units in number words are incongruent (i.e., German and Hebrew) exhibited more pronounced unit interference in place-value integration. A within-group comparison indicated that this effect was not due to differences in education. Thus, basic cultural differences in numerical cognition were driven by natural language variables and their specific combination.
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The term working memory refers to a brain system that provides temporary storage and manipulation of the information necessary for such complex cognitive tasks as language comprehension, learning, and reasoning. This definition has evolved from the concept of a unitary short-term memory system. Working memory has been found to require the simultaneous storage and processing of information. It can be divided into the following three subcomponents: (i) the central executive, which is assumed to be an attentional-controlling system, is important in skills such as chess playing and is particularly susceptible to the effects of Alzheimer's disease; and two slave systems, namely (ii) the visuospatial sketch pad, which manipulates visual images and (iii) the phonological loop, which stores and rehearses speech-based information and is necessary for the acquisition of both native and second-language vocabulary.

Approximate processing of numerosities is a universal and preverbal skill, while exact number processing above 4 involves the use of culturally acquired number words and symbols. The authors first review core concepts of numerical cognition, including number representation in the brain and the influential view that numbers are associated with space along a “mental number line.” Then, they discuss how cultural influences, such as reading direction, finger counting, and the transparency of the number word system, can influence the representation and processing of numbers. Spatial mapping of numbers emerges as a universal cognitive strategy. The authors trace the impact of cultural factors on the development of number skills and conclude that a cross-cultural perspective can reveal important constraints on numerical cognition.

Two experiments compared rates of solving simple and complex addition and multiplication problems in groups of speakers of French or English in Experiment 1 (n = 35) and Spanish or English in Experiment 2 (n = 84). Subjects were divided into groups of English unilinguals, weak bilinguals, and strong bilinguals according to their performance on a naming task. In both experiments, simple problems consisted of two single-digit numbers. At least three single-digit numbers were used for complex problems in Experiment 1 and double-digit numbers in Experiment 2. Mean solution times, particularly for complex problems, were lowest for the monolingual group, followed in turn by the weak bilingual and strong bilingual groups, but these differences were not statistically reliable in either experiment. In Experiment 2, however, componential analyses of solution times indicated that strong bilingual subjects were slower at executing the carry operation when solving complex problems, relative to the two remaining groups. Results were interpreted in terms of the relationship between bilingualism and the representation and processing of numerical information.

Neuroimaging studies have revealed a strong link between mental calculation and the angu- lar gyrus (AG) which has been interpreted to reflect arithmetic fact retrieval. Moreover, a stronger AG activation in individuals with higher mathematical competence has been reported. The present fMRI study investigates the specificity of the AG for arithmetic fact learning and the interplay between train- ing and mathematical competence on brain activation. Adults of lower and higher mathematical com- petence underwent a five-day training on sets of complex multiplication and figural-spatial problems. In the following fMRI test session, trained and untrained problems were presented. Similar training effects were observed in both problem types, consisting of AG activation increases bilaterally and wide-spread activation decreases in frontal and parietal regions. This finding indicates that the AG is not specifically involved in the learning of arithmetic facts. Competence-related differences in the AG only emerged in untrained but not in trained multiplication problems. The relation between AG activa- tion and mathematical competence in arithmetic problem solving therefore seems to be due to differen- ces in arithmetic fact retrieval which can be attenuated through training. Hum Brain Mapp 30:2936- 2952, 2009. V V C 2009 Wiley-Liss, Inc.

The aim of this study was to investigate numerical
difficulties in 50 patients with left hemispheric lesions.
Aphasic patients were grouped according to their type of
aphasia diagnosed by the Aachener Aphasia Test. The overall
error rate in various transcoding and calculation tasks
was clearly correlated with the severity of the language
deficit, global aphasics being the most impaired patients.
Broca's and Wernicke's aphasics scored similarly
at the quantitative level, and amnesic aphasics were less
impaired. Interestingly, qualitative analysis of the errors
indicated that each group presented with specific difficulties,
partially reflecting the nature of the language problems.
In simple calculation, multiplication was found to be the
most impaired operation, in particular in Broca's
aphasics. This result supports the hypothesis that the
retrieval of multiplication facts is preferentially mediated
by verbal processing. Calculation procedures were mainly
impaired in Wernicke's and global aphasics. (JINS,
1999, 5, 213–221.)

The typical functional magnetic resonance (fMRI) study presents a formidable problem of multiple statistical comparisons (i.e, > 10,000 in a 128 x 128 image). To protect against false positives, investigators have typically relied on decreasing the per pixel false positive probability. This approach incurs an inevitable loss of power to detect statistically significant activity. An alternative approach, which relies on the assumption that areas of true neural activity will tend to stimulate signal changes over contiguous pixels, is presented. If one knows the probability distribution of such cluster sizes as a function of per pixel false positive probability, one can use cluster-size thresholds independently to reject false positives. Both Monte Carlo simulations and fMRI studies of human subjects have been used to verify that this approach can improve statistical power by as much as fivefold over techniques that rely solely on adjusting per pixel false positive probabilities.

We report a case study of a patient (IH) with a progressive impairment of semantic memory affecting all categories of knowledge apart from numbers. Pictorial material was better understood than words, but was still severely impaired. The selective preservation of nearly all aspects of numerical knowledge suggested that this domain might have different neuropsychological status from other aspects of semantic memory.

A series of experiments explored the role of information storage in working memory in performing mental arithmetic. Experiment 1 assessed the strategies people report for solving auditorily presented multidigit problems such as 325 + 46. As expected, all subjects reported breaking down the problems into a series of elementary stages, though there were considerable individual differences with regard to the order of their execution. Strategies of this type necessitate both the temporary storage of information and the mobilization of long-term knowledge. Experiments 2 and 3 examined the effects of delaying the output of individual partial results on calculation accuracy and showed that interim information is forgotten if it is not utilized immediately. Experiment 4 showed that forgetting the initial information is also a source of error and suggested that forgetting increases as a function of the number of calculation stages intervening between initial presentation and subsequent utilization of information. Two simple quantitative models were derived from a general task analysis, one of which assumed a decay process in working storage and the other no decay. The decay model gave a reasonable fit to data from Experiments 2–4, and in doing so it coped appreciably well with the effects of a large variety of task variables (e.g., carrying, the provision of written notes, calculation strategy, output order). The decay model is a tractable analysis of a complex task, and it is suggested that similar analyses may prove fruitful for other problem-solving activities which involve the use of working memory.

Recent imaging studies could show that fact acquisition in arithmetic is associated with decreasing activation in several frontal and parietal areas, and relatively increasing activation within the angular gyrus, indicating a switch from direct calculation to retrieval of a learned fact from memory. So far, however, little is known about the transfer of learned facts between arithmetic operations. The aim of the present fMRI study was to investigate whether and how newly acquired arithmetic knowledge might transfer from trained multiplication problems to related division problems. On the day before scanning, ten complex multiplication problems were trained. Within the scanner, trained multiplication problems were compared with untrained multiplication problems, and division problems related to multiplication (transfer condition) were compared with unrelated division problems (no-transfer condition). Replicating earlier results, untrained multiplication problems activated several frontal and parietal brain areas more strongly than trained multiplication problems, while trained multiplication problems showed relatively stronger activation in the left angular gyrus than untrained multiplication problems. Concerning division, an ROI analysis indicated that activation in the left angular gyrus was relatively stronger for the transfer condition than for the no-transfer condition. We also observed distinct inter-individual differences with regard to transfer that modulated activation within the left angular gyrus. Activation within the left angular gyrus was generally higher for participants who showed a transfer effect for division problems. In conclusion, the present study yielded some evidence that successful transfer of knowledge between arithmetic operations is accompanied by modifications of brain activation patterns. The left angular gyrus seems not only to be involved in the retrieval of stored arithmetic facts, but also in the transfer between arithmetic operations.

Precuneus responds to a wide range of cognitive processes. Here, we examined how the patterns of resting state connectivity may define functional subregions in the precuneus. Using a K-means algorithm to cluster the whole-brain "correlograms" of the precuneus in 225 adult individuals, we corroborated the dorsal-anterior, dorsal-posterior, and ventral subregions, each involved in spatially guided behaviors, mental imagery, and episodic memory as well as self-related processing, with the ventral precuneus being part of the default mode network, as described extensively in earlier work. Furthermore, we showed that the lateral/medial volumes of dorsal anterior and dorsal posterior precuneus are each connected with areas of motor execution/attention and motor/visual imagery, respectively. Compared to the ventral precuneus, the dorsal precuneus showed greater connectivity with occipital and posterior parietal cortices, but less connectivity with the medial superior frontal and orbitofrontal gyri, anterior cingulate cortex as well as the parahippocampus. Compared to dorsal-posterior and ventral precuneus, the dorsal-anterior precuneus showed greater connectivity with the somatomotor cortex, as well as the insula, supramarginal, Heschl's, and superior temporal gyri, but less connectivity with the angular gyrus. Compared to ventral and dorsal-anterior precuneus, dorsal-posterior precuneus showed greater connectivity with the middle frontal gyrus. Notably, the precuneus as a whole has negative connectivity with the amygdala and the lateral and inferior orbital frontal gyri. Finally, men and women differed in the connectivity of precuneus. Men and women each showed greater connectivity with the dorsal precuneus in the cuneus and medial thalamus, respectively. Women also showed greater connectivity with ventral precuneus in the hippocampus/parahippocampus, middle/anterior cingulate gyrus, and middle occipital gyrus, compared to men. Taken together, these new findings may provide a useful platform upon which to further investigate sex-specific functional neuroanatomy of the precuneus and to elucidate the pathology of many neurological illnesses.

English-Spanish bilinguals solved simple arithmetic problems and were required to respond In their preferred (P) language. the language In which they originally learned arithmetic, or In their nonpreferred (NP) language. Each arithmetic problem required one. two, or three addition operations. Reaction time was a linear function of number of operations. The intercept for the P language was lower than that for the NP language. but there were no differences In slope. The intercept difference was interpreted In terms of translation time. either as translation of the sum from the P to the NP language or as translation from an abstract representation to the NP as opposed to the P language.

Most of us use numbers daily for counting, estimating quantities or formal mathematics, yet despite their importance our understanding of the brain correlates of these processes is still evolving. A neurofunctional model of mental arithmetic, proposed more than a decade ago, stimulated a substantial body of research in this area. Using quantitative meta-analyses of fMRI studies we identified brain regions concordant among studies that used number and calculation tasks. These tasks elicited activity in a set of common regions such as the inferior parietal lobule; however, the regions in which they differed were most notable, such as distinct areas of prefrontal cortices for specific arithmetic operations. Given the current knowledge, we propose an updated topographical brain atlas of mental arithmetic with improved interpretative power.

Removal of the anterior temporal lobe (ATL) is an effective surgical treatment for intractable temporal lobe epilepsy but carries a risk of language and verbal memory deficits. Preoperative localization of functional zones in the ATL might help reduce these risks, yet fMRI protocols in current widespread use produce very little activation in this region. Based on recent evidence suggesting a role for the ATL in semantic integration, we designed an fMRI protocol comparing comprehension of brief narratives (Story task) with a semantically shallow control task involving serial arithmetic (Math task). The Story > Math contrast elicited strong activation throughout the ATL, lateral temporal lobe, and medial temporal lobe bilaterally in an initial cohort of 18 healthy participants. The task protocol was then implemented at 6 other imaging centers using identical methods. Data from a second cohort of participants scanned at these centers closely replicated the results from the initial cohort. The Story-Math protocol provides a reliable method for activation of surgical regions of interest in the ATL. The bilateral activation supports previous claims that conceptual processing involves both temporal lobes. Used in combination with language lateralization measures, reliable ATL activation maps may be useful for predicting cognitive outcome in ATL surgery, though the validity of this approach needs to be established in a prospective surgical series.

It is widely accepted that the human brain is remarkably adaptive not only in child development, but also during adulthood. Aim of this work is to offer an overview and a systematic analysis of neuroimaging studies on the acquisition of arithmetic expertise. In normally developing children and adults, the gain of arithmetic competence is reflected by a shift of activation from frontal brain areas to parietal areas relevant for arithmetic processing. A shift of activation is also observed within the parietal lobe from the intraparietal sulci to the left angular gyrus. Increases in angular gyrus activation with gaining of expertise have also been documented in other cognitive domains. It appears that the left angular gyrus activation is modulated by inter-individual differences in arithmetic performance. The comparison of normal individuals with exceptionally performing individuals (e.g., calculating prodigies) suggests that the experts' arithmetic proficiency relies on a more extended activation network than the network found in non-experts. In expert individuals with long-lasting, extensive mathematical training, specific structural brain modifications are also evident.

Semantic memory refers to knowledge about people, objects, actions, relations, self, and culture acquired through experience. The neural systems that store and retrieve this information have been studied for many years, but a consensus regarding their identity has not been reached. Using strict inclusion criteria, we analyzed 120 functional neuroimaging studies focusing on semantic processing. Reliable areas of activation in these studies were identified using the activation likelihood estimate (ALE) technique. These activations formed a distinct, left-lateralized network comprised of 7 regions: posterior inferior parietal lobe, middle temporal gyrus, fusiform and parahippocampal gyri, dorsomedial prefrontal cortex, inferior frontal gyrus, ventromedial prefrontal cortex, and posterior cingulate gyrus. Secondary analyses showed specific subregions of this network associated with knowledge of actions, manipulable artifacts, abstract concepts, and concrete concepts. The cortical regions involved in semantic processing can be grouped into 3 broad categories: posterior multimodal and heteromodal association cortex, heteromodal prefrontal cortex, and medial limbic regions. The expansion of these regions in the human relative to the nonhuman primate brain may explain uniquely human capacities to use language productively, plan, solve problems, and create cultural and technological artifacts, all of which depend on the fluid and efficient retrieval and manipulation of semantic knowledge.

Language and arithmetic are both lateralized to the left hemisphere in the majority of right-handed adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall "dominance" of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific cerebral subregions? Or is it merely coincidental? To shed light on this issue, we performed a "colateralization analysis" over 209 healthy subjects: We investigated whether normal variations in the degree of left hemispheric asymmetry in areas involved in sentence listening and reading are mirrored in the asymmetry of areas involved in mental arithmetic. Within the language network, a region-of-interest analysis disclosed partially dissociated patterns of lateralization, inconsistent with an overall "dominance" model. Only two of these areas presented a lateralization during sentence listening and reading which correlated strongly with the lateralization of two regions active during calculation. Specifically, the profile of asymmetry in the posterior superior temporal sulcus during sentence processing covaried with the asymmetry of calculation-induced activation in the intraparietal sulcus, and a similar colateralization linked the middle frontal gyrus with the superior posterior parietal lobule. Given recent neuroimaging results suggesting a late emergence of hemispheric asymmetries for symbolic arithmetic during childhood, we speculate that these colateralizations might constitute developmental traces of how the acquisition of linguistic symbols affects the cerebral organization of the arithmetic network.

This article discusses cognitive neuropsychological research on acquired dyscalculia (i.e., impaired numerical processing resulting from brain damage), surveying issues of current interest, and illustrating the ways in which analyses of acquired deficits can contribute to an understanding of normal processing. I first review the logic whereby inferences concerning normal cognition are drawn from patterns of impaired performance. I then consider research exploring the general functional architecture of the cognitive numerical processing mechanisms, and finally turn to studies aimed at probing the internal structure and functioning of individual processing components.

This paper provides a tutorial introduction to numerical cognition, with a review of essential findings and current points of debate. A tacit hypothesis in cognitive arithmetic is that numerical abilities derive from human linguistic competence. One aim of this special issue is to confront this hypothesis with current knowledge of number representations in animals, infants, normal and gifted adults, and brain-lesioned patients. First, the historical evolution of number notations is presented, together with the mental processes for calculating and transcoding from one notation to another. While these domains are well described by formal symbol-processing models, this paper argues that such is not the case for two other domains of numerical competence: quantification and approximation. The evidence for counting, subitizing and numerosity estimation in infants, children, adults and animals is critically examined. Data are also presented which suggest a specialization for processing approximate numerical quantities in animals and humans. A synthesis of these findings is proposed in the form of a triple-code model, which assumes that numbers are mentally manipulated in an arabic, verbal or analogical magnitude code depending on the requested mental operation. Only the analogical magnitude representation seems available to animals and preverbal infants.

This study examines the abstractness of children's mental representation of counting, and their understanding that the last number word used in a count tells how many items there are (the cardinal word principle). In the first experiment, twenty-four 2- and 3-year-olds counted objects, actions, and sounds. Children counted objects best, but most showed some ability to generalize their counting to actions and sounds, suggesting that at a very young age, children begin to develop an abstract, generalizable mental representation of the counting routine. However, when asked "how many" following counting, only older children (mean age 3.6) gave the last number word used in the count a majority of the time, suggesting that the younger children did not understand the cardinal word principle. In the second experiment (the "give-a-number" task), the same children were asked to give a puppet one, two, three, five, and six items from a pile. The older children counted the items, showing a clear understanding of the cardinal word principle. The younger children succeeded only at giving one and sometimes two items, and never used counting to solve the task. A comparison of individual children's performance across the "how-many" and "give-a-number" tasks shows strong within-child consistency, indicating that children learn the cardinal word principle at roughly 3 1/2 years of age. In the third experiment, 18 2- and 3-year-olds were asked several times for one, two, three, five, and six items, to determine the largest numerosity at which each child could succeed consistently. Results indicate that children learn the meanings of smaller number words before larger ones within their counting range, up to the number three or four. They then learn the cardinal word principle at roughly 3 1/2 years of age, and perform a general induction over this knowledge to acquire the meanings of all the number words within their counting range.

We describe two acalculic patients, one with a left subcortical lesion and the other with a right inferior parietal lesion and Gerstmann's syndrome. Both suffered from "pure anarithmetia": they could read arabic numerals and write them to dictation, but experienced a pronounced calculation deficit. On closer analysis, however, distinct deficits were found. The subcortical case suffered from a selective deficit of rote verbal knowledge, including but not limited to arithmetic tables, while her semantic knowledge of numerical quantities was intact. Conversely the inferior parietal case suffered from a category-specific impairment of quantitative numerical knowledge, particularly salient in subtraction and number bissection tasks, with preserved knowledge of rote arithmetic facts. This double dissociation suggests that numerical knowledge is processed in different formats within distinct cerebral pathways. We suggest that a left subcortical network contributes to the storage and retrieval of rote verbal arithmetic facts, while a bilateral inferior parietal network is dedicated to the mental manipulation of numerical quantities.