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Mental arithmetic in the bilingual brain: Language matters

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Abstract

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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... 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. ...
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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.
... 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]. ...
Article
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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 5 th , 8 th , 11 th graders and adults. In the Luxembourgish educational system, children acquire mathematics in German (LM1) until the 7 th 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. ...
Article
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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. ...
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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.
... Much English vocabulary has French roots whereas common words are often Germanic. PATHWAYS TO LEARNING MATHEMATICS 15 language as well as instructional experiences (Frenck-Mestre & Vaid, 1993;Salillas & Wicha, 2012;Van Rinsveld et al., 2017). ...
Article
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. ...
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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). ...
Article
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. ...
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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. ...
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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). ...
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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. Copyright © 2014 Elsevier B.V. All rights reserved.
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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.
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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.
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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.
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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.
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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.)
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.