Comparing Numerical Comparison Tasks: A Meta-Analysis of the Variability of the Weber Fraction Relative to the Generation Algorithm

in Frontiers in Psychology (2018)

Since more than 15 years, researchers have been expressing their interest in evaluating the Approximate Number System (ANS) and its potential influence on cognitive skills involving number processing ... [more ▼]

Since more than 15 years, researchers have been expressing their interest in evaluating the Approximate Number System (ANS) and its potential influence on cognitive skills involving number processing, such as arithmetic. Although many studies reported significant and predictive relations between ANS and arithmetic abilities, there has recently been an increasing amount of published data that failed to replicate such relationship. Inconsistencies lead many researchers to question the validity of the assessment of the ANS itself. In the current meta-analysis of over 68 experimental studies published between 2004 and 2017, we show that the mean value of the Weber fraction (w), the minimal amount of change in magnitude to detect a difference, is very heterogeneous across the literature. Within young adults, w might range from <10 to more than 60, which is critical for its validity for research and diagnostic purposes. We illustrate here the concern that different methods controlling for non-numerical dimensions lead to substantially variable performance. Nevertheless, studies that referred to the exact same method (e.g., Panamath) showed high consistency among them, which is reassuring. We are thus encouraging researchers only to compare what is comparable and to avoid considering the Weber fraction as an abstract parameter independent from the context. Eventually, we observed that all reported correlation coefficients between the value of w and general accuracy were very high. Such result calls into question the relevance of computing and reporting at all the Weber fraction. We are thus in disfavor of the systematic use of the Weber fraction, to discourage any temptation to compare given data to some values of w reported from different tasks and generation algorithms. [less ▲]

Functional connectivity and structural analyses in the bilingual brain: implications for arithmetic.

Poster (2015, June)

Do bilinguals use the same brain networks than monolinguals when they solve arithmetic problems? We investigated this question by using resting-state functional connectivity and cortical thickness ... [more ▼]

Do bilinguals use the same brain networks than monolinguals when they solve arithmetic problems? We investigated this question by using resting-state functional connectivity and cortical thickness measurements. Recent studies highlighted differences of functional connectivity (e.g. Grady et al., 2015) and of brain structure (e.g. Klein et al., 2014) between bilinguals and monolinguals. However, no study so far has linked these differences to arithmetic problem solving, a cognitive skill that may at least partially rely on language processing. Our study population was composed of carefully selected German-French bilinguals (N = 20) who acquired each language at the same age, leading to high proficiency levels in both languages. These bilinguals all attended university in their second language at the time of the experiment, namely French. Therefore we selected a control group of French-speaking monolinguals (N = 12). Structural and functional images of brain activity were collected using a 3T MRI scanner. Functional scans of resting-state were acquired during a 6-minute session, with eyes closed. A 3D T1-weighted data set encompassing the whole brain was acquired to provide detailed anatomy (1 mm3), which was used both for the co-registration of functional data and for morphometric analyses. Prior to the scanning session, all participants took a behavioral test measuring their arithmetic skill. For the resting-state part of the study, we generated spheres based on ROIs reported in the literature as magnitude manipulation- and language-related areas during arithmetic problem solving (Klein et al. 2013), and addition-related areas reported in a recent meta-analysis (Arsalidou & Tayor, 2011). We used these spheres as seed regions for the analyses. We correlated resting activations between these regions and compared these correlations in bilinguals versus monolinguals. Results showed significantly higher correlations between the three seed regions in monolinguals than in bilinguals (all ts > 2.306; ps < .05), suggesting that regions used to solve arithmetic problems form a different network in bilinguals than in monolinguals. To control for general differences between both populations, we also created two spheres in areas not specifically related to neither arithmetic nor language regions. There were no significant differences between groups in terms of correlations of these regions with resting-state activations. These results suggest that the differences observed in arithmetic problem solving regions could not account for by general differences between groups. In the second part of the study, we aimed at verifying whether the differences in functional connectivity we observed between bilinguals and monolinguals coincide with structural brain differences. We measured and compared cortical thickness in both groups. Then we compared the correlations between cortical thickness and arithmetic skill in both groups (considering differences with corrected p < .001). Cortical thickness of areas commonly associated to language or number processing correlated differently with arithmetic skill as a function of the group: Higher cortical thickness of left pars triangularis, bilateral superior parietal gyri and precuneus positively correlated with arithmetic skill in monolinguals but negatively correlated with arithmetic skill in bilinguals. These results highlight that there are different relations between brain structure and arithmetic skills in bilinguals and monolinguals. In conclusion the current study provides new evidence for differences between bilinguals’ and monolinguals’ brain networks engaged in arithmetic problem solving, even without any arithmetic task during the data acquisition. These findings based on functional connectivity and brain structure analyses also reveal the general involvement of language in arithmetic problem solving in bilingual as well as non-bilingual individuals. [less ▲]

Do you speak numbers? The relation between language and numerical cognition through the prism of bilingualism and cross-linguistic investigations

Doctoral thesis (2015)

The overarching objective of the thesis was to investigate the link between numbers and language by examining numerical abilities in bilinguals and in cross-linguistic comparisons. I conducted my research ... [more ▼]

The overarching objective of the thesis was to investigate the link between numbers and language by examining numerical abilities in bilinguals and in cross-linguistic comparisons. I conducted my research mainly in Luxembourg where the educational context provides a highly standardized framework concerning age of acquisition and performance level achieved in the two school languages German and French. In Luxembourg, it is thus easily possible to directly benefit from very homogenous populations of highly proficient bilingual participants. Consequently this environment provides an exceptionally interesting framework to study numerical cognition and its relation to language. Firstly, two behavioral studies investigated numerical performances (i.e., magnitude judgments and arithmetic problem solving) in bilinguals at progressive stages of their bilingual language acquisition. More specifically, we used both within-subject and between-subject cross-linguistic comparison experimental designs on respectively bilingual and monolingual participants. Secondly, a short cross-linguistic comparison study assessed number transcoding skills in English- and French-speaking children in order to highlight the specific difficulties due to the use of French verbal numbers constructed on vigesimal structures. Thirdly, we adopted a more applied approach with outlooks towards direct educational outcomes for mathematical learning and teaching. We set up an experimental behavioral study that highlighted the importance of language context for efficient arithmetic problem solving in bilinguals’ second language. In a second study, we used a large-scale school assessment dataset to examine language effects on more complex mathematical problem solving. Finally, we used fMRI to identify the neural correlates underlying arithmetic problem solving in bilinguals’ languages and bring additional neuro-scientific insights into the field of language and numbers. [less ▲]

The relation between language and arithmetic in bilinguals: insights from different stages of language acquisition

in Frontiers in Psychology (2015), 6

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 ... [more ▼]

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. [less ▲]

The effect of languages on the production and recognition of numbers in German-French bilinguals

Poster (2014, April)

How do bilinguals produce and recognize two-digit number words? We investigated this question at different language proficiency levels in German-French bilinguals. German two-digit number words indeed ... [more ▼]

How do bilinguals produce and recognize two-digit number words? We investigated this question at different language proficiency levels in German-French bilinguals. German two-digit number words indeed follow the unit-decade order, whereas in French the order is decade-unit. Our study was conducted in Luxembourg where pupils learn both languages at primary school. Moreover mathematics are taught in German at primary school but in French at secondary school. Pupils from grades 5 (primary school), 8 (beginning of secondary school) and 11 (middle of secondary school) performed two numerical tasks: In the number recognition task, participants were presented a spoken number word that they had to recognize among four visually presented Arabic numbers. In the number production task, participants had to pronounce visually presented Arabic numbers. Both tasks were performed in German and in French and we compared language-related performance differences for the 3 levels of language proficiencies. Participants of all levels recognized and produced number-words more efficiently in their dominant language (i.e. German). However, this advantage for the dominant language was especially prominent at the lowest level of language proficiency when mathematics education was implemented in the dominant language (i.e. German). Furthermore, performance levels decreased with increasing number size, but over and above this general trend, participants of all proficiency levels showed specific difficulties with the complex structure of French number words over 60. Taken together, these results support the view that number and language processing are tightly associated, since language proficiency and language structure influence very simple and basic numerical tasks. [less ▲]

Language influences number processing: the case of bilingual Luxembourg

Scientific Conference (2014)

The influence of language on exact additions in bilinguals.

Scientific Conference (2013, May)

To which degree is language involved in arithmetic and dependent on language proficiency? We investigated this question in a German-French educational bilingual setting in Luxembourg, where there is a ... [more ▼]

To which degree is language involved in arithmetic and dependent on language proficiency? We investigated this question in a German-French educational bilingual setting in Luxembourg, where there is a progressive transition from German to French as a teaching language. Due to this shift, students become increasingly more proficient in the non-dominant language (French) throughout the school years. Interestingly, the decades and units of two-digit number names follow the unit-decade order in German but the decade-unit order in French. Students from grades 7, 8, 10, 11, and German-French adults (total N = 200) solved simple and complex additions presented in different conditions: (1) visual Arabic digits, (2) auditory presentation, and (3) as a dual task in which visually presented additions were preceded by visually presented semantic judgements to indirectly activate a language context. Participants performed each condition in a German and a French testing session. Participants were asked to respond orally in the testing language. Measures include correct responses and response times. The results suggest that language proficiency is crucial for the computation of complex additions, whereas simple additions can be retrieved equally well in both languages. Furthermore, additional error analyses showed more errors on the decade or on the unit digit depending on the language of the task. However, providing a language context seems to enhance performances only in the non-dominant language. Taken together, these results support the view of a strong language influence on arithmetic. [less ▲]

The influence of language on exact additions in bilingual pupils and adults.

Poster (2013, March)

To which degree is language involved in arithmetic? We investigated this question in a German-French bilingual setting. In Luxembourg, bilingualism is acquired through education: mathematics are taught in ... [more ▼]

To which degree is language involved in arithmetic? We investigated this question in a German-French bilingual setting. In Luxembourg, bilingualism is acquired through education: mathematics are taught in German in primary and in French in secondary school. Interestingly, the decades and units within two-digit number names follow the unit-decade order in German but the decade-unit order in French. We studied our research question in the multi-lingual educational context of Luxembourg by applying a developmental design. The present sample (total N = 200) included students from grades 7, 8, 10 and 11, as well as an adult bilingual group. This sample takes advantage of following the progressive transition from German to French as teaching languages. All participants performed simple and complex additions that they had to orally respond either in German or in French. Additions were presented in different conditions: (1) visual Arabic presentation, (2) auditory presentation (in German or in French), and (3) as a dual task in which visually presented additions were preceded by visually presented semantic judgements to indirectly activate a German or French language context. The results suggested that language proficiency seems to be crucial for the computation of more complex calculations, whereas simple additions can be retrieved equally well in both languages. Taken together, these results support the view of a strong language impact on calculations. Further results and implications will be discussed. [less ▲]

How does language affect numerical processing? The role of the teaching language on two-digit magnitude judgments in German-French bilingual 7- to-11 graders

Poster (2012, May)

The effect of number syntax on two-digit magnitude judgments in German-French bilinguals.

Poster (2012, February)

The study examined the effect of language and presentation mode on numerical processing skills in German-French bilinguals. This bilingual combination is particularly interesting because the order of two ... [more ▼]

The study examined the effect of language and presentation mode on numerical processing skills in German-French bilinguals. This bilingual combination is particularly interesting because the order of two digit number words is inversed in both languages: decade-unit in French but unit-decade in German. Further, previous studies used written number word presentations as verbal notation to activate language, which are, however, rarely used in everyday life. The present study therefore tackled the question whether two-digit magnitude judgments are affected by the presentation mode (visual Arabic vs. auditory words) and the language (German vs. French)? Data stem from adult participants (mean age: 25,3 years) who were proficient German-French bilinguals. The within-subject design involved two-digit number pair comparisons presented visually and auditory in German and in French. In line with previous studies, participants responded faster and more accurately on compatible than on incompatible trials in the visual Arabic presentation mode in both languages (compatibility effect): In compatible number pairs, the decades and units concord to the same magnitude decision (e.g. 23_57; decade: 2<5 and unit:3<7) whereas decade and units discord (47_82; decade: 4<8 but 7>2) for incompatible number pairs. In the auditory mode, the results showed a tendency for a regular compatibility effect in German and an inverse compatibility effect in French with participants responding faster on incompatible trials suggesting that bilinguals process numerical tasks in the language of presentation similar to monolinguals using the same language. Conclusively, the results imply differential numerical processing according to the presentation mode (visual Arabic vs. auditory words) and the language (German vs. French). [less ▲]