Solving arithmetic problems in first and second language: Does the language context matter?

in Learning and instruction (2016)

Learning mathematics in a second language is a challenge for many learners. The purpose of the study was to provide new insights into the role of the language context in mathematic learning and more ... [more ▼]

Learning mathematics in a second language is a challenge for many learners. The purpose of the study was to provide new insights into the role of the language context in mathematic learning and more particularly arithmetic problem solving. We investigated this question in a GermaneFrench bilingual educational setting in Luxembourg. Participants with increasing bilingual proficiency levels were invited to solve additions in both their first and second instruction languages: German and French. Arithmetic problems were presented in two different conditions: preceded by a semantic judgment or without additional language context. In the French session we observed that additions were systematically performed faster in the condition with an additional language context. In contrast no effect of the context was observed in the German session. In conclusion, providing a language context enhanced arithmetic performances in bilinguals' second instruction language. This finding entails implications for designing optimal mathematic learning environments in multilingual educational settings. [less ▲]

Math anxiety is predicted by the strength of number-space associations, over and beyond arithmetic ability and WM

Poster (2015, October)

Math skills are undeniably important in everyday life. Math anxiety can, however, threaten their optimal development. Given that a fifth of the population experiences high math anxiety, it is important to ... [more ▼]

Math skills are undeniably important in everyday life. Math anxiety can, however, threaten their optimal development. Given that a fifth of the population experiences high math anxiety, it is important to identify its origins in order to improve mathematical learning. Research on math anxiety typically focusses on the effects of math ability, WM, and spatial performance. Recent evidence, however, suggests that it also depends on basic numerical processes, with high math anxious individuals featuring less precise numerical representations, as indexed by stronger distance effects. Another marker for the nature of numerical representations is the SNARC effect, alluding to their spatial organization. Although number-space associations depend on WM, spatial performance and arithmetic ability - all related to math anxiety - their relationship with the latter has never been tested. We thus determined whether math anxiety is related to the strength of number-space associations. All participants (n=60, 28 female) completed the r-MARS, the parity judgment, an arithmetic, and visuospatial WM task. We replicated previous findings on the negative relationships between math anxiety and arithmetic ability (r=-0.3, p=0.02), and WM (r=-0.29, p=0.03). But most importantly, we found a significant negative correlation between the SNARC effect and math anxiety (slope=-11.42, r=-0.43, p<0.001), with high math anxious individuals featuring greater interference of the irrelevant magnitude-associated spatial code. Interestingly, number-space associations were the only significant predictor of math anxiety in a multiple regression analysis. Our findings thus provide further evidence for the association between numerical representations and math anxiety, over and beyond arithmetic ability and WM. [less ▲]

The link between number-space associations and visuospatial abilities depends on visualization profile

Poster (2015, September)

Background: Evidence for number-space associations comes from the spatial-numerical association of response-codes (SNARC) effect, consisting in faster RTs to small/large digits with the left/right hand ... [more ▼]

Background: Evidence for number-space associations comes from the spatial-numerical association of response-codes (SNARC) effect, consisting in faster RTs to small/large digits with the left/right hand respectively. However, the cognitive origin of the effect remains elusive. Previous studies suggested that it might depend on visuospatial processes, since individuals with better performances in 2D (but not 3D) mental rotation tasks displayed weaker number-space associations (Viarouge et al., 2014). Aims: Given the high inter-individual variability of number-space associations, we determined whether the SNARC effect always relies on visuospatial processes or whether its cognitive origin varies with visualization preferences. Method: We distinguished between object-visualizers (n=42, 23 female, age=22.93) and spatial-visualizers (n=42, 15 female, age=23.9) using the Object-Spatial Imagery Questionnaire (Blajenkova et al., 2006). All participants performed the parity judgment task, a 2D visuospatial test and a 3D mental rotation task. Results: In object-visualizers, weaker SNARC slopes were associated with better performances in the 2D (r=0.46, p=0.004), but not 3D (r=-0.04, p=0.79) task, thereby replicating previous observations. Conversely, in spatial-visualizers, the performances in both visuospatial tasks were unrelated to the SNARC effect (2D: r=0.02, p=0.89; 3D: r=0.2, p=0.22). Conclusions: These findings suggest that in object-visualizers, number-space associations and 2D performances underlie common visuospatial processes. Conversely, in spatial-visualizers, number-space associations seem to result from cognitive mechanisms other than those recruited during the aforementioned visuospatial tasks (e.g., verbal-spatial coding mechanisms). All in all, we were able to further unravel the mechanisms underlying number-space associations and could highlight visualization preferences as an additional explanation for the great inter-individual variability of the SNARC effect. [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 ▲]

Neural correlates of arithmetic problem solving in bilinguals: an fMRI study.

Poster (2015, May)

Inhibitory Control Influences the SNARC Effect in Tasks without Explicit Reference to Numerical Magnitude

Poster (2015, March)

Evidence for number-space associations comes from the spatial-numerical association of response-codes (SNARC) effect, consisting in faster reaction times to small/large digits with the left/right hand ... [more ▼]

Evidence for number-space associations comes from the spatial-numerical association of response-codes (SNARC) effect, consisting in faster reaction times to small/large digits with the left/right hand respectively. Although the SNARC effect has now been extensively replicated, it is characterized by high inter-individual variability (Wood et al., 2008). For instance, it has been shown to depend on inhibitory control as indexed by the color Stroop effect in the elderly, with individuals having weaker inhibitory control displaying stronger SNARC effects (Hoffmann et al., 2014). Apart from these well-documented inter-individual differences, number-space associations are also influenced by intra-individual factors. Georges et al. (2014) found that in a population of healthy young university students (n=85, 39 females, mean age=23.44 years), the SNARC effect was qualitatively different within single individuals depending on the number-processing task that they performed. While the strength of the SNARC effects were related in a parity and color judgment task (parity slope=-11.58; color slope=-6.79; r=0.36, p=0.001), as well as in the parity and a magnitude comparison task (magnitude slope=-6.98; r=0.36, p=0.001), no relation could be observed between number-space associations in the color and magnitude tasks (r=0.18, p=0.11). These findings indicate that two distinct factors seem to account for the variance related to number-space associations observed during the three tasks. In the present study, we built on these findings while investigating how inhibitory control influences variance in the SNARC effect observed during different numerical tasks. To this aim, we performed a principle component analysis followed by varimax rotation to combine the color and parity SNARC effects (i.e. number-space associations in tasks without explicit reference to numerical magnitude) and the parity and magnitude SNARC effects (i.e. number-space associations in tasks involving semantic number processing) into single factors (color-parity-SNARC and parity-magnitude-SNARC factors respectively). We then investigated how these two extracted SNARC factors were influenced by inter-individual characteristics such as inhibitory control. Inhibitory control was evaluated in a task that involved responding to the color (green or red) of a centrally presented arrow pointing either in the left or right direction by pressing on the left or right hand-side. To get a single inhibitory control measure for each individual, we calculated inverse efficiency scores on compatible and incompatible trials and computed performance differences between those two conditions. The scores of the extracted parity-color-SNARC factor significantly correlated with the inhibitory control measure (μ=109.98ms, SD=85.82ms; r=-0.26, p=0.02), while no relation was observed between inhibitory control and the parity-magnitude SNARC factor scores (r=-0.1, p=0.42). This suggests that individuals with better inhibitory control (i.e. smaller performance differences between compatible and incompatible trials) displayed weaker SNARC effects only in number-processing tasks that required the suppression of an irrelevant numerical (magnitude) code for successful task completion. Number-space associations are characterized by high inter- and intra-individual variability. We determined how the SNARC effect observed in tasks with and without explicit numerical magnitude processing related to inhibitory control. Individuals with better inhibitory control displayed weaker SNARC effects only in tasks requiring the suppression of an irrelevant numerical magnitude. [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 ▲]

Inhibition of return and attentional facilitation: Numbers can be counted in, letters tell a different story.

in Acta psychologica (2015), 163

Prior research has provided strong evidence for spatial-numerical associations. Single digits can for instance act as attentional cues, orienting visuo-spatial attention to the left or right hemifield ... [more ▼]

Prior research has provided strong evidence for spatial-numerical associations. Single digits can for instance act as attentional cues, orienting visuo-spatial attention to the left or right hemifield depending on the digit's magnitude, thus facilitating target detection in the cued hemifield (left/right hemifield after small/large digits, respectively). Studies using other types of behaviourally or biologically relevant central cues known to elicit automated symbolic attention orienting effects such as arrows or gaze have shown that the initial facilitation of cued target detection can turn into inhibition at longer stimulus onset asynchronies (SOAs). However, no studies so far investigated whether inhibition of return (IOR) is also observed using digits as uninformative central cues. To address this issue we designed an attentional cueing paradigm using SOAs ranging from 500ms to 1650ms. As expected, the results showed a facilitation effect at the relatively short 650ms SOA, replicating previous findings. At the long 1650ms SOA, however, participants were faster to detect targets in the uncued hemifield compared to the cued hemifield, showing an IOR effect. A control experiment with letters showed no such congruency effects at any SOA. These findings provide the first evidence that digits not only produce facilitation effects at shorter intervals, but also induce inhibitory effects at longer intervals, confirming that Arabic digits engage automated symbolic orienting of attention. [less ▲]

Horizontal tuning of face-specific processing from childhood to elderly adulthood.

Poster (2015)

Face recognition in adults recruits specialised mechanisms that are selectively driven by horizontal information. This range indeed conveys the most optimal and stable cues to identity. Whether the ... [more ▼]

Face recognition in adults recruits specialised mechanisms that are selectively driven by horizontal information. This range indeed conveys the most optimal and stable cues to identity. Whether the horizontal tuning of adult face recognition reflects horizontal bias already active at infancy and/or whether it also results from the extensive experience acquired with faces over the lifespan is elusive. Answering these questions is crucial to determine the information constraining the developmental specialisation of core visual functions such as face perception. Participants aged between 6 and 74 years matched unfamiliar faces that were filtered to retain information in narrow ranges centred on horizontal (H), vertical (V), or both orientation ranges (HV). H and V ranges respectively maximize and minimize the recruitment of face-specific mechanisms (Goffaux and Dakin, 2010). Stimuli were presented at upright and inverted planar orientations and the face inversion effect (FIE; i.e., better performance for upright than inverted faces) was taken as a marker of face-specific processing. In H and HV conditions, FIE size increased linearly from childhood to adulthood, manifesting the progressive specialization of face perception. FIE emerged earlier when processing HV than H faces (FIE onset: 6 and 12 years, respectively) indicating that until 12 years horizontal information is necessary but not sufficient to trigger face-specialised processing. Partial correlations further showed that FIE development in HV condition was not fully explained by FIE development in H condition. Besides a progressive maturation of horizontal processing, the specialization of the face processing system thus also depends on the improved integration of horizontal range with other orientations. In contrast, FIE size was small and stable when processing V information. These results show that the face processing system matures over the life span based on the refined encoding of horizontally-oriented (upright) face cues. Meeting abstract presented at VSS 2015. [less ▲]

Horizontal tuning for faces originates in high-level Fusiform Face Area.

in Neuropsychologia (2015), 81

Recent work indicates that the specialization of face visual perception relies on the privileged processing of horizontal angles of facial information. This suggests that stimulus properties assumed to be ... [more ▼]

Recent work indicates that the specialization of face visual perception relies on the privileged processing of horizontal angles of facial information. This suggests that stimulus properties assumed to be fully resolved in primary visual cortex (V1; e.g., orientation) in fact determine human vision until high-level stages of processing. To address this hypothesis, the present fMRI study explored the orientation sensitivity of V1 and high-level face-specialized ventral regions such as the Occipital Face Area (OFA) and Fusiform Face Area (FFA) to different angles of face information. Participants viewed face images filtered to retain information at horizontal, vertical or oblique angles. Filtered images were viewed upright, inverted and (phase-)scrambled. FFA responded most strongly to the horizontal range of upright face information; its activation pattern reliably separated horizontal from oblique ranges, but only when faces were upright. Moreover, activation patterns induced in the right FFA and the OFA by upright and inverted faces could only be separated based on horizontal information. This indicates that the specialized processing of upright face information in the OFA and FFA essentially relies on the encoding of horizontal facial cues. This pattern was not passively inherited from V1, which was found to respond less strongly to horizontal than other orientations likely due to adaptive whitening. Moreover, we found that orientation decoding accuracy in V1 was impaired for stimuli containing no meaningful shape. By showing that primary coding in V1 is influenced by high-order stimulus structure and that high-level processing is tuned to selective ranges of primary information, the present work suggests that primary and high-level levels of the visual system interact in order to modulate the processing of certain ranges of primary information depending on their relevance with respect to the stimulus and task at hand. [less ▲]