Automatic Integration of Numerical Formats Examined with Frequency-tagged EEG

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in Scientific Reports (2021)

How humans integrate and abstract numerical information across different formats is one of the most debated questions in human cognition. We addressed the neuronal signatures of the numerical integration using an EEG technique tagged at the frequency of visual stimulation. In an oddball design, participants were stimulated with standard sequences of numbers (<5) depicted in single (digits, dots, number words) or mixed notation (dots – digits, number words – dots, digits – number words), presented at 10Hz. Periodically, a deviant stimulus (>5) was inserted at 1.25 Hz. We observed significant oddball amplitudes for all single notations, showing for the first time using this EEG technique, that the magnitude information is spontaneously and unintentionally abstracted, irrespectively of the numerical format. Significant amplitudes were also observed for digits – number words and number words – dots, but not for digits – dots, suggesting an automatic integration across some numerical formats. These results imply that direct and indirect neuro-cognitive links exist across the different numerical formats.

Number Line Tasks and Their Relation to Arithmetics in Second to Fourth Graders

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in Journal of Numerical Cognition (2021), 7(1), 20--41

The importance of visuospatial abilities for verbal number skills in preschool: Adding spatial language to the equation

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in Journal of Experimental Child Psychology (2021)

Not all elementary school teachers are scared of math

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in Journal of Numerical Cognition (2021)

A robust electrophysiological marker of spontaneous numerical discrimination

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in Scientific Reports (2020)

A minority pulls the sample mean: on the individual prevalence of robust group-level cognitive phenomena - the instance of the SNARC effect

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Presentation (2019, January)

Spatial Skills First: The Importance of Mental Rotation for Arithmetic Skill Acquisition

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in Journal of Numerical Cognition (2019)

Implicit and explicit number-space associations differentially relate to interference control in young adults with ADHD

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in Frontiers in Psychology (2018)

Developmental changes in the effect of active left and right head rotation on random number generation

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in Frontiers in Psychology (2018)

Spatial skills first: The importance of mental rotation for arithmetic skill acquisition

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Poster (2017, September)

Mathematical abilities in elementary school: Do they relate to number–space associations?

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in Journal of Experimental Child Psychology (2017)

Considering the importance of mathematics in Western societies, it is crucial to understand the cognitive processes involved in the acquisition of more complex mathematical skills. The current study, therefore, investigated how the quality of number–space mappings on the mental number line, as indexed by the parity SNARC (spatial–numerical association of response codes) effect, relates to mathematical performances in third- and fourth-grade elementary school children. Mathematical competencies were determined using the “Heidelberger Rechentest,” a standardized German math test assessing both arithmetical and visuospatial math components. Stronger parity SNARC effects significantly related to better arithmetical but not visuospatial math abilities, albeit only in the relatively younger children. These findings highlight the importance of spatial–numerical interactions for arithmetical (as opposed to visuospatial) math skills at the fairly early stages of mathematical development. Differential relations might be explained by the reliance on problem-solving strategies involving number–space mappings only for arithmetic tasks mainly in younger children.

How and Why Do Number-Space Associations Co-Vary in Implicit and Explicit Magnitude Processing Tasks?

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in Journal of Numerical Cognition (2017)

How Math Anxiety relates to Number-Space Associations.

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in Frontiers in Psychology (2016), 7(1401),

Given the considerable prevalence of math anxiety, it is important to identify the factors contributing to it in order to improve mathematical learning. Research on math anxiety typically focusses on the effects of more complex arithmetic skills. Recent evidence, however, suggests that deficits in basic numerical processing and spatial skills also constitute potential risk factors of math anxiety. Given these observations, we determined whether math anxiety also depends on the quality of spatial-numerical associations. Behavioral evidence for a tight link between numerical and spatial representations is given by the SNARC (spatial-numerical association of response codes) effect, characterized by faster left-/right-sided responses for small/large digits respectively in binary classification tasks. We compared the strength of the SNARC effect between high and low math anxious individuals using the classical parity judgment task in addition to evaluating their spatial skills, arithmetic performance, working memory and inhibitory control. Greater math anxiety was significantly associated with stronger spatio-numerical interactions. This finding adds to the recent evidence supporting a link between math anxiety and basic numerical abilities and strengthens the idea that certain characteristics of low-level number processing such as stronger number-space associations constitute a potential risk factor of math anxiety.

Age modulates the relation between number-space associations and arithmetical abilities in elementary school children

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Poster (2016, September)

Evidence for number-space associations comes from the SNARC effect, consisting in faster RTs to small/large digits with the left/right hand respectively. In adults, number-space associations relate to mathematical proficiency in that individuals with weaker arithmetic performances feature stronger SNARC effects (Hoffmann et al., 2014). However, in children far less is known about number-space associations and how they affect arithmetic performance. We therefore investigated the relationship between the classical parity SNARC effect and mathematical proficiency, assessed using the Heidelberger Rechentest, in elementary school children aged 8-11 years (n=55, mean=9.5). Overall, the parity SNARC regression slopes (-11.37, p<.001) negatively correlated with HRT arithmetical (r=-.28, p=.04; even when controlling for parity judgment RTs: r=-.37, p=.01), but not HRT visuo-spatial subscale scores (r=-.03, p=.82), indicating better arithmetic performances with stronger number-space associations. However, this relation was significantly moderated by age, since the interaction between the parity SNARC effect and age accounted for a significant proportion of the variance in HRT arithmetical scores (ΔR2=.07, b=0.26, t(51)=2.29, p=.03). A significant negative association was observed only in younger children (b=-0.35, t=-3.49, p=.001) aged below 9.5 years (n=29), while the SNARC effect did not relate to arithmetic performance in the remaining older children. This suggests that number-space associations are beneficial for arithmetic performance at relatively early stages of mathematical learning. During the course of mathematical development in childhood, number-space associations then turn superfluous for arithmetic achievement until they possibly become interfering in young adults, who have reached the peak of their developmental trajectory.

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

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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 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.

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

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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 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.

Inhibitory control influences number-space associations in atypical young adults with ADHD

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Poster (2015, May)

Evidence for number-space associations comes from the spatial-numerical association of response-codes (SNARC) effect, consisting in faster reaction times (RTs) to small/large digits with the left/right hand respectively. The SNARC effect is, however, characterized by high inter-individual variability, depending amongst others on inhibition capacities. Hoffmann et al. (2014) showed that individuals more sensitive to the interference of irrelevant information in the classical color-word Stroop task displayed stronger number-space associations. This relation was most pronounced in elderly, but did not reach significance in young healthy adults. To determine whether the negligible correlation in the young resulted from their near ceiling performances on the color-word Stroop task, we recruited young adults featuring atypically weak and variable inhibitory control. Our study population consisted of individuals (n=32; 18 females; age=27.28 years) formally diagnosed with attention-deficit/hyperactivity disorder (ADHD; n=4) and/or displaying symptoms consistent with ADHD according to the Adult ADHD Self-Report Scale (ASRS-v1.1; n=29). Within this population, a significant negative correlation (r=-0.45; p=0.009) could be observed between the parity SNARC effect (mean slope=-14.17; p<0.001) and Stroop interference, as indexed by the color-word Stroop ratio score (i.e. the difference in RTs between the color-word interference condition and the color naming condition divided by the RT in the word reading condition; mean ratio=0.82). The relationship remained significant even after controlling for arithmetic performance and general processing speed, as assessed using the arithmetic battery (Rubinsten & Henik, 2005; Shalev et al., 2001; mean accuracy=84.61%) and a speeded matching-to-sample task respectively (mean RT=671.86ms; r=-0.47; p=0.008). Our findings thus reveal that stronger number-space associations are associated with weaker Stroop inhibitory control in young adults with atypical attentional profiles, thereby further confirming the similarities between SNARC effects and Stroop-like interference effects.

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

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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 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.

Task instructions determine the visuospatial and verbal-spatial nature of number-space associations

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in Quarterly Journal of Experimental Psychology [=QJEP] (2015), 68(9),

Different number-processing tasks entail qualitatively different SNARC effects

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Poster (2014, October)

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 been extensively replicated, it is characterized by high inter-individual variability (e.g. Hoffmann et al., 2014). Moreover, even though number-space associations have been observed when numerical magnitude is both relevant (e.g. magnitude comparison) and irrelevant (e.g. parity and color judgment) for successful task completion, their strengths and underlying cognitive processes seem to vary depending on whether explicit reference to numerical magnitude is drawn or not (Fias et al., 2001; Mitchell et al., 2012). To further evaluate this hypothesis, we examined whether the SNARC effects observed in a single individual during distinct number-processing tasks were systematically linked. We computed correlations between the SNARC effects measured during a parity, magnitude and color judgment task in a population of 85 healthy university students (39 females, mean age=23.44 years). Interestingly, no relation could be observed between the color (slope=-6.79) and magnitude SNARC effects (slope=-6.98; r=0.18, p=0.11), indicating that number-space associations potentially underlie different cognitive operations in tasks with and without explicit numerical magnitude processing. Conversely, the parity SNARC effect (slope=-11.58) correlated with both the color (r=0.36, p=0.001) and magnitude SNARC effects (r=0.36, p=0.001). This suggests that although no explicit numerical magnitude treatment is required in the parity task – explaining its relationship with the color task – the involvement of number semantics is sufficient to position it in line with the magnitude judgment task.

Cognitive style influences number-space associations

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Poster (2014, May)

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. The cognitive processes underlying the SNARC effect are suggested to be task-dependent, such that number-space interactions result from verbal-spatial and visual-spatial number coding in parity and magnitude judgment tasks respectively (van Dijck et al., 2009). Moreover, the SNARC effect is characterized by high inter-individual variability (Hoffmann et al., 2014). Here we aimed to determine whether differences between the cognitive styles of individuals could influence the SNARC effect in a parity and magnitude judgment task. To distinguish between verbal and visual cognitive styles and between object- and spatial-visualizers, participants (n=74, 36 females, mean age=23.45 years) completed a modified version of Kirby et al.’s (1988) Verbalizer-Visualizer Questionnaire (VVQ, as in Mendelson & Thorson, 2004) and the Object-Spatial Imagery Questionnaire (OSIQ, Blajenkova et al., 2006, purchased from MM Virtual Design, LLC) respectively. Each item was placed on a five-point rating scale between strongly agree and strongly disagree, allowing us to compute verbal, visual, object and spatial scores for each participant. Participants that featured visual/verbal and spatial/object score ratios that were either both below or above the respective median ratio (visual/verbal ratio: M=1.09; spatial/object ratio: M=0.87) were classified as verbalizers (n=25, 16 females) and spatial-visualizers (n=25, 10 females) respectively. Participants subsequently performed the classical parity and magnitude judgment tasks. In verbalizers, the SNARC effect was significantly negative in the parity (slope=-11.2, p=0.001), but not the magnitude judgment task (slope=-1.2, p=0.53). Their verbal cognitive style might thus have induced a strong number-space association in tasks that supposedly draw on these cognitive processes, while it prevented spatial-numerical interactions in tasks that activate visuo-spatial number coding. Conversely, spatial-visualizers featured a significantly negative magnitude SNARC effect (slope=-4.8, p=0.04), indicating that a visuo-spatial style is not only necessary but sufficient to generate a number-space association in tasks that favour visuo-spatial number coding. Interestingly, they also manifested a significantly negative parity SNARC effect (slope=-9.9, p<0.001). It is likely that the spatial-visualizers switched strategy for the parity judgment task and - despite their visuo-spatial preferences - adopted the better-suited verbal strategy. Indeed, in contrast to verbalizers, their parity and magnitude SNARC effects did not correlate (spatial-visualizers: r=0.14, p=0.5; verbalizers: r=0.4, p=0.05). All in all, differences in cognitive styles might provide an additional explanation for the high inter-individual variability of the SNARC effect. Moreover, we provided further evidence for the verbal-spatial and visuo-spatial nature of the parity and magnitude SNARC effects respectively.

Task instructions determine the visuo-spatial and verbal-spatial nature of number-space associations

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Poster (2014, April)

Evidence for number-space associations comes from the spatial-numerical association of response-codes (SNARC) effect, consisting in faster reaction times (RTs) to small/large digits with the left/right hand respectively. Classically, they are thought to result from numerical coding along a left-to-right-oriented mental number line (visuo-spatial account; Dehaene et al., 1993). Recently, an association between the verbal concepts “small”/“left” and “large”/“right” has been suggested as an alternative explanation (verbal-spatial account; Gevers et al., 2010). Since the predominance of these accounts remains debated, we aimed to determine whether task instructions influence their extent of explaining the SNARC effect. A magnitude comparison task where the verbal labels “left”/“right” were displayed on the left/right response side alternatively allowed us to directly contrast the two accounts by comparing verbal SNARC slopes (based on differences in RTs to the labels “left” and “right”) with classical spatial SNARC slopes (based on differences in RTs to the left and right response side). In the verbal condition, participants (41 students, 20 female, mean age=21.6) responded to the assigned labels irrespective of their side of appearance, whereas the spatial condition required responding to the left or right response side irrespective of the displayed label. Under verbal instructions, only the verbal slope was significantly negative (verbal slope=-67.54, spatial slope=-4.82). Conversely, no significant difference was observed between verbal and spatial slopes under spatial instructions – both slopes being significantly negative (verbal slope=-15.12, spatial slope=-29.39). Taken together, number-space associations arise from verbal coding regardless of task instructions, while spatial coding only occurs under spatial instructions.

The SNARC effect and its relationship to spatial abilities in women

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Poster (2013)

A classical demonstration of number-space associations is the so-called SNARC (Spatial Numerical Association of Response Codes) effect. It consists in faster reaction times to small/large digits with the left/right hand respectively. To get a better understanding of the well-documented inter-individual variability in the SNARC effect, we investigated the relationship between the classically used parity SNARC and spatial abilities, as indexed by visuo-spatial working memory capacity (WMC). The study population consisted of female university students (n=20; mean age=23.79; SD=2.50) recruited in the fields of humanities and educational sciences. Since systematic studies on the reliability of the SNARC effect are still lacking, we first measured the internal consistency, as assessed by split-half reliability, as well as test-retest reliability of the parity SNARC. Split-half and test-retest correlation coefficients were (r(19)=0.41; p<0.05) and (r(19)=0.25; p=0.14) respectively, indicating a trend towards consistency. In the present female population, a significant negative correlation was revealed between the strength of the parity SNARC effect (mean slope=-10.04; SD=8.66) and visuo-spatial WMC (mean WMC=2.85; SD=1.12; r(19)=-0.51; p<0.05). This finding thus indicates that number-space associations as measured by the parity SNARC effect tend to be stronger in young female adults with higher spatial abilities.