Dénes Szűcs

Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety.

BackgroundMathematics anxiety (MA), a state of discomfort associated with performing mathematical tasks, is thought to affect a notable proportion of the school age population. Some research has indicated that MA negatively affects mathematics performance and that girls may report higher levels of MA than boys. On the other hand some research has indicated that boys’ mathematics performance is more negatively affected by MA than girls’ performance is. The aim of the current study was to measure girls’ and boys’ mathematics performance as well as their levels of MA while controlling for test anxiety (TA) a construct related to MA but which is typically not controlled for in MA studies.MethodsFour-hundred and thirty three British secondary school children in school years 7, 8 and 10 completed customised mental mathematics tests and MA and TA questionnaires.ResultsNo gender differences emerged for mathematics performance but levels of MA and TA were higher for girls than for boys. Girls and boys showed a positive correlation between MA and TA and a negative correlation between MA and mathematics performance. TA was also negatively correlated with mathematics performance, but this relationship was stronger for girls than for boys. When controlling for TA, the negative correlation between MA and performance remained for girls only. Regression analyses revealed that MA was a significant predictor of performance for girls but not for boys.ConclusionsOur study has revealed that secondary school children experience MA. Importantly, we controlled for TA which is typically not controlled for in MA studies. Girls showed higher levels of MA than boys and high levels of MA were related to poorer levels of mathematics performance. As well as potentially having a detrimental effect on ‘online’ mathematics performance, past research has shown that high levels of MA can have negative consequences for later mathematics education. Therefore MA warrants attention in the mathematics classroom, particularly because there is evidence that MA develops during the primary school years. Furthermore, our study showed no gender difference in mathematics performance, despite girls reporting higher levels of MA. These results might suggest that girls may have had the potential to perform better than boys in mathematics however their performance may have been attenuated by their higher levels of MA. Longitudinal research is needed to investigate the development of MA and its effect on mathematics performance.

Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: A developmental study

BackgroundThe development of an evolutionarily grounded analogue magnitude representation linked to the parietal lobes is frequently thought to be a major factor in the arithmetic development of humans. We investigated the relationship between counting and the development of magnitude representation in children, assessing also childrens knowledge of number symbols, their arithmetic fact retrieval, their verbal skills, and their numerical and verbal short-term memory.MethodsThe magnitude representation was tested by a non-symbolic magnitude comparison task. We have perfected previous experimental designs measuring magnitude discrimination skills in 65 children kindergarten (4-7-year-olds) by controlling for several variables which were not controlled for in previous similar research. We also used a large number of trials which allowed for running a full factorial ANOVA including all relevant factors. Tests of verbal counting, of short term memory, of number knowledge, of problem solving abilities and of verbal fluency were administered and correlated with performance in the magnitude comparison task.Results and discussionVerbal counting knowledge and performance on simple arithmetic tests did not correlate with non-symbolic magnitude comparison at any age. Older children performed successfully on the number comparison task, showing behavioural patterns consistent with an analogue magnitude representation. In contrast, 4-year-olds were unable to discriminate number independently of task-irrelevant perceptual variables. Sensitivity to irrelevant perceptual features of the magnitude discrimination task was also affected by age, and correlated with memory, suggesting that more general cognitive abilities may play a role in performance in magnitude comparison tasks.ConclusionWe conclude that young children are not able to discriminate numerical magnitudes when co-varying physical magnitudes are methodically pitted against number. We propose, along with others, that a rather domain general magnitude representation provides the later basis for a specialized representation of numerical magnitudes. For this representational specialization, the acquisition of the concept of abstract numbers, together with the development of other cognitive abilities, is indispensable.

Visual stimulus parameters seriously compromise the measurement of approximate number system acuity and comparative effects between adults and children

It has been suggested that a simple non-symbolic magnitude comparison task is sufficient to measure the acuity of a putative Approximate Number System (ANS). A proposed measure of the ANS, the so-called “internal Weber fraction” (w), would provide a clear measure of ANS acuity. However, ANS studies have never presented adequate evidence that visual stimulus parameters did not compromise measurements of w to such extent that w is actually driven by visual instead of numerical processes. We therefore investigated this question by testing non-symbolic magnitude discrimination in seven-year-old children and adults. We manipulated/controlled visual parameters in a more stringent manner than usual. As a consequence of these controls, in some trials numerical cues correlated positively with number while in others they correlated negatively with number. This congruency effect strongly correlated with w, which means that congruency effects were probably driving effects in w. Consequently, in both adults and children congruency had a major impact on the fit of the model underlying the computation of w. Furthermore, children showed larger congruency effects than adults. This suggests that ANS tasks are seriously compromised by the visual stimulus parameters, which cannot be controlled. Hence, they are not pure measures of the ANS and some putative w or ratio effect differences between children and adults in previous ANS studies may be due to the differential influence of the visual stimulus parameters in children and adults. In addition, because the resolution of congruency effects relies on inhibitory (interference suppression) function, some previous ANS findings were probably influenced by the developmental state of inhibitory processes especially when comparing children with developmental dyscalculia and typically developing children.

Representational change and strategy use in children's number line estimation during the first years of primary school

BackgroundThe objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children.MethodsTypically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy.ResultsOur results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development.ConclusionIn terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.

Event-related potentials dissociate facilitation and interference effects in the numerical Stroop paradigm.

In the numerical Stroop paradigm (NSP) participants compare simultaneously presented Arabic digits based on either their numerical or on their physical size dimension. Responses are faster when the numerical and size dimensions are congruent with each other (facilitation), and responses are slower when the numerical and size dimensions are incongruent with each other (interference). We aimed to find out whether facilitation and interference appears during the course of perceptual or response processing. To this end, facilitation and interference effects in the amplitude of event-related brain potentials (ERPs) were examined. The onset of motor preparation was determined by monitoring the lateralized readiness potential. In numerical comparison one facilitation effect was related to perceptual processing at the level of the magnitude representation. A second facilitation effect and interference effects appeared during response processing. In size comparison facilitation and interference appeared exclusively during response processing. In both tasks, ERP interference effects were probably related to contextual analysis and to the conflict monitoring and selection for action activity of the anterior cingulate cortex. The results demonstrate that facilitation and interference effects in the NSP appear during multiple stages of processing, and that they are related to different cognitive processes. Therefore these effects should be clearly separated in studies of the NSP. A model of the processes involved in the NSP is provided and implications for studies of the NSP are drawn.

Cognitive Components of a Mathematical Processing Network in 9-Year-Old Children.

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular ‘number sense’. We suggest an ‘executive memory function centric’ model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

A combined event-related potential and neuropsychological investigation of developmental dyscalculia

Adolescents with developmental dyscalculia (DD) but no other impairments were examined with neuropsychological tests and with event-related brain potentials (ERPs). A matched control group and an adult control group were tested as well. Behavioural and ERP markers of the magnitude representation were examined in a task where subjects decided whether visually presented Hindu-Arabic digits were smaller or larger than 5. There was a normal behavioural numerical distance effect (better performance for digits closer to the reference number than for digits further away from it) in DD. This suggests that semantic magnitude relations depend on a phenomenologically (nearly) normal magnitude representation in DD, at least in the range of single-digit numbers. However, minor discrepancies between DD subjects and controls suggest that the perception of the magnitude of single digits may be slightly impaired in DD. Early ERP distance effects were similar in DD and in control subjects. In contrast, between 400 and 440 ms there was a focused right-parietal ERP distance effect in controls, but not in DD. This suggests that early, more automatic processing of digits was similar in both groups, and between-group processing differences arose later, during more complex controlled processing. This view is supported by signs of decelerated executive functioning in developmental dyscalculia. Further, DD subjects did not differ from controls in general mental rotation and in body parts knowledge, but were markedly impaired in mental finger rotation, finger knowledge, and tactile performance.

Motor conflict in Stroop tasks: Direct evidence from single-trial electro-myography and electro-encephalography

Several brain imaging studies have assumed that response conflict is present in Stroop tasks. However, this has not been demonstrated directly. We examined the time-course of stimulus and response conflict resolution in a numerical Stroop task by combining single-trial electro-myography (EMG) and event-related brain potentials (ERP). EMG enabled the direct tracking of response conflict and the peak latency of the P300 ERP wave was used to index stimulus conflict. In correctly responded trials of the incongruent condition EMG detected robust incorrect response hand activation which appeared consistently in single trials. In 50-80% of the trials correct and incorrect response hand activation coincided temporally, while in 20-50% of the trials incorrect hand activation preceded correct hand activation. EMG data provides robust direct evidence for response conflict. However, congruency effects also appeared in the peak latency of the P300 wave which suggests that stimulus conflict also played a role in the Stroop paradigm. Findings are explained by the continuous flow model of information processing: Partially processed task-irrelevant stimulus information can result in stimulus conflict and can prepare incorrect response activity. A robust congruency effect appeared in the amplitude of incongruent vs. congruent ERPs between 330-400 ms, this effect may be related to the activity of the anterior cingulate cortex.

The parietal distance effect appears in both the congenitally blind and matched sighted controls in an acoustic number comparison task

Visual world experience is thought to play a significant role in the development of an abstract representation of quantity in the human brain. Nevertheless, some congenitally blind individuals demonstrate excellent numerical abilities. We show that blind adults have a phenomenologically normal semantic representation of number. Electro-encephalography data demonstrate that the numerical distance effect has similar parietal correlates both in the blind and in matched sighted controls. Our interpretation is that number comparison in the blind relies on a compensation network in the initial phase of number comparison. In a second phase, an evolutionarily hardwired parietal system is exploited. The representation of number meaning has both plastic and evolutionarily hardwired components.

Educational neuroscience: Developmental mechanisms: towards a conceptual framework.

In the last decade, there has been an explosion of research which can be clustered into the rather broad church of “educational neuroscience.” With respect to children, this research has been focused largely on disorders of development, in particular developmental dyslexia and autism. Nevertheless, important neural insights about structure–function relations have galvanised basic behavioural work in cognitive development, with important implications for education. For example, some cognitive neuroscience explorations of autism suggest that the mirror neuron system plays a role in social cognitive development (Dapretto et al., 2006). Such studies have led to renewed efforts to understand how infant imitation, social referencing and gaze following contribute to the typical developmental trajectory for social cognition (e.g., Gergely, 2010; Meltzoff, 2010). Related empirical work exploring the importance of the sharing of psychological states and thereby of cultural and familial contexts for social cognition (“collective intentionality,” e.g., Carpenter, 2010) link directly to socio-cultural perspectives in education. These socio-cultural perspectives foreground the insights of Vygotsky into the importance of cultural contexts in learning (Vygotsky, 1978). As another example, the cognitive neuroscience of (mainly adult) reading and number has turned out to have important implications for education. For example, research on the cognitive neuroscience of number suggests that not all number concepts are represented in the same neural system (Dehaene, 1997). Some kinds of number knowledge (for example, knowledge of multiplication tables and number facts) appear to be associated with neural structures active during language tasks rather than quantity tasks (Dehaene et al., 2003). Other kinds of number knowledge, such as knowledge about inexact quantities, appear to be linked to an amodal “analogue magnitude representation” in intraparietal sulcus. These data from neuroimaging have supported novel cognitive–developmental approaches to understanding number concepts in children, such as the theoretical claim that there are two distinct systems for representing number, one for small numbers up to 4, thought to rely on an “object file” system, and another for larger numbers, thought to rely on the analogue magnitude representation (e.g., Feigenson et al., 2004). Again, these insights link directly to education, for example in terms of their implications for the early teaching of counting and number concepts. At the same time, neuroscience as a field has progressed extremely rapidly. It is becoming clear that brain imaging studies using fMRI that seek to correlate structure with function, and EEG studies that correlate a particular ERP component with a particular cognitive behaviour, are not particularly informative with respect to developmental mechanisms. These approaches thus have limited potential