Multidimensional components of (state) mathematics anxiety: Behavioral, cognitive, emotional, and psychophysiological consequences.

The present study aimed to analyze the different components of state mathematics anxiety that students experienced while solving calculation problems by manipulating their stress levels. A computerized mathematical task was administered to 165 fifth-graders randomly assigned to three different groups: positive, negative, and control conditions, in which positive, negative, or no feedback during the task was given, respectively. Behavioral (task performance), emotional (negative feelings), cognitive (worrisome thoughts and perceived competence), and psychophysiological responses (skin conductance and vagal withdrawal) were analyzed. Behavioral responses did not differ in the positive and negative conditions, while the latter was associated with children's reportedly negative emotional states, worries, and perceived lack of competence. The stress induced in the negative condition led to an increase in skin conductance and cardiac vagal withdrawal in children. Our data suggest the importance of considering students' interpretation of mathematics-related experiences, which might affect their emotional, cognitive, and psychophysiological responses.

Learning a new geometric concept: The role of working memory and of domain-specific abilities.

It has been suggested that not only domain-specific factors but also working memory (WM) may play a crucial role in mathematical learning included Geometry, but the issue has not been deeply explored. In the present study, we examined the role of domain-specific factors and of verbal versus visuospatial WM on geometric learning of a new geometrical figure (trapezoid), never presented previously by the teachers participating to the study, after a lecture also involving manipulatives. Results on 105 children in their Year 4 indicated that not only some domain-specific components (geometric declarative knowledge and calculation) but also visuospatial working memory had a significant specific impact on the ability of solving geometric problems requiring to calculate the perimeter and the area of the new figure. On the contrary, verbal WM and geometrical mental imagery did not offer a specific contribution. These findings could have important educational implications, stressing the importance of taking into account the main different aspects supporting the acquisition of geometry.

Executive Functions in Neurodevelopmental Disorders: Comorbidity Overlaps Between Attention Deficit and Hyperactivity Disorder and Specific Learning Disorders.

The present study examines the comorbidity between specific learning disorders (SLD) and attention deficit and hyperactivity disorder (ADHD) by comparing the neuropsychological profiles of children with and without this comorbidity. Ninety-seven schoolchildren from 8 to 14 years old were tested: a clinical sample of 49 children with ADHD (n = 18), SLD (n = 18) or SLD in comorbidity with ADHD (n = 13), and 48 typically-developing (TD) children matched for age and intelligence. Participants were administered tasks and questionnaires to confirm their initial diagnosis, and a battery of executive function (EF) tasks testing inhibition, shifting, and verbal and visuospatial updating. Using one-way ANOVAs, our results showed that all children in the clinical samples exhibited impairments on EF measures (inhibition and shifting tasks) when compared with TD children. A more specific pattern only emerged for the updating tasks. Only children with SLD had significant impairment in verbal updating, whereas children with ADHD, and those with SLD in comorbidity with ADHD, had the worst performance in visuospatial updating. The clinical and educational implications of these findings are discussed.

No evidence for a core deficit in developmental dyscalculia or mathematical learning disabilities.

BACKGROUND: Two hypotheses were tested regarding the characteristics of children with mathematical learning disabilities (MLD): (a) that children with MLD would have a 'core deficit' in basic number processing skills; and (b) that children with MLD would be at the end of a developmental continuum and have impairments in many cognitive skills. METHODS: From a large sample (N = 1,303) of typically developing children, we selected a group definable as having MLD. The children were given measures of basic number processing and domain-general constructs. Differences between the observed sample and a simulated population were estimated using Cohen's d and Bayes factors. Receiver operating characteristic curves were plotted, and the area under the curve was computed to ascertain the diagnostic power of measures. RESULTS: Results suggest that the differences between the MLD and control group can be defined along with general characteristics of the population rather than assuming single or multiple 'core deficits'. None of the measures of interest exceeded the diagnostic power that could be derived via simulation from the dimensional characteristics of the general population. CONCLUSIONS: There is no evidence for core deficit(s) in MLD. We suggest that future research should focus on representative samples of typical populations and on carefully tested clinical samples confirming to the criteria of international diagnostic manuals. Clinical diagnoses require that MLD is persistent and resistant to intervention, so studies would deliver results less exposed to measurement fluctuations. Uniform diagnostic criteria would also allow for the easy cross-study comparison of samples overcoming a serious limitation of the current literature.

Predictors of mathematics in primary school: Magnitude comparison, verbal and spatial working memory measures.

We determined the relative importance of the so-called approximate number system (ANS), symbolic number comparison (SNC) and verbal and spatial short-term and working memory (WM) capacity for mathematics achievement in 1,254 Grade 2, 4 and 6 children. The large sample size assured high power and low false report probability and allowed us to determine effect sizes precisely. We used reading decoding as a control outcome measure to test whether findings were specific to mathematics. Bayesian analysis allowed us to provide support for both null and alternative hypotheses. We found very weak zero-order correlations between ANS measures and math achievement. These correlations were not specific to mathematics, became non-significant once intelligence was considered and ANS measures were not selected as predictors of math by regression models. In contrast, overall SNC accuracy and spatial WM measures were reliable and mostly specific predictors of math achievement. Verbal short-term and WM and SNC reaction time were predictors of both reading and math achievement. We conclude that ANS tasks are not suitable as measures of math development in school-age populations. In contrast, all other cognitive functions we studied are promising markers of mathematics development.

Children's Strategy Choices on Complex Subtraction Problems: Individual Differences and Developmental Changes.

We examined how children's strategy choices in solving complex subtraction problems are related to grade and to variations in problem complexity. In two studies, third- and fifth-grade children (N≈160 each study) solved multi-digit subtraction problems (e.g., 34-18) and described their solution strategies. In the first experiment, strategy selection was investigated by means of a free-choice paradigm, whereas in the second study a discrete-choice approach was implemented. In both experiments, analyses of strategy repertoire indicated that third-grade children were more likely to report less-efficient strategies (i.e., counting) and relied more on the right-to-left solution algorithm compared to fifth-grade children who more often used efficient memory-based retrieval and conceptually-based left-to-right (i.e., decomposition) strategies. Nevertheless, all strategies were reported or selected by both older and younger children and strategy use varied with problem complexity and presentation format for both age groups. These results supported the overlapping waves model of strategy development and provide detailed information about patterns of strategy choice on complex subtraction problems.

The underlying structure of visuospatial working memory in children with mathematical learning disability.

This study examined visual, spatial-sequential, and spatial-simultaneous working memory (WM) performance in children with mathematical learning disability (MLD) and low mathematics achievement (LMA) compared with typically developing (TD) children. Groups were matched on reading decoding performance and verbal intelligence. Besides statistical significance testing, we used bootstrap confidence interval estimation and computed effect sizes. Children were individually tested with six computerized tasks, two for each visuospatial WM subcomponent. We found that both MLD and LMA children had low visuospatial WM function in both spatial-simultaneous and spatial-sequential WM tasks. The WM deficit was most expressed in MLD children and less in LMA children. This suggests that WM scores are distributed along a continuum with TD children achieving top scores and MLD children achieving low scores. The theoretical and practical significance of findings is discussed. Statement of Contribution What is already known on this subject? Working memory plays an important role in mathematical achievement. Children with mathematical learning disability (MLD) usually have low working memory resources. Conflicting results have been reported concerning the role of VSWM in individuals with MLD. What the present study adds? Children with different degree of impairment in math achievement and typically developing children were tested. Visual, spatial-sequential, and spatial-simultaneous working memory tasks were examined. Only spatial-sequential and spatial-simultaneous working memory tasks discriminated the two impairments groups.

Separating math from anxiety: The role of inhibitory mechanisms.

Deficits in executive functions have been hypothesized and documented for children with severe mathematics anxiety (MA) or developmental dyscalculia, but the role of inhibition-related processes has not been specifically explored. The main aim of the present study was to shed further light on the specificity of these profiles in children in terms of working memory (WM) and the inhibitory functions involved. Four groups of children between 8 and 10 years old were selected: one group with developmental dyscalculia (DD) and no MA, one with severe MA and developmental dyscalculia (MA-DD), one with severe MA and no DD (MA), and one with typical development (TD). All children were presented with tasks measuring two inhibition-related functions, that is, proactive interference and prepotent response, and a WM task. The results showed that children with severe MA (but no DD) were specifically impaired in the proactive interference task, while children with DD (with or without MA) failed in the WM task. Our findings point to the importance of distinguishing the cognitive processes underlying these profiles.

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature.

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth "strategy selection") in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research.

The role of practice and strategy in mental rotation training: transfer and maintenance effects.

Research in the domain of spatial abilities is now focusing on whether spatial abilities can be trained, and whether this can produce gains and maintenance effects in other, untrained skills. The aim of the present study was to assess the benefit and maintenance effects of two types of mental rotation training, one based on mental rotation practice alone, the other combining mental rotation practice with the use of a spatial (rotation) strategy. Seventy-two females took part in the study: 24 practiced with a rotation task that involved comparing pairs of 3D objects [the mental rotation (MR) group], 24 were taught to use the rotation strategy while practicing with the rotation task [the strategy + mental rotation (S + MR) group], and 24 were involved in parallel non-spatial activities (the active control group). Transfer effects were sought on both untrained spatial tasks (testing object rotation and perspective taking) and fluid ability tasks; self-reported strategy use was also examined. Our results showed short-term benefits and maintenance effects in the MR and the S + MR groups in terms of their accuracy in both the MR tasks considered (a 3D same/different task, and the Mental Rotations Test). The S + MR group was more accurate at follow-up than at post-test in both MR tasks, and reported using the rotation strategy in association with the tasks; this group was also more accurate at follow-up than at pre-test in the perspective-taking and fluid intelligence tasks. These findings are discussed from the spatial cognition standpoint and with reference to the (rotation) training literature.

Computer-based training for improving mental calculation in third- and fifth-graders.

The literature on intervention programs to improve arithmetical abilities is fragmentary and few studies have examined training on the symbolic representation of numbers (i.e. Arabic digits). In the present research, three groups of 3rd- and 5th-grade schoolchildren were given training on mental additions: 76 were assigned to a computer-based strategic training (ST) group, 73 to a process-based training (PBT) group, and 71 to a passive control (PC) group. Before and after the training, the children were given a criterion task involving complex addition problems, a nearest transfer task on complex subtraction problems, two near transfer tasks on math fluency, and a far transfer task on numerical reasoning. Our results showed developmental differences: 3rd-graders benefited more from the ST, with transfer effects on subtraction problems and math fluency, while 5th-graders benefited more from the PBT, improving their response times in the criterion task. Developmental, clinical and educational implications of these findings are discussed.

Mathematics Anxiety, Working Memory, and Mathematics Performance in Secondary-School Children.

Mathematics anxiety (MA) has been defined as "a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations." Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM) also plays an important part in such anxious feelings. The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA) and low math anxiety (LMA). Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information) than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA.

Anxiety and Depression in Children With Nonverbal Learning Disabilities, Reading Disabilities, or Typical Development.

The main goal of the present study was to shed further light on the psychological characteristics of children with different learning disability profiles aged between 8 and 11 years, attending from third to sixth grade. Specifically, children with nonverbal learning disabilities (NLD), reading disabilities (RD), or a typical development (TD) were tested. In all, 15 children with NLD, 15 with RD, and 15 with TD were administered self-report questionnaires to assess different types of anxiety and depression symptoms. Both NLD and RD children reported experiencing more generalized and social anxiety than TD, the NLD children reported more severe anxiety about school and separation than TD, and the children with RD had worse depressive symptoms than those with NLD or TD.

Math anxiety and developmental dyscalculia: A study on working memory processes.

INTRODUCTION: Although many children encounter difficulties in arithmetic, the underlying cognitive and emotive factors are still not fully understood. This study examined verbal and visuospatial short-term memory (STM) and working memory (WM) performance in children with developmental dyscalculia (DD) and high mathematics anxiety (MA) compared with typically developing (TD) children. METHOD: Groups were matched on reading comprehension performance and IQ as well as on general anxiety. We aimed to test whether children with DD and MA were differently impaired in verbal and visuospatial STM and WM. Children were individually tested with four computerized tasks: two STM tasks (forward verbal and visuospatial recall) and two WM tasks (backward verbal and visuospatial recall). RESULTS: Relative to children with TD, those with DD did not show impairments on the forward or backward verbal tasks, but showed specific impairments in the visuospatial WM task. In contrast, children with MA were particularly impaired in the verbal WM task. CONCLUSIONS: Knowing the underlying cognitive processes that differentiate why children with DD and MA fail in math could have both educational and clinical implications.

Visuospatial working memory in children with autism: the effect of a semantic global organization.

It has been reported that individuals with Autism Spectrum Disorders (ASD) perceive visual scenes as a sparse set of details rather than as a congruent and meaningful unit, failing in the extraction of the global configuration of the scene. In the present study, children with ASD were compared with typically developing (TD) children, in a visuospatial working memory task, the Visual Patterns Test (VPT). The VPT array was manipulated to vary the semantic affordance of the pattern, high semantic (global) vs. low semantic; temporal parameters were also manipulated within the change detection protocol. Overall, there was no main effect associated with Group, however there was a significant effect associated with Semantics, which was further qualified by an interaction between the Group and Semantic factors; there was only a significant effect of semantics in the TD group. The findings are discussed in light of the weak central coherence theory where the ASD group are unable to make use of long term memory semantics in order to construct global representations of the array.

Mathematical difficulties in nonverbal learning disability or co-morbid dyscalculia and dyslexia.

The main goal of the present study was to shed further light on the weaknesses of children with different profiles of mathematical difficulties, testing children with nonverbal learning disability (NLD), co-morbid dyscalculia and dyslexia (D&D), or typical development (TD). Sixteen children with NLD, 15 with D&D, and 16 with TD completed tasks derived from Butterworth (2003 ) and divided into: a capacity subscale (i.e., a number-dots comparison task, a number comparison task, and a dots comparison task); and an achievement subscale (i.e., mental calculations and arithmetical fact retrieval). Children with NLD were impaired in the dots comparison task, children with D&D in the mental calculation and arithmetical facts.

Mental additions and verbal-domain interference in children with developmental dyscalculia.

This study examined the involvement of verbal and visuo-spatial domains in solving addition problems with carrying in a sample of children diagnosed with developmental dyscalculia (DD) divided into two groups: (i) those with DD alone and (ii) those with DD and dyslexia. Age and stage matched typically developing (TD) children were also studied. The addition problems were presented horizontally or vertically and associated with verbal or visuo-spatial information. Study results showed that DD children's performance on mental calculation tasks was more impaired when they tackled horizontally presented addition problems compared to vertically presented ones that are associated to verbal domain involvement. The performance pattern in the two DD groups was found to be similar. The theoretical, clinical and educational implications of these findings are discussed.

The role of numerosity in processing nonsymbolic proportions.

The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.

The involvement of working memory in children's exact and approximate mental addition.

The involvement of working memory (WM) was examined in two types of mental calculation tasks: exact and approximate. Specifically, children attending Grades 3 and 4 of primary school were involved in three experiments that examined the role of verbal and visuospatial WM in solving addition problems presented in vertical or horizontal format. For Experiment 1, the children were required to solve addition problems with carrying. For Experiment 2, they were required to solve addition problems without carrying. Then, for Experiment 3, the children needed to solve approximate problems with and without carrying. Results confirmed that different WM components are involved in solving mental addition problems. In Experiment 1, horizontally presented addition problems were more impaired than vertically presented ones, according to a verbal WM load; conversely, vertically presented addition problems were more affected by a visuospatial WM load, especially when the children were required to perform approximate calculations. In Experiment 2, this pattern emerged in neither exact nor approximate calculations. Finally, in Experiment 3, the specific involvement of WM components was observed only in problems with carrying. Overall, these results reveal that both approximate calculation and carrying procedures demand particularly high WM resources that vary according to the task's constraints.