Geometry, working memory and intelligence

Geometry is a fundamental part of mathematical learning. Since ancient time the study of geometry was considered as one of the most important subjects in school. In the arcade of the famous school of Athens, where Plato taught, it was written that entry was not permitted to people who did not know geometry. In the Renaissance period, geometry was part of the 'quadrivium', which was considered a needed work preparatory for a serious study of philosophy. Nevertheless, despite geometry is one of the main areas of mathematical learning, the cognitive processes underlying geometry-related academic achievement have not been studied in detail. The present dissertation has three important aims. First, to investigate the relationship between various aspects of geometry and visuospatial working memory (VSWM). Second, to investigate whether the children with nonverbal learning disabilities (NLD) symptoms present difficulties in various aspects of geometry. Third, to investigate the relationship between various aspect of geometry, working memory (WM) and intelligence (g). In the second chapter, a general overview of the relationship between geometry, WM and g is provided. Since geometry concerns the study of the space, it requires a particular involvement of spatial abilities. Thus, WM, and in particular VSWM should be crucially involved. In addition, solving geometrical problems requires to reason and to find out a solution among various alternatives. Thus, g should be crucially involved in solving geometrical problems. In the third chapter, the relationship between academic achievement in geometry, intuitive geometry (i.e., a part of geometry which seems to be independent from the culture), and VSWM will be examined. Two studies will be presented. In the first study, the involvement of VSWM in intuitive geometry and in school performance in geometry at secondary school was tested. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and Spelke (2006), which distinguishes between core, presumably independent form the culture, and culturally-mediated principles of geometry; and (3) a task measuring academic achievement in geometry. In the second study, VSWM and intuitive geometry were examined in two groups aged 1113; one with children displaying symptoms of NLD, and the other, a control group without learning disabilities. The two groups were matched for general verbal abilities, age, gender, and socioeconomic level. The children were presented with simple storage and complex-span tasks involving VSWM and with the intuitive geometry task devised by Dehaene and colleagues (Dehaene et al., 2006). In the fourth chapter, we report a study on the relationship between geometry, WM, and intelligence aimed to find out the model of WM which provided the best fit to the data and to examine the strength of the relations between WM and intelligence (part I) and the relationship between geometry (intuitive geometry and geometrical achievement), WM and g testing several models (part II). In the last chapter a general overview of the important theoretical and applied implications of the three studies will be discussed. The limits of the present dissertation and possible future researches will also be outline

A distinction between working memory components as unique predictors of mathematical components in 7–8 year old children

Despite evidence for the involvement of working memory in mathematics attainment, the understanding of its components relationship to individual areas of mathematics is somewhat restricted. This study aims to better understand this relationship. Two-hundred and fourteen year 3 children in the UK were administered tests of verbal and visuospatial working memory, followed by a standardised mathematics test. Confirmatory factor analyses and variance partitioning were then performed on the data to identify the unique variance accounted for by verbal and visuospatial working memory measures for each component of mathematics assessed. Results revealed contrasting patterns between components, with those typically visual components demonstrating a larger proportion of unique variance explained by visuospatial measures. This pattern reveals a level of specificity with regard to the component of working memory engaged depending on the component of mathematics being assessed. Implications for educators and further research are discussed

Entia Non Sunt Multiplicanda … Shall I look for clusters in my cognitive data?

Unsupervised clustering methods are increasingly being applied in psychology. Researchers may use such methods on multivariate data to reveal previously undetected sub-populations of individuals within a larger population. Realistic research scenarios in the cognitive science may not be ideally suited for a successful use of these methods, however, as they are characterized by modest effect sizes, limited sample sizes, and non-orthogonal indicators. This combination of characteristics even presents a high risk of detecting non-existing clusters. A systematic review showed that, among 191 studies published in 2016–2020 that used different clustering methods to classify human participants, the median sample size was only 322, and a median of 3 latent classes/clusters were detected. None of them concluded in favor of a one-cluster solution, potentially giving rise to an extreme publication bias. Dimensionality reduction techniques are almost never used before clustering. In a subsequent simulation study, we examined the performance of popular clustering techniques, including Gaussian mixture model, a partitioning, and a hierarchical agglomerative algorithm. We focused on their ability to detect the correct number of clusters, and on their classification accuracy. Under a reasoned set of scenarios that we considered plausible for the cognitive research, none of the methods adequately discriminates between one vs two true clusters. In addition, non-orthogonal indicators lead to a high risk of incorrectly detecting multiple clusters where none existed, even in the presence of only modest correlation (a frequent case in psychology). In conclusion, it is hard for researchers to be in a condition to achieve a valid unsupervised clustering for inferential purposes with a view to classifying individuals

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

The Structure of Working Memory and Its Relationship with Intelligence in Japanese Children

There is a host of research on the structure of working memory (WM) and its relationship with intelligence in adults, but only a few studies have involved children. In this paper, several different WM models were tested on 170 Japanese school children (from 7 years and 5 months to 11 years and 6 months). Results showed that a model distinguishing between modalities (i.e., verbal and spatial WM) fitted the data well and was therefore selected. Notably, a bi-factor model distinguishing between modalities, but also including a common WM factor, presented with a very good fit, but was less parsimonious. Subsequently, we tested the predictive power of the verbal and spatial WM factors on fluid and crystallized intelligence. Results indicated that the shared contribution of WM explained the largest portion of variance of fluid intelligence, with verbal and spatial WM independently explaining a residual portion of the variance. Concerning crystallized intelligence, however, verbal WM explained the largest portion of the variance, with the joint contribution of verbal and spatial WM explaining the residual part. The distinction between verbal and spatial WM could be important in clinical settings (e.g., children with atypical development might struggle selectively on some WM components) and in school settings (e.g., verbal and spatial WM might be differently implicated in mathematical achievement)

Dyslexia treatment studies: A systematic review and suggestions on testing treatment efficacy with small effects and small samples

Funder: Università degli Studi di PadovaAbstract: Poor response to treatment is a defining characteristic of reading disorder. In the present systematic review and meta-analysis, we found that the overall average effect size for treatment efficacy was modest, with a mean standardized difference of 0.38. Small true effects, combined with the difficulty to recruit large samples, seriously challenge researchers planning to test treatment efficacy in dyslexia and potentially in other learning disorders. Nonetheless, most published studies claim effectiveness, generally based on liberal use of multiple testing. This inflates the risk that most statistically significant results are associated with overestimated effect sizes. To enhance power, we propose the strategic use of repeated measurements with mixed-effects modelling. This novel approach would enable us to estimate both individual parameters and population-level effects more reliably. We suggest assessing a reading outcome not once, but three times, at pre-treatment and three times at post-treatment. Such design would require only modest additional efforts compared to current practices. Based on this, we performed ad hoc a priori design analyses via simulation studies. Results showed that using the novel design may allow one to reach adequate power even with low sample sizes of 30–40 participants (i.e., 15–20 participants per group) for a typical effect size of d = 0.38. Nonetheless, more conservative assumptions are warranted for various reasons, including a high risk of publication bias in the extant literature. Our considerations can be extended to intervention studies of other types of neurodevelopmental disorders

Forward and backward digit span difficulties in children with specific learning disorder

This study examined performance in the forward and backward digit span task of the Wechsler Intelligence Scale for Children–Fourth Edition (WISC–IV) in a large group of children with specific learning disorder (SLD) as compared with a group of typically developing children matched for age and sex. Our results further support the hypothesis that the intellectual difficulties of children with SLD involve working memory in the forward digit span task to a greater extent than in the backward digit span task. The correlation of the two spans with a General Ability Index (GAI) was similar in SLD, and smaller in magnitude than in typically developing children. Despite a GAI within normal range, children with SLD had difficulty with both digit span tasks, but more so for forward span. This pattern was similar for different SLD profiles with clinical diagnoses of dyslexia and mixed disorder, but the impairments were more severe in the latter. Age differences were also investigated, demonstrating larger span impairment in older children with SLD than in younger

Differences in the intellectual profile of children with intellectual vs. learning disability.

The WISC-IV was used to compare the intellectual profile of two groups of children, one with specific learning disorders (SLDs), the other with intellectual disabilities (ID), with a view to identifying which of the four main factor indexes and two additional indexes can distinguish between the groups. We collected information on WISC-IV scores for 267 children (Mage=10.61 [SD=2.51], range 6-16 years, females=99) with a diagnosis of either SLD or ID. Children with SLD performed better than those with ID in all measures. Only the SLD children, not the ID children, revealed significant differences in the four main factor indexes, and their scores for the additional General Ability Index (GAI) were higher than for the Cognitive Proficiency Index (CPI). Children with a diagnosis of SLD whose Full-Scale Intelligence Quotient (FSIQ) was <85 showed a similar pattern. Our findings confirm the hypothesis that children with SLD generally obtain high GAI scores, but have specific deficiencies relating to working memory and processing speed, whereas children with ID have a general intellectual impairment. These findings have important diagnostic and clinical implications and should be considered when making diagnostic decisions in borderline cognitive cases

The relationship among geometry, working memory, and intelligence in children.

Although geometry is one of the main areas of mathematical learning, the cognitive processes underlying geometry-related academic achievement have not been studied in detail. This study explored the relationship among working memory (WM), intelligence (g factor), and geometry in 176 typically developing children attending school in their fourth and fifth grades. Structural equation modeling showed that approximately 40% of the variance in academic achievement and in intuitive geometry (which is assumed to be independent of a person's cultural background) was explained by WM and the g factor. After taking intelligence and WM into account, intuitive geometry was no longer significantly related to academic achievement in geometry. We also found intuitive geometry to be closely related to fluid intelligence (as measured by Raven's colored progressive matrices) and reasoning ability, whereas academic achievement in geometry depended largely on WM. These results were confirmed by a series of regressions in which we estimated the contributions of WM, intelligence, and intuitive geometry to the unique and shared variance explaining academic achievement in geometry. Theoretical and educational implications of the relationship among WM, intelligence, and academic achievement in geometry are discussed

The structure of intelligence in children with specific learning disabilities is different as compared to typically development children

Children with specific learning disabilities (SLDs) are characterized by a poor academic achievement despite an average intelligence. They are therefore typically assessed not only with achievement tests, but also with intelligence tests, usually the Wechsler Intelligence Scale for Children (WISC). The assumption of a discrepancy between IQ and achievement in children with SLD has been questioned, however, and the implications of using different measures in batteries of intellectual subtests have not been thoroughly investigated. The present study examined these issues, taking advantage of a large database of scores obtained in the ten core subtests of the WISC-IV by a group of 910 Italian children with a clinical diagnosis of SLD, who were compared with the children considered for national standardization purposes. Our results support the doubts raised concerning the IQ-achievement discrepancy model, showing that relevant discrepancies can emerge even within the WISC profile. The four main WISC-IV indexes were found differently related to intelligence (measured by means of the g-factor) and the g content of many subtests differed in childrenwith SLD vis-\ue0-vis typically-developing children. These results have important implications both theoretical, indicating that the g-factor isweakly identified in children with SLD children, and practical, indicating that the QI obtained with the WISC-IV may not be a good measure of intellectual functioning for children with SLD, which are discussed