The importance of domain-specific number abilities and domain-general cognitive abilities for early arithmetic achievement and development.

BACKGROUND: Children's numerical and arithmetic skills differ greatly already at an early age. Although research focusing on accounting for these large individual differences clearly demonstrates that mathematical performance draws upon several cognitive abilities, our knowledge concerning key abilities underlying mathematical skill development is still limited. AIMS: First, to identify key cognitive abilities contributing to children's development of early arithmetic skills. Second, to examine the extent to which early arithmetic performance and early arithmetic development rely on different or similar constellations of domain-specific number abilities and domain-general cognitive abilities. SAMPLE: In all, 134 Swedish children (Mage = 6 years and 4 months, SD = 3 months, 74 boys) participated in this study. METHOD: Verbal and non-verbal logical reasoning, non-symbolic number comparison, counting knowledge, spatial processing, verbal working memory and arithmetic were assessed. Twelve months later, arithmetic skills were reassessed. A latent change score model was computed to determine whether any of the abilities accounted for variations in arithmetic development. RESULTS: Arithmetic performance was supported by counting knowledge, verbal and non-verbal logical reasoning and spatial processing. Arithmetic skill development was only supported by spatial processing. CONCLUSIONS: Results show that young children's early arithmetic performance and arithmetic development are supported by different cognitive processes. The findings regarding performance supported Fuchs et al.'s model (Dev Psychol, 46, 2010b, 1731) but the developmental findings did not. The developmental findings align partially to Geary et al.'s (J Educ Psychol, 109, 2017, 680) hypothesis stating that young children's early arithmetic development is more dependent on general cognitive abilities than number abilities.

Development of Cognitive Functions and Academic Skills in 9- to 10-year-old Children with Borderline Intellectual Functioning.

This longitudinal study examined whether the cognitive and academic development of children (Mage = 10.52 years) with Borderline Intellectual Functioning (BIF), is characterized by developmental delay or atypical development. Cognitive tasks, arithmetic tasks, and reading tasks were administrated during three succeeding years to the BIF group and a Chronological Age-Matched Comparison (CAMC) group. The BIF children displayed weaknesses in relation to all tasks, and slower developmental rates on four arithmetic tasks and word reading. The results provide evidence in support of the developmental delay model as the BIF children overall displayed similar developmental growth and trends as the CAMC group.

Development of early domain-specific and domain-general cognitive precursors of high and low math achievers in grade 6.

This study investigated from a longitudinal retrospective perspective what characterizes and predicts 6th graders (Mage = 12.95, SD = 0.27) with low (LMA) or high (HMA) math achievement concerning the development of early domain-specific and domain-general cognitive abilities. They were examined and compared to average achievers (n = 88) at four-time points from kindergarten (Mage = 6.58, SD = 0.36) to third grade (Mage = 9.53, SD = 0.33). The LMA (n = 27) or HMA (n = 41) children exhibited persistent multi-weakness and multi-strength profiles, respectively, present already prior to formal schooling. The cognitive profiles of the two groups, and their development, were mostly qualitatively similar, but there were also important qualitative differences. Logistic regression analyzes showed that superior verbal arithmetic, logical reasoning, and executive functions are vital for developing superior mathematical skills while inferior verbal arithmetic, logical reasoning, and spatial processing ability constitute unique potential risk factors for low mathematical skills.

Number Magnitude Processing and Verbal Working Memory in Children with Mild Intellectual Disabilities.

This study examined if children (Mage = 14.60) with Mild Intellectual Disabilities (MID) display weaknesses in number processing and verbal working memory. An age-matched and mental age-matched (MA, Mage = 6.17) design extended by a group of 9-10-year-olds, and a group of 11-12-year-olds were used. The MID children's working memory was equal to the MA group but poorer than the other groups. On number tasks, the MID group was faster than the MA group but slower than the other groups. All groups obtained equal Weber fraction scores and distance effects on the number comparison tasks. The MID group performed subitizing and counting faster than the MA group, but slower than the 11-12-year-olds. The results demonstrate that number processing and working memory in children with MID is characterized by a developmental delay, not a deficit. Their main problem is to access the quantitative meaning of Arabic numerals. The development of different types of cognitive abilities is differently affected by educational experience and intellectual ability. The innate number system appears to be unaffected by intellectual capacity or educational experience, while the innate working memory ability is affected by intellectual capacity but not by educational experience. Culturally acquired symbolic number abilities are strongly affected by educational experience.

Logical Reasoning, Spatial Processing, and Verbal Working Memory: Longitudinal Predictors of Physics Achievement at Age 12-13 Years.

To date, few studies have tried to pinpoint the mechanisms supporting children's skills in science. This study investigated to what extent logical reasoning, spatial processing, and working memory, tapped at age 9-10 years, are predictive of physics skills at age 12-13 years. The study used a sample of 81 children (37 girls). Measures of arithmetic calculation and reading comprehension were also included in the study. The multiple regression model accounted for 24% of the variation in physics achievement. The model showed that spatial processing (4.6%) and verbal working memory (4.5%) accounted for a similar amount of unique variance, while logical reasoning accounted for 5.7% variance. The measures of arithmetic calculation and reading comprehension did not account for any unique variance. Nine percent of the accounted variance was shared variance. The results demonstrate that physics is a multivariate discipline that draws upon numerous cognitive resources. Logical reasoning ability is a key component in order for children to learn about abstract physics facts, concepts, theories, and applying complex scientific methods. Spatial processing is important as it may sub-serve the assembly of diverse sources of visual-spatial information into a spatial-schematic image. The working memory system provides a flexible and efficient mental workspace that can supervise, coordinate, and execute processes involved in physics problem-solving.

How does mathematics anxiety impair mathematical abilities? Investigating the link between math anxiety, working memory, and number processing.

In contemporary society, it is essential to have adequate mathematical skills. Being numerate has been linked to positive life outcomes and well-being in adults. It is also acknowledged that math anxiety (MA) hampers mathematical skills increasingly with age. Still, the mechanisms by which MA affect performance remain debated. Using structural equation modeling (SEM), we contrast the different ways in which MA has been suggested to interfere with math abilities. Our models indicate that MA may affect math performance through three pathways: (1) indirectly through working memory ability, giving support for the 'affective drop' hypothesis of MA's role in mathematical performance, (2) indirectly through symbolic number processing, corroborating the notion of domain-specific mechanisms pertaining to number, and (3) a direct effect of MA on math performance. Importantly, the pathways vary in terms of their relative strength depending on what type of mathematical problems are being solved. These findings shed light on the mechanisms by which MA may interfere with mathematical performance.

Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills.

Pathways to arithmetic fact retrieval and percentage calculation in adolescents.

BACKGROUND: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. AIMS: The purpose was to examine whether the pathways to mathematics model provides a valid account of the cognitive mechanisms underlying symbolic-number processing and mathematics in adolescents. The pathways model states that the three pathways should provide independent support to symbolic-number skill. Each pathway's unique contribution to formal mathematics varies depending on the complexity and demand of the tasks. SAMPLE: The study used a sample of 114 adolescents (71 girls). Their mean age was 14.60 years (SD = 1.00). METHODS: The adolescents were assessed on tests tapping the three pathways and general cognitive abilities (e.g., working memory). A structural equation path analysis was computed. RESULTS: Symbolic-number comparison was predicted by the linguistic pathway, the quantitative pathway, and processing speed. The linguistic pathway, quantitative pathways, and symbolic-number comparison predicted arithmetic fact retrieval. The linguistic pathway, working memory, visual analogies, and symbolic-number comparison predicted percentage calculation. CONCLUSIONS: There are both similarities and differences in the cognitive mechanisms underlying arithmetic fact retrieval and percentage calculation in adolescents. Adolescents' symbolic-number processing, arithmetic fact retrieval, and percentage calculation continue to rely on the linguistic pathways, whereas the reliance upon the spatial pathway has ceased. The reliance upon the quantitative pathway varies depending on the task.

Heterogeneity of Developmental Dyscalculia: Cases with Different Deficit Profiles.

Developmental Dyscalculia (DD) has long been thought to be a monolithic learning disorder that can be attributed to a specific neurocognitive dysfunction. However, recent research has increasingly recognized the heterogeneity of DD, where DD can be differentiated into subtypes in which the underlying cognitive deficits and neural dysfunctions may differ. The aim was to further understand the heterogeneity of developmental dyscalculia (DD) from a cognitive psychological perspective. Utilizing four children (8-9 year-old) we administered a comprehensive cognitive test battery that shed light on the cognitive-behavioral profile of each child. The children were compared against norm groups of aged-matched peers. Performance was then contrasted against predominant hypotheses of DD, which would also give insight into candidate neurocognitive correlates. Despite showing similar mathematical deficits, these children showed remarkable interindividual variability regarding cognitive profile and deficits. Two cases were consistent with the approximate number system deficit account and also the general magnitude-processing deficit account. These cases showed indications of having domain-general deficits as well. One case had an access deficit in combination with a general cognitive deficit. One case suffered from general cognitive deficits only. The results showed that DD cannot be attributed to a single explanatory factor. These findings support a multiple deficits account of DD and suggest that some cases have multiple deficits, whereas other cases have a single deficit. We discuss a previously proposed distinction between primary DD and secondary DD, and suggest hypotheses of dysfunctional neurocognitive correlates responsible for the displayed deficits.

Early number knowledge and cognitive ability affect early arithmetic ability.

Previous literature suggests that early number knowledge is important for the development of arithmetic calculation ability. The domain-general ability of verbal working memory also has an impact on arithmetic ability. This longitudinal study tested the impact of early number knowledge and verbal working memory on the arithmetic calculation ability of children in preschool (N=315) and then later in Grade 1 using structural equation modeling. Three models were used to test hypotheses drawn from previous literature. The current study demonstrates that both early number knowledge and the domain-general ability of verbal working memory affect preschool and Grade 1 arithmetic ability. Early number knowledge had a direct impact on the growth of arithmetic ability, whereas verbal working memory had only an indirect effect via number knowledge and preschool arithmetic ability. These results fit well with von Aster and Shalev's developmental model of numerical cognition (Developmental Medicine & Child Neurology, 2007, Vol. 49, pp. 868-873) and highlight the importance of considering arithmetic ability as independent from early number knowledge. Results also emphasize the importance of training early number knowledge before school entry to promote the development of arithmetic ability.