Numerical matching judgments in children with mathematical learning disabilities

Mapping skills between symbols and quantities in preschoolers: The role of finger patterns

Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non-symbolic quantities. Preschool children (3-year-olds, N = 113, Mage = 40.8 months, SDage = 3.6 months; 4-year-olds, N = 103, Mage = 52.9 months, SDage = 3.4 months) both cardinality knowers and subset-knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence. RESEARCH HIGHLIGHTS: Children are more accurate in mapping between finger patterns and symbols (number words and Arabic digits) than in mapping finger patterns and quantities, indicating that fingers are processed holistically as symbolic codes. Children can map finger patterns to symbols above their corresponding cardinality level even in subset-knowers. Finger patterns may play a role in the process by which children learn to map symbols to quantities. Fingers patterns' use in the classroom context may be an adequate instructional and diagnostic tool.

Children's comparison of different-length numbers: Managing different attributes in multidigit number processing

In everyday life the comparison of numbers usually occurs between numbers with different numbers of digits. However, experimental research here is scarce. Recent research has shown that adults respond faster to congruent pairs (the initial digit in the number with more digits is larger, e.g., 2384 vs. 107) than to incongruent pairs (the initial digit is larger in the number with fewer digits, e.g., 2675 vs. 398). This has been interpreted as support for the processing of multiple attributes in parallel and against serial accounts. The current research asked whether there is a change in the relevance of these attributes as school grades increase. School-age children from the second to sixth grades (N = 206) were presented with pairs of numbers that had either the same number of digits (3 vs. 3 or 4 vs. 4) or a different number of digits (3 vs. 4). In this latter condition, the stimuli, matched by distance, could be either length/digit congruent (e.g., 2384 vs. 107) or length/digit incongruent (e.g., 2675 vs. 398). Linear mixed models showed a length/digit congruity effect from second graders. Interestingly, in the response time measure, congruity interacted with school grade and the side in which the larger number of the pair was presented. Whereas these results support a model that considers number comparison as a process that weighs different attributes in parallel, it is also argued that developmental changes are associated with differences in the level of automatization of the componential skills involved in the comparison.

Two Dyscalculia Subtypes With Similar, Low Comorbidity Profiles: A Mixture Model Analysis

Several studies have aimed to identify subtypes of dyscalculia. In many of these studies, either pre-defined groups (e.g., children with reading and mathematical difficulties vs. children with isolated mathematical difficulties) were analyzed regarding their cognitive profiles (top-down approach), or clusters of children with dyscalculia (CwD) were identified based on a narrow range of cognitive and mathematical skills (data-driven or bottom-up approach). However, it has remained difficult to establish robust subtypes of dyscalculia across studies. Against this background, we conducted a mixture model analysis in order to explore and identify subtypes of dyscalculia based on a broad range of variables (intelligence, reading fluency, working memory, attention, and various mathematical skills). The total sample comprised 174 elementary school CwD (IQ > 70; mathematical abilities: percentile rank <10), which consisted of two subsamples. The first subsample was based on a diagnostic test focusing on calculation (HRT 1–4; n = 71; 46 girls, 25 boys; age: M = 9.28 years, SD = 0.94) whereas the second subsample was based on a diagnostic test with a strong focus on basic numerical capacities (ZAREKI-R; n = 103; 78 girls, 25 boys; age: M = 8.94 years, SD = 1.05). Results provided convincing evidence for the existence of two subtypes in CwD: A slightly impaired subtype and a strongly impaired subtype. Subtypes differed most strongly regarding mathematical abilities, but the analyses suggest that differences in attention could also be a key factor. Therefore, comorbid attention difficulties seem to be a relevant factor that needs to be considered when establishing subtypes. Substantial intelligence differences between dyscalculia subtypes could not be found. Differences in working memory and reading fluency were negligible. Overall, the results seemed to be robust regardless of the diagnostic test used for assessing dyscalculia. When planning interventions for CwD, the existence of a subtype with substantial attention problems should be kept in mind.

Frequency of Home Numeracy Activities Is Differentially Related to Basic Number Processing and Calculation Skills in Kindergartners

Home numeracy has been shown to play an important role in children's mathematical performance. However, findings are inconsistent as to which home numeracy activities are related to which mathematical skills. The present study disentangled between various mathematical abilities that were previously masked by the use of composite scores of mathematical achievement. Our aim was to shed light on the specific associations between home numeracy and various mathematical abilities. The relationships between kindergartners' home numeracy activities, their basic number processing and calculation skills were investigated. Participants were 128 kindergartners (Mage = 5.43 years, SD = 0.29, range: 4.88-6.02 years) and their parents. The children completed non-symbolic and symbolic comparison tasks, non-symbolic and symbolic number line estimation tasks, mapping tasks (enumeration and connecting), and two calculation tasks. Their parents completed a home numeracy questionnaire. Results indicated small but significant associations between formal home numeracy activities that involved more explicit teaching efforts (i.e., identifying numerals, counting) and children's enumeration skills. There was no correlation between formal home numeracy activities and non-symbolic number processing. Informal home numeracy activities that involved more implicit teaching attempts, such as "playing games" and "using numbers in daily life," were (weakly) correlated with calculation and symbolic number line estimation, respectively. The present findings suggest that disentangling between various basic number processing and calculation skills in children might unravel specific relations with both formal and informal home numeracy activities. This might explain earlier reported contradictory findings on the association between home numeracy and mathematical abilities.

The Relationship Between Accuracy of Numerical Magnitude Comparisons and Children's Arithmetic Ability: A Study in Iranian Primary School Children

The relationship between children's accuracy during numerical magnitude comparisons and arithmetic ability has been investigated by many researchers. Contradictory results have been reported from these studies due to the use of many different tasks and indices to determine the accuracy of numerical magnitude comparisons. In the light of this inconsistency among measurement techniques, the present study aimed to investigate this relationship among Iranian second grade children (n = 113) using a pre-established test (known as the Numeracy Screener) to measure numerical magnitude comparison accuracy. The results revealed that both the symbolic and non-symbolic items of the Numeracy Screener significantly correlated with arithmetic ability. However, after controlling for the effect of working memory, processing speed, and long-term memory, only performance on symbolic items accounted for the unique variances in children's arithmetic ability. Furthermore, while working memory uniquely contributed to arithmetic ability in one-and two-digit arithmetic problem solving, processing speed uniquely explained only the variance in single-digit arithmetic skills and long-term memory did not contribute to any significant additional variance for one-digit or two-digit arithmetic problem solving.

Comorbidity of Arithmetic and Reading Disorder

The aim of the present study was to investigate the cognitive profiles of primary school children (age 82-133 months) on a battery of basic number processing and calculation tasks. The sample consisted of four groups matched for age and IQ: arithmetic disorder only (AD; n = 20), reading disorder only (RD; n = 40), a comorbid group ( n = 27), and an unimpaired control group ( n = 40). Multiple 2 (RD vs. No RD) × 2 (AD vs. No AD) factorial ANCOVAs showed that children with RD had selective impairments in counting and number transcoding efficiency. In contrast, children with AD performed poorly in most tasks, including symbolic and nonsymbolic magnitude comparisons, subitizing, number line estimation, number sets, number transcoding accuracy, and calculation. These findings provide further support that AD is characterized by multiple, heterogeneous underlying deficits. In contrast, RD is associated with specific number processing impairments only if tasks require verbal processing. Taken together, the results fully support the assumption of comorbid additivity of AD and RD.

Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence

Early number competence, grounded in number-specific and domain-general cognitive abilities, is theorized to lay the foundation for later math achievement. Few longitudinal studies have tested a comprehensive model for early math development. Using structural equation modeling and mediation analyses, the present work examined the influence of kindergarteners' nonverbal number sense and domain-general abilities (i.e., working memory, fluid intelligence, and receptive vocabulary) and their early number competence (i.e., symbolic number skills) on first grade math achievement (i.e., arithmetic, shape and space skills, and number line estimation) assessed 1 year later. Latent regression models revealed that nonverbal number sense and working memory are central building blocks for developing early number competence in kindergarten and that early number competence is key for first grade math achievement. After controlling for early number competence, fluid intelligence significantly predicted arithmetic and number line estimation while receptive vocabulary significantly predicted shape and space skills. In sum we suggest that early math achievement draws on different constellations of number-specific and domain-general mechanisms.