Typical and atypical development of basic numerical skills in elementary school

Deficits in basic numerical processing have been identified as a central and potentially causal problem in developmental dyscalculia; however, so far not much is known about the typical and atypical development of such skills. This study assessed basic number skills cross-sectionally in 262 typically developing and 51 dyscalculic children in Grades 2, 3, and 4. Findings indicate that the efficiency of number processing improves over time and that dyscalculic children are generally less efficient than children with typical development. For children with typical arithmetic development, robust effects of numerical distance, size congruity, and compatibility of ten and unit digits in two-digit numbers could be identified as early as the end of Grade 2. Only the distance effect for comparing symbolic representations of numerosities changed developmentally. Dyscalculic children did not show a size congruity effect but showed a more marked compatibility effect for two-digit numbers. We did not find strong evidence that dyscalculic children process numbers qualitatively differently from children with typical arithmetic development.     

Time Reading in Middle and Secondary School Students: The Influence of Basic-Numerical Abilities

Abstract

Time reading skills are central for the management of personal and professional life. However, little is known about the differential influence of basic numerical abilities on analog and digital time reading in general and in middle and secondary school students in particular. The present study investigated the influence of basic numerical skills separately for analog and digital time reading in N?=?709 students from 5th to 8th grade. The present findings suggest that the development of time reading skills is not completed by the end of primary school. Results indicated that aspects of magnitude manipulation and arithmetic fact knowledge predicted analog time reading significantly over and above the influence of age. Furthermore, results showed that spatial representations of number magnitude, magnitude manipulation, arithmetic fact knowledge, and conceptual knowledge were significant predictors of digital time reading beyond general cognitive ability and sex. To the best of our knowledge, the present study is the first to show differential effects of basic numerical abilities on analog and digital time reading skills in middle and secondary school students. As time readings skills are crucial for everyday life, these results are highly relevant to better understand basic numerical processes underlying time reading.     

Depth Psychology and Symbolic Anthropology: Toward a Depth Sociology of Psychocultural Interaction

Research on the moral faculty indicates that morality emerges naturally over the course of normal human development, similar to other competencies such as face perception, language, numerical reasoning, and some motor skills (running, jumping, etc.). One implication of this is that there should be a roughly normal distribution of moral skills. Thus, while most people develop competent moral skills, a few fail to develop these skills and a few develop them to an “expert” level. The skill development literature indicates that deliberate practice is necessary for the acquisition of expertise. Religious participation appears to provide the basic elements of deliberate “moral practice.” Empirical evidence is reviewed supporting the notion that religion provides the means and opportunity for the acquisition of moral expertise. A program of research into moral expertise is proposed with testable hypotheses presented.     

Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement

Although it is often assumed that abilities that reflect basic numerical understanding, such as numerical comparison, are related to children’s mathematical abilities, this relationship has not been tested rigorously. In addition, the extent to which symbolic and nonsymbolic number processing play differential roles in this relationship is not yet understood. To address these questions, we collected mathematics achievement measures from 6- to 8-year-olds as well as reaction times from a numerical comparison task. Using the reaction times, we calculated the size of the numerical distance effect exhibited by each child. In a correlational analysis, we found that the individual differences in the distance effect were related to mathematics achievement but not to reading achievement. This relationship was found to be specific to symbolic numerical comparison. Implications for the role of basic numerical competency and the role of accessing numerical magnitude information from Arabic numerals for the development of mathematical skills and their impairment are discussed.     

Sources of Group and Individual Differences in Emerging Fraction Skills

Results from a two year longitudinal study of 181 children from fourth through fifth grade are reported. Levels of growth in children's computation, word problem, and estimation skills using common fractions were predicted by working memory, attentive classroom behavior, conceptual knowledge about fractions, and simple arithmetic fluency. Comparisons of 55 participants identified as having mathematical difficulties to those without mathematical difficulties revealed that group differences in emerging fraction skills were consistently mediated by attentive classroom behavior and conceptual knowledge about fractions. Neither working memory nor arithmetic fluency mediated group differences in growth in fraction skills. It was also found that the development of basic fraction skills and conceptual knowledge are bidirectional in that conceptual knowledge exerted strong influences on all three types of basic fraction skills, and basic fraction skills exerted a more modest influence on subsequent conceptual knowledge. Results are discussed with reference to how the identification of potentially malleable student characteristics that contribute to the difficulties that some students have with fractions informs interventions and also will contribute to a future theoretical account concerning how domain general and domain specific factors influence the development of basic fraction skills.     

Atypical trajectories of number development: a neuroconstructivist perspective

Despite the fact that number deficits are as prevalent as literacy deficits, research on basic numerical skills lags seriously behind the successful studies identifying low-level deficits in dyslexia. We review current debates on number, discussing how the competing theories pertain to mathematical disabilities in normal children and numeracy deficits in genetic disorders. We stress the need to consider these issues within the framework of a developing system rather than from the neuropsychological perspective of focal damage. The earlier the exploration of atypical trajectories in very basic numerical skills, the better we will be able to chart their developmental impact on subsequent, higher-level arithmetic abilities.     

Relations of basic arithmetic and motor skills in deaf elementary school children

3 segregated groups of Arab and Jewish deaf children of CA 10;9 (n = 28) were compared with a group of hearing Arab first graders (CA = 6;10, n = 32) on tests of basic arithmetic, static balance control, and the ability to suppress synkinetic finger movements. The hearing-impaired performed as well on arithmetic tasks and on the tests of synkinetic control as their normal peers who were four years younger, while on static balance they were even inferior to the latter. Significant correlations were found between the basic arithmetic and motor skills, within the hearing as well as within the hearing-impaired groups; these remained significant even within the small subgroups of the latter. As these results cannot be accounted for by low intelligence and neurological disturbances, or by direct or indirect effects of deficient language development, the assumption is supported that some type of neurological immaturity, unrelated to hearing loss, interferes with the acquisition of numerical skills in deaf children.     

The link between deductive reasoning and mathematics

ABSTRACT

Recent studies have shown that deductive reasoning skills (including transitive and conditional inferences) are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions.     

Differential impact of preschool models on development and early learning of inner-city children: a three-cohort study

Three different preschool models operating in an urban school district were identified through cluster analysis of teacher responses to the Pre-K Survey of Beliefs and Practices. The language, self-help, social, motor, and adaptive development, along with mastery of basic skills, of 721 4-year-olds randomly selected from these models were compared. Children in the child-initiated model demonstrated greater mastery of basic skills than did children in programs in which academics were emphasized and skills were taught. Children in the combination model did significantly poorer on all measures except self-help and development of social coping skills compared with children in either the child-initiated or academically directed models. Girls outperformed boys in all areas except gross motor development and play and leisure skills. Implications for educational policymakers are discussed.     

Number-processing skills in adults with dyslexia

The present study investigated basic numerical skills and arithmetic in adults with developmental dyslexia. Participants performed exact and approximate calculation, basic numerical tasks (e.g., counting; symbolic number comparison; spatial–numerical association of response codes, SNARC), and visuospatial tasks (mental rotation and visual search tasks). The group with dyslexia showed a marginal impairment in counting compared to age- and IQ-matched controls, and they were impaired in exact addition, in particular with respect to speed. They were also significantly slower in multiplication. In basic number processing, however, there was no significant difference in performance between those with dyslexia and controls. Both groups performed similarly on subtraction and approximate addition tasks. These findings indicate that basic number processing in adults with dyslexia is intact. Their difficulties are restricted to the verbal code and are not associated with deficits in nonverbal magnitude representation, visual Arabic number form, or spatial cognition.     

Trends in Advertised Entry-Level Technology,Interpersonal, and Basic Communication Job Skills, 1992–1994

This study identifies entry-level employment trends in technology, interpersonal, and basic communication job skills over time using classified newspaper advertisements from standard metropolitan statistical areas (SMSAs) in the United States. These skills were selected from a set of workplace know-hows listed in two editions of a U.S. Department of Labor report, the Secretary's Commission on Achieving Necessary Skills (SCANS; 1991, 1992). The results indicate that classified ads specifically requesting technical and interpersonal job skills have declined, yet ads requesting basic communication skills have remained constant, with a high percentage specifically requesting these basic skills.     

Numerical ordering ability mediates the relation between number-sense and arithmetic competence

What predicts human mathematical competence? While detailed models of number representation in the brain have been developed, it remains to be seen exactly how basic number representations link to higher math abilities. We propose that representation of ordinal associations between numerical symbols is one important factor that underpins this link. We show that individual variability in symbolic number-ordering ability strongly predicts performance on complex mental-arithmetic tasks even when controlling for several competing factors, including approximate number acuity. Crucially, symbolic number-ordering ability fully mediates the previously reported relation between approximate number acuity and more complex mathematical skills, suggesting that symbolic number-ordering may be a stepping stone from approximate number representation to mathematical competence. These results are important for understanding how evolution has interacted with culture to generate complex representations of abstract numerical relationships. Moreover, the finding that symbolic number-ordering ability links approximate number acuity and complex math skills carries implications for designing math-education curricula and identifying reliable markers of math performance during schooling.     

Life skills development in physical education: A self-determination theory-based investigation across the school term

ObjectivesGrounded in self-determination theory (SDT), the main aim of this study was to examine the longitudinal associations between teacher autonomy support, students’ basic psychological need satisfaction and life skills development in physical education (PE).DesignThis study employed a two-wave longitudinal research design.MethodStudents (N = 266, Mage = 12.94 years, SD = 0.70) completed measures assessing perceived autonomy-supportive teaching, need satisfaction (autonomy, competence, and relatedness), and life skills development in PE (teamwork, goal setting, social skills, problem solving and decision making, emotional skills, leadership, time management, and interpersonal communication). Data collections took place during week 6 (timepoint 1; T1) and week 15 (timepoint 2; T2) of the autumn school term.ResultsCross-lagged panel analyses showed that T1 teacher autonomy support did not significantly predict students’ three basic psychological needs, total need satisfaction or life skills development at T2. Students’ T1 total need satisfaction positively predicted their development of all eight life skills at T2. Additionally, students’ T1 autonomy satisfaction positively predicted their teamwork, social skills, emotional skills, leadership, and interpersonal communication skills at T2, T1 competence satisfaction positively predicted students’ teamwork skills at T2, and students’ T1 relatedness satisfaction positively predicted their social skills at T2.ConclusionsProviding partial support for SDT, the findings highlighted that satisfaction of students’ three basic psychological needs had some positive effects on students’ life skills development in PE. As such, a climate that satisfies students’ basic psychological needs should help to develop their life skills in PE.     

Assessment of children's social skills: A review of methods

Social skills of children is a topic receiving increasing attention, particularly from clinical researchers. The present paper reviews methods that have been used to assess children's social skills. Four methods are identified and described: sociometric instruments, behavioral observations, teacher reports, and child self-reports. Their relationships to one another are examined in terms of predictive, concurrent, and construct validity. It appears that the social skills construct is in need of basic development if it is to have any clinical utility. It is suggested that future research utilize knowledge from fields closely related to clinical psychology (e.g., developmental and social psychology) and methods of assessment from traditional test theory.     

Distinct Pathways From Parental Beliefs and Practices to Children’s Numeric Skills

It is imperative to identify contextual factors contributing to the development of early math skills, considering their role in later academic achievement. To pursue this goal, the present study investigated the paths connecting parental beliefs and practices during the preschool years to children’s numeric skills at the end of kindergarten (N = 98). Results were consistent with theoretical predictions of specific relations between particular types of parental input and different aspects of number knowledge. Direct math learning activities mediated the relation between parental beliefs and children’s number identification skills. Daily activities involving quantitative components mediated the relation between parental beliefs and children’s numerical magnitude understanding. Both types of activities predicted arithmetic skills that integrate the basic aspects of symbolic number knowledge. These findings contribute to developmental theory by specifying how characteristics of children’s environments are related to particular aspects of their development, which is critical for informing intervention work to improve early math skills.     

Numerical predictors of arithmetic success in grades 1–6

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1–6. In grades 1–2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing.     

Continuity and change in children's longitudinal neural responses to numbers

Human children possess the ability to approximate numerical quantity nonverbally from a young age. Over the course of early childhood, children develop increasingly precise representations of numerical values, including a symbolic number system that allows them to conceive of numerical information as Arabic numerals or number words. Functional brain imaging studies of adults report that activity in bilateral regions of the intraparietal sulcus (IPS) represents a key neural correlate of numerical cognition. Developmental neuroimaging studies indicate that the right IPS develops its number‐related neural response profile more rapidly than the left IPS during early childhood. One prediction that can be derived from previous findings is that there is longitudinal continuity in the number‐related neural responses of the right IPS over development while the development of the left IPS depends on the acquisition of numerical skills. We tested this hypothesis using fMRI in a longitudinal design with children ages 4 to 9. We found that neural responses in the right IPS are correlated over a 1–2‐year period in young children whereas left IPS responses change systematically as a function of children's numerical discrimination acuity. The data are consistent with the hypothesis that functional properties of the right IPS in numerical processing are stable over early childhood whereas the functions of the left IPS are dynamically modulated by the development of numerical skills.     

Hyperlexia profiles

Two hyperlexic individuals were tested on reading outcome measures and on basic skills shown to be critical in reading acquisition. Results suggested distinct pathways to superior word recognition skills that can be described under a contemporary model of skilled reading, with differential acquisition of basic skills; superior word recognition skill was associated in both cases with specialized development in one basic area, that of orthographic processing. Results supported an asset rather than a deficit analysis of hyperlexia: Rather than assimilating to reading pathology (dyslexia) subtypes, hyperlexia was seen to be accompanied by assets that are absent in dyslexic profiles.     

Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals

In recent years, there has been an increasing focus on the role played by basic numerical magnitude processing in the typical and atypical development of mathematical skills. In this context, tasks measuring both the intentional and automatic processing of numerical magnitude have been employed to characterize how children’s representation and processing of numerical magnitude changes over developmental time. To date, however, there has been little effort to differentiate between different measures of ‘number sense’. The aim of the present study was to examine the relationship between automatic and intentional measures of magnitude processing as well as their relationships to individual differences in children’s mathematical achievement. A group of 119 children in 1st and 2nd grade were tested on the physical size congruity paradigm (automatic processing) as well as the number comparison paradigm to measure the ratio effect (intentional processing). The results reveal that measures of intentional and automatic processing are uncorrelated with one another, suggesting that these tasks tap into different levels of numerical magnitude processing in children. Furthermore, while children’s performance on the number comparison paradigm was found to correlate with their mathematical achievement scores, no such correlations could be obtained for any of the measures typically derived from the physical size congruity task. These findings therefore suggest that different tasks measuring ‘number sense’ tap into different levels of numerical magnitude representation that may be unrelated to one another and have differential predictive power for individual differences in mathematical achievement.     

Assessing therapeutic problem solving skills: Empirical analysis of a measuring operation

Employment of caregivers as trainers is an imperative in the training and treatment of mentally retarded persons. Besides being taught specific behavior modification skills, these paraprofessional trainers have to obtain a set of general skills in order to adjust their specific skills to new clients, situations, and behaviors across time. Empirical research on the characteristics of therapeutic problem-solving skills are scarce. This may be due to a reluctance of behavior researchers against including cognitive factors in the analysis of behavior influence. However, the development of basic knowledge on the existence of therapeutic problem-solving skills should be one of the primary research goals. This article describes the development and application of four scales assumed to be representative of an important set of general skills—therapeutic problem-solving skills. By means of these four scales 21 caregivers were evaluated before and after extensive training. A multifaceted measuring operation is employed with the main objective of empirically testing the dimensionality of problem-solving skills. Rater consistency and individual differences in change from pre- to post-training level are also uncovered. It is concluded that the four scales of therapeutic skills, largely reflect the same underlying concept of a rather general therapeutic problem-solving skill. Discussion of the findings also pointed to future research.