(1998). Human cognitive abilities: A survey of factor analytic studies. Gifted and Talented International: Vol. 13, No. 2, pp. 97-98.

Human cognitive abilities: A survey of factor analytic studies

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The Cambridge Handbook Of The Learning Sciences

The purpose of this meta-analysis was to determine the relation between mathematics and working memory (WM) and to identify possible moderators of this relation including domains of WM, types of mathematics skills, and sample type. A meta-analysis of 110 studies with 829 effect sizes found a significant medium correlation of mathematics and WM, r = .35, 95% confidence interval [.32, .37]. Moderation analyses indicated that mathematics showed comparable association with verbal WM, numerical WM, and visuospatial WM. Word-problem solving and whole-number calculations showed the strongest relation with WM whereas geometry showed the weakest relation with WM. The relation between WM and mathematics was stronger among individuals with mathematics difficulties that are associated with other disorders or cognitive deficits compared with that among typically developing individuals and individuals with only mathematics difficulties. The implications of these findings with respect to mathematics instruction and WM training are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved)

A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics

The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the within domain analyses, all of the measures formed single factors at each age, suggesting consistent, unitary structures across this age range. Yet, as in previous work, the 2 domains were highly correlated, both in terms of overall composite score and pairwise comparisons of individual tasks. When both spatial and mathematics scores were submitted to the same factor analysis, the 2 domain specific factors again emerged, but there also were significant cross-domain factor loadings that varied with age. Multivariate regressions replicated the factor analysis and further revealed that mental rotation was the best predictor of mathematical performance in kindergarten, and visual-spatial working memory was the best predictor of mathematical performance in sixth grade. The mathematical tasks that predicted the most variance in spatial skill were place value (K, 3rd, 6th), word problems (3rd, 6th), calculation (K), fraction concepts (3rd), and algebra (6th). Thus, although spatial skill and mathematics each have strong internal structures, they also share significant overlap, and have particularly strong cross-domain relations for certain tasks. (PsycINFO Database Record

https://psycnet.apa.org/journals/xge/145/9/1206.pdf

Separate but correlated: The latent structure of space and mathematics across development.

Understanding of numerical development is growing rapidly, but the volume and diversity of findings can make it difficult to perceive any coherence in the process. The integrative theory of numerical development posits that a coherent theme does exist—progressive broadening of the set of numbers whose magnitudes can be accurately represented—and that this theme unifies numerical development from infancy to adulthood. From this perspective, development of numerical representations involves four major acquisitions: (a) representing magnitudes of nonsymbolic numbers increasingly precisely, (b) linking nonsymbolic to symbolic numerical representations, (c) extending understanding to increasingly large whole numbers, and (d) extending understanding to all rational numbers. Thus, the mental number line expands rightward to encompass larger whole numbers, leftward to encompass negatives, and interstitially to include fractions and decimals.

An Integrative Theory of Numerical Development

The study assessed the relations among acuity of the inherent approximate number system (ANS), performance on measures of symbolic quantitative knowledge, and mathematics achievement for a sample of 138 (64 boys) preschoolers. The Weber fraction (a measure of ANS acuity) and associated task accuracy were significantly correlated with mathematics achievement following one year of preschool, and predicted performance on measures of children's explicit knowledge of Arabic numerals, number words, and cardinal value, controlling for age, sex, parental education, intelligence, executive control, and preliteracy knowledge. The relation between ANS acuity, as measured by the Weber fraction and task accuracy, and mathematics achievement was fully mediated by children's performance on the symbolic quantitative tasks, with knowledge of cardinal value emerging as a particularly important mediator. The overall pattern suggests that ANS acuity facilitates the early learning of symbolic quantitative knowledge and indirectly influences mathematics achievement through this knowledge.

Acuity of the approximate number system and preschoolers’ quantitative development.

Visuospatial competencies are related to performance in mathematical domains in adulthood, but are not consistently related to mathematics achievement in children. We confirmed the latter for first graders and demonstrated that children who show above average first-to-fifth grade gains in visuospatial memory have an advantage over other children in mathematics. The study involved the assessment of the mathematics and reading achievement of 177 children in kindergarten to fifth grade, inclusive, and their working memory capacity and processing speed in first and fifth grade. Intelligence was assessed in first grade and their second to fourth grade teachers reported on their in-class attentive behavior. Developmental gains in visuospatial memory span (d = 2.4) were larger than gains in the capacity of the central executive (d = 1.6) that in turn were larger than gains in phonological memory span (d = 1.1). First to fifth grade gains in visuospatial memory and in speed of numeral processing predicted end of fifth grade mathematics achievement, as did first grade central executive scores, intelligence, and in-class attentive behavior. The results suggest there are important individual differences in the rate of growth of visuospatial memory during childhood and that these differences become increasingly important for mathematics learning.

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Developmental gains in visuospatial memory predict gains in mathematics achievement.

The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects and domain-specific effects were indexed by prior grade mathematics achievement and mathematical cognition measures of prior grade number knowledge, addition skills, and fraction knowledge. Use of functional data analysis enabled grade-by-grade estimation of overall domain-general and domain-specific effects on subsequent mathematics achievement, the relative importance of individual domain-general and domain-specific variables on this achievement, and linear and non-linear across-grade estimates of these effects. The overall importance of domain-general abilities for subsequent achievement was stable across grades, with working memory emerging as the most important domain-general ability in later grades. The importance of prior mathematical competencies on subsequent mathematics achievement increased across grades, with number knowledge and arithmetic skills critical in all grades and fraction knowledge in later grades. Overall, domain-general abilities were more important than domain-specific knowledge for mathematics learning in early grades but general abilities and domain-specific knowledge were equally important in later grades.

Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study.

The current study aims to explore predictors that independently contribute to high school teacher use of technology in general and for different teaching purposes (student-centered and traditional). High school teachers (N = 928) responded to a survey that consisted of measures in several categories: (1) teachers’ background variables, (2) teachers’ pedagogical beliefs, (3) teachers’ attitudes or beliefs towards technology, (4) teachers’ perceived training effectiveness. A series of multilevel models were used to explore the independent effects of these factors on teacher use of technology in general and for different teaching purposes. The results showed that teachers’ technology self-efficacy was a significant predictor of teacher use of technology. More importantly, teachers’ instructional approach, openness towards technology, and perceived teaching training effectiveness were more salient when predicting teacher use technology to support student-centered teaching than when predicting teacher use technology to support traditional teaching. Our findings suggest that teachers’ pedagogical readiness is as important as technological readiness for teachers to integrate technology in teaching to serve more advanced teaching purposes. This study has important implications for organizing professional learning experiences for teachers.

Predicting High School Teacher Use of Technology: Pedagogical Beliefs, Technological Beliefs and Attitudes, and Teacher Training

A previous study showed that gains in visuospatial memory from first to fifth grade predicted end-of-fifth grade mathematics but not reading achievement, controlling other factors. In this follow up study, these relations were assessed from sixth to ninth grade, inclusive (n = 145). The results showed that growth in visuospatial memory across the elementary school years was related to growth in mathematics achievement after fifth grade, controlling intelligence, the central executive and phonological memory components of working memory, in-class attentive behavior, parental education, and fifth grade mathematics achievement. As found for fifth grade, this relation was not found for reading achievement after fifth grade. In total, the results suggest that visuospatial memory has a unique influence on ease of learning some types of mathematics and that this influence becomes more important across successive grades.

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Yaoran Li

Papers

Acuity of the approximate number system and preschoolers’ quantitative development.

Developmental gains in visuospatial memory predict gains in mathematics achievement.

Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study.

Predicting High School Teacher Use of Technology: Pedagogical Beliefs, Technological Beliefs and Attitudes, and Teacher Training

Children's visuospatial memory predicts mathematics achievement through early adolescence.