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This study investigated the direct and indirect effects of general intelligence and 7 broad cognitive abilities on mathematics achievement. Structural equation modeling was used to investigate the simultaneous effects of both general and broad cognitive abilities on students' mathematics achievement. A hierarchical model of intelligence derived from the Cattell-Horn-Carroll (CHC) taxonomy of intelligence was used for all analyses. The participants consisted of 4 age-differentiated subsamples (ranging from ages 5 to 19) from the standardization sample of the Woodcock-Johnson III (WJ III; Woodcock, McGrew, & Mather, 2001). Data from each of the 4 age-differentiated subsamples were divided into 2 data sets. At each age level, one data set was used for model testing and modification, and a second data set was used for model validation. The following CHC broad cognitive ability factors demonstrated statistically significant direct effects on the mathematics achievement variables: Fluid Reasoning, Crystallized Intelligence, and Processing Speed. In contrast, across all age levels, the general intelligence factor demonstrated indirect effects on the mathematics achievement variable. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

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... Although some single study found no significant e ect of intelligence (e.g. Jones & Byrnes), most studies demonstrated a significant relationship between intelligence ( Floyd et al., 2003;Kucian & von Aster, 2015;Primi et al., 2010;Roth et al., 2015;Taub et al., 2008) and academic performance. Finally, some researchers focused on non-cognitive predictors (Schoenfeld, 1983) such as motivation (Deci & Ryan, 2008a&b;Froiland & Worrell, 2016;Ryan & Deci, 2000) and well-being or positive and negative a ect (Awang-Hashim et al., 2015;Diener, 1984;Diener et al., 2005;McLeod, 1990;McLeod & Adams, 1989;Peixoto et al., 2016;Pekrun et al., 2006). ...

... The study also included propensity factors, such as intelligence (Floyd et al., 2003;Kucian & von Aster, 2015;Primi et al., 2010;Roth et al., 2015;Taub et al., 2008), positive and negative a ect related to mathematics (Peixoto et al., 2016;Pekrun, 2006) and motivation (Nurmi & Aunola, 2005;Pantziara & Philippou, 2014;Steinmayr & Spinath, 2009). ...

... These findings are in contrast with the findings of Steinmayr and Spinath (2009) who found that higher motivation resulted in better math results. Intelligence was a significant predictor for math fluency and calculation accuracy, confirming previous studies (Baten & Desoete, 2018;Floyd et al., 2003;Kucian & von Aster, 2015;Primi et al., 2010;Roth et al., 2015;Taub et al., 2008). In this study there was a significant e ect of positive a ect on math fluency and a significant e ect of negative a ect on calculation accuracy, where in a previous study we found the reversed picture (Baten & Desoete, 2018). ...

Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive affect for arithmetic fluency and negative affect for calculation accuracy) predicted math learning, and pointed to the importance of the propensity factors. We have to be careful not to interpret gender differences, since this is a social construct, our analyses pointed to the relevance of including antecedent factors in the model as well . The Implications of the study for math learning will be discussed below.

... EFs are strong predictors of academic achievement throughout childhood and adolescence (Best et al., 2011;Cowan, 2014;Ferrer et al., 2007;Ferrer & McArdle, 2004;Richland et al., 2007;St Clair-Thompson & Gathercole, 2006). This relation has been particularly well-documented in the domain of mathematics: children who score higher on EF assessments also typically score higher on lab-based and school-based math assessments (Bull & Scerif, 2001;Fuchs et al., 2012;Geary, 2011;Green et al., 2017;Purpura & Ganley, 2014;Richland et al., 2007;St Clair-Thompson & Gathercole, 2006;Taub et al., 2008). Some of the ways EFs support math achievement include helping learners maintain relevant knowledge in mind (working memory), inhibit inappropriate strategies (inhibitory control), and switching between different strategies (cognitive flexibility) (Bull & Lee, 2014;Cragg & Gilmore, 2014). ...

... In parallel to the research linking canonical EFs to math achievement, a number of studies have demonstrated that reasoning ability predicts both current and future math abilities (Fuchs et al., 2006;Green et al., 2017;Taub et al., 2008). Mathematical thinking is inherently relational (DeWolf et al., 2015;Miller Singley & Bunge, 2014;Richland et al., 2007). ...

... Given the inherently relational nature of many mathematical concepts, it is not surprising that relational thinking contributes to math performance throughout grade school. Our findings are consistent with previous work demonstrating that reasoning relates to math achievement (Fuchs et al., 2006;Green et al., 2017;Taub et al., 2008), and suggest, specifically, that the relational thinking component of reasoning supports mathematical thinking. In addition, our findings add to the growing body of literature that suggests that relational thinking is particularly important for mathematical concepts like fractions and decimals (DeWolf et al., 2015;Kalra et al., 2020). ...

Relational thinking, the ability to represent abstract, generalizable relations, is a core component of reasoning and human cognition. Relational thinking contributes to fluid reasoning and academic achievement, particularly in the domain of math. However, due to the complex nature of many fluid reasoning tasks, it has been difficult to determine the degree to which relational thinking has a separable role from cognitive processes collectively known as executive functions (EFs). Here, we used a simplified reasoning task to better understand how relational thinking contributes to math achievement in a large, diverse sample of elementary and middle school students (N = 942). Students also performed a set of ten adaptive EF assessments, as well as tests of math fluency and fraction magnitude comparison. We found that relational thinking was significantly correlated with each of the three EF composite scores previously derived from this dataset, albeit no more strongly than they were with each other. Further, relational thinking predicted unique variance in students’ math fluency and fraction magnitude comparison scores over and above the three EF composites. Thus, we propose that relational thinking be considered an EF in its own right as one of the core mid-level cognitive abilities that supports cognition and goal-directed behavior.

... When judging academic performance, the teacher relies on a larger amount of informationin the context of the Brunswik's (1955) lens model, it can be said that he or she has more proximal cues available: among others, the student's cognitive abilities, his or her motivation, non-cognitive determinants of academic success, etc. which increases the ability of accurate prediction. However, note that we used the test of mathematical reasoning as math achievement, which is strongly related to fluid intelligence (Taub et al., 2008). Generalizability of our results is therefore questionable; the result could differ even with an achievement test based more heavily on mathematical knowledge. ...

... In this regard, TIM 3-5 is similar to subtests of complex batteries measuring academic performance that also comprise mathematical problems of a similar type, such as the subtest Applied Problems of Woodcock-Johnson IV Tests of Achievement (Schrank et al., 2014). On the other hand, the results in fluid intelligence tests are in general very closely connected with mathematical performance (Taub et al., 2008), especially in word problems of the Applied Problems type where correlation typically reaches the values of 0.7 and more (e.g. Green et al., 2017). A similar strong relationship was observed between the CFT 20-R and TIM 3-5 tests in our study (r = 0.685, p <.001). ...

The aim of the study was to determine the factors affecting teacher’s judgment accuracy while estimating performance in tests of cognitive abilities and academic achievement of students, and on which student abilities the evaluation was based on. The study included 223 students (38% females) of the fourth grade who were administered the test of cognitive abilities CFT 20-R and the test of academic (mathematical) achievement TIM3–5. Their performance was estimated by 10 teachers (8 females) using a 9-point scale and percentile. Furthermore, for a part of the children (n = 130), 6 of these teachers determined the probability with which the child would correctly solve two particular items of test TIM3–5. The most accurate method of estimation is the percentile rating, both for the cognitive abilities (r = .56) and the academic achievement (r = .63). The length of teacher experience and the level of evaluated student ability has no effect on the accuracy of judgment. The student’s gender has no effect on the accuracy of estimation or the level of ascribed ability. Teachers tended to underestimate students in a moderately difficult item of test TIM3–5, and overestimate in case of a difficult item. The study further presents a theoretical model in which the teacher’s impression of the student is based on the student’s cognitive abilities and academic achievement. Empirical verification of this model has shown that the basis for teacher’s judgment is primarily the student’s intelligence, which is manifested indirectly in the student’s academic achievement.

... For academic skills, the focus was on literacy and maths. For cognitive skills, assessments of processing speed, working memory, executive function, and nonverbal reasoning were included, all of which have been previously linked to academic performance in both typical and atypical learners (Altemeier et al., 2008;Booth et al., 2010;Gathercole et al., 2004;Geary, 2011;Green et al., 2017;Holmes et al., 2020;Mayes & Calhoun, 2007;Peng & Fuchs, 2016;Taub et al., 2008;Yeniad et al., 2013). To my knowledge, this was the first application of network science to cognitive-academic interrelationships in learners of different abilities. ...

Neurodevelopmental difficulties can have a substantial impact on children’s lives and often have lasting effects in adult life. The scientific study of the causes and consequences of neurodevelopmental difficulties has arguably been slowed by the overreliance on case-control designs, which fail to capture the overlap across different neurodevelopmental disorders and the heterogeneity within them. The work presented in this thesis applies a transdiagnostic framework to large developmental datasets to advance our understanding of neurodevelopmental diversity. Three empirical studies were conducted with a cohort of children with a range of diagnosed and undiagnosed needs. The first study explored the interrelationships between language, communication, cognitive, and behavioural difficulties using network science (Chapter I). A subsequent study investigated how children vary in their relative strengths and weakness across these domains, and how this variation relates to socio-emotional functioning, academic skills, and neural white matter organisation (Chapter II). The third study compared the pattern of interrelationships between cognitive and academic skills observed in this cohort to those found in a community sample (Chapter III). Collectively, the studies presented in this thesis demonstrate the value of studying neurodevelopmental diversity transdiagnostically. I argue that the field needs to move away from studying groups of children with restricted difficulties and dedicate more effort towards understanding how multiple developmental factors interact to shape individual trajectories over developmental time.

... Furthermore, a large number of studies have found that general intelligence (e.g., Floyd et al., 2003;Taub et al., 2008), inhibitory control ability (e.g., Bull & Lee, 2014;Kroesbergen et al., 2009) and working memory (e.g., Hornung et al., 2014;Passolunghi & Costa, 2019;Toll et al., 2016;Xenidou-Dervou et al., 2014) have significant effects on preschool children's mathematical ability. That is, it is necessary to control these general cognitive abilities to examine the effect of ANS training on the mathematics ability of preschool children. ...

Recent studies show that comparison or arithmetic training in the approximate number system (ANS) can improve the early mathematics ability of preschool children. However, no studies have compared the training effects of ANS comparison training with those of ANS arithmetic training on the early mathematics ability of preschool children. The current study pseudorandomly assigned 87 children aged 4–5 years to one of three training groups (the ANS comparison, ANS arithmetic, and control groups) for 4 weeks of training. The results showed that compared with the control group, the ANS comparison training and ANS arithmetic training equally improved the ANS acuity and informal mathematics ability of preschool children. In addition, the study found that there may be a bidirectional causal relationship between ANS and mathematics in preschoolers, but this relationship needs to be further investigated using longitudinal studies. Taken together, these findings emphasize the importance of ANS-based training in improving preschoolers' ANS acuity and informal mathematics ability before formal school enrollment.

... As the separated/ homogenous format demonstrated a substantial congruency effect, we assume that the RTs in separated formats may reflect general processing speed or the speed of estimating visual cues rather than the speed of numerosity estimation. Thus, general processing speed may explain the variance in math performance in addition to accuracy (Geary, 2011;Taub, Keith, Floyd, & McGrew, 2008). ...

... Psychometric intelligence, or general cognitive ability, is one of the most important sources of the individual differences in learning performance [11,12]. It is a powerful predictor of the achievement across different academic domains [13,14] and individual behavior; in particular, the strategic behavior required for day-to-day decision-making processes [15]. Cognitive abilities are also associated with wages, education and employment [16]. ...

Adolescents face many barriers on the path towards a STEM profession, especially girls. We examine the gender stereotypes, cognitive abilities, self-perceived ability and intrinsic values of 546 Russian school children from 12 to 17 years old by sex and STEM preferences. In our sample, STEM students compared to no-STEM have higher cognitive abilities, intrinsic motivation towards math and science, are more confident in their math abilities and perceive math as being easier. Boys scored higher in science, math and overall academic self-efficacy, intrinsic learning motivation and math’s importance for future careers. Meanwhile, girls displayed higher levels of gender stereotypes related to STEM and lower self-efficacy in math. A network analysis was conducted to identify the structure of psychological traits and the position of the stem-related stereotypes among them. The analysis arrived at substantially different results when adolescents were grouped by sex or preference towards STEM. It also demonstrated that gender stereotypes are connected with cognitive abilities, with a stronger link in the no-STEM group. Such stereotypes play a more important role for girls than boys and, jointly with the general self-efficacy of cognitive and academic abilities, are associated with the factors that distinguish groups of adolescents in their future careers.

There has been little research investigating the predictive validity of modern intelligence tests for racially and ethnically diverse students. The validity of test score interpretation within educational and psychological assessment assumes that test scores predict educationally relevant phenomena equally well for individuals, regardless of group membership (American Educational Research Association et al., 2014; Messick, 1995; Warne et al., 2014). We used multiple group latent variable structural equation modeling (SEM) to investigate Cattell-Horn-Carroll general (g) and broad cognitive abilities on reading and mathematics achievement and whether these differed between racial (African American, Asian, and Caucasian) and ethnic (Hispanic, non-Hispanic) children and adolescents within the Woodcock-Johnson IV norming sample (N = 3127). After establishing construct equivalence across racial and ethnic groups, supporting the consistent calculation of composite scores regardless of group membership, we then examined the predictive validity of intelligence on achievement. After controlling for parent education, findings suggested two instances of differential predictive relations: (a) general intelligence had larger influences on basic reading skills for Caucasians when compared to Asian peers, and (b) comprehension-knowledge had larger influences on basic reading skills for Asians when compared to Caucasian peers. The overall pattern of findings suggests there is little to no predictive bias with the WJ IV. However, the findings indicate that when latent mean differences exist (after establishing strong factorial invariance), then bias will be introduced into the estimation of regression parameters used to identify differential predictive validity. Thus, even when measurement invariance is supported, differential prediction bias is inevitable when there are mean differences in the scores used as predictors. Future test bias research should consider latent ability differences and how that may impact findings of bias, and possibly, socioeconomic status-related indicators when assessing for measurement or prediction bias in intelligence and achievement tests.

The article provides an overview of modern works devoted to the study of cognitive predictors of academic success. The general patterns of forecasting are revealed: the most powerful and universal predictor of academic success at different stages of school education is psychometric intelligence; creativity is less significant and rather unstable. It is argued that these patterns are poorly traced at the level of preschool education. Particular cognitive functions are significant for predicting the future educational achievements of preschoolers: information processing speed, visual perception (in combination with motor functions), short-term memory, and attention. Spatial abilities have a certain prognostic potential, though reasoning in preschoolers is not a strong predictor of academic success; executive functions have the greatest predictive power. It is noted that the general patterns in predicting the academic success of students can be traced in elementary school: the predictive potentials of psychometric intelligence are revealed, the power of individual cognitive abilities (in particular, spatial abilities) increases, the contribution of executive functions to the prediction decreases. The general tendency for non-cognitive factors (educational motivation, some personality traits) to increase with age also begins to appear in elementary school.

Results of recent research by Kranzler and Keith (1999) raised important questions concerning the construct validity of the Cognitive Assessment System (CAS; Naglieri & Das, 1997), a new test of intelligence based on the planning, attention, simultaneous, and sequential (PASS) processes theory of human cognition. Their results indicated that the CAS lacks structural fidelity, leading them to hypothesize that the CAS Scales are better understood from the perspective of Cattell-Horn-Carroll (CHC) theory as measures of psychometric g, processing speed, short-term memory span, and fluid intelligence/broad visualization. To further examine the constructs measured by the CAS, this study reports the results of the first joint confirmatory factor analysis (CFA) of the CAS and a test of intelligence designed to measure the broad cognitive abilities of CHC theory - the Woodcock-Johnson Tests of Cognitive Abilities-3rd Edition (WJ III; Woodcock, McGrew, & Mather, 2001). In this study, 155 general education students between 8 and 11 years of age (M = 9.81) were administered the CAS and the WJ III. A series of joint CFA models was examined from both the PASS and the CHC theoretical perspectives to determine the nature of the constructs measured by the CAS. Results of these analyses do not support the construct validity of the CAS as a measure of the PASS processes. These results, therefore, question the utility of the CAS in practical settings for differential diagnosis and intervention planning. Moreover, results of this study and other independent investigations of the factor structure of preliminary batteries of PASS tasks and the CAS challenge the viability of the PASS model as a theory of individual differences in intelligence.

Wechsler's beliefs about the nature of human intelligence and its measurement have profoundly influenced contemporary theory and practice. He encouraged interpretations not only of more global intellective indices, such as IQ but encouraged as well the search for pathognomonic meaning in patterns of underlying, more specific, subtest scores. This article examines the evidence that concerns the interpretation of Wechsler and similar tests as measures of specific rather than global ability. Popular practices that involve use of subtests for both intraindividual and interindividual assessment are viewed in the light of empirical research, and recommendations are presented.

The predictive validity of cognitive constructs taken from Cattell-Horn's Gf-Gc Model was examined. Gf-Gc cognitive constructs were measured using the Woodcock-Johnson-Revised Tests of Cognitive Ability; they include processing speed, fluid reasoning, acculturation-knowledge, short-term memory, long-term retrieval, auditory processing, and visual processing. Scores from the Comprehensive Test of Basic Skills were used as the criterion measures for 104 elementary, middle, and high school students. Using multiple regression equations, various combinations of the Comprehension-Knowledge, Fluid Reasoning, and Processing Speed variables were consistently found to be the best predictors of achievement. Multiple Rs ranged from the .60s to .70s. Results provide evidence for the importance of cognitive constructs for predicting achievement and are potentially useful for understanding program planning and Aptitude x Treatment Interaction research.

Three cognitive factors have been suggested as responsible for children's learning problems in simple arithmetic: (a) the encoding of numbers, (b) the efficiency of operation execution, and (c) strategies for carrying out the operations. The study reported here compares these cognitive components across three groups of Grade 5 children: a group having problems in arithmetic, a group having problems in reading, and a control group. The method of subtraction is applied to response times in various arithmetic tasks to yield measures of the cognitive components of single digit addition and subtraction. Results indicate that children with arithmetic learning problems are characterized by very slow operation execution; there is less support for inefficient number encoding, and none for inappropriate strategies. The implications for the design of remedial instruction and for further studies of learning problems are discussed.