ArticlePDF Available

Effects of General and Broad Cognitive Abilities on Mathematics Achievement

DOI:10.1037/1045-3830.23.2.187
Authors:
Gordon E. Taub at University of Central Florida
Gordon E. Taub
Randy Granville Floyd at The University of Memphis
Randy Granville Floyd
Timothy Z. Keith at University of Texas at Austin
Timothy Z. Keith
Kevin McGrew at Institute for Applied Psychometrics
Kevin McGrew
  • Institute for Applied Psychometrics
Download full-text PDF
Read full-text
Download citation

Abstract

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)
Content uploaded by Kevin McGrew
Author content
All content in this area was uploaded by Kevin McGrew
Content may be subject to copyright.
A preview of the PDF is not available
  • A preview of this full-text is provided by American Psychological Association.
  • Learn more
Preview content only
Content available from School Psychology Quarterly
This content is subject to copyright. Terms and conditions apply.
... Similarly, sustained attention highly correlates with reasoning (Buehner et al., 2006). In the same way, processing speed is a predictor of reasoning (Kail et al., 2015) and one of the most determinant factors in the acquisition of mathematical skills (Floyd et al., 2003), which have a strong relationship with both performance in this subject and in computational automaticity (Taub et al., 2008). Besides, people with musical studies show significantly higher scores in fluid cognition than those without them, fluid intelligence being understood as the ability to think abstractly and to solve problems (Meyer et al., 2020). ...
... As reinforcement to these arguments, we appeal to the results of previous research showing that musical training improves the general intelligence of adolescents (Rickard et al., 2012) and mathematics (Mehr et al., 2013). Ultimately, we believe that the music employed, including adolescents' musical preferences, has had a role in increasing sustained attention, processing speed, and fluid cognition, which have in turn favored mathematical performance (Buehner et al., 2006;Floyd et al., 2003;Kail et al., 2015;Meyer et al., 2020;Schrank & Wendling, 2018;Taub et al., 2008). Furthermore, from these results, we support the hypothesis of Thompson et al. (2001) that the underlying mechanism of the effects of music listening on academic performance is due to increased arousal, which then leads to improved cognitive performance. ...
Eficacia de la escucha musical en el rendimiento matemático
Article
  • Sep 2023
Si bien numerosos estudios han mostrado que la música de fondo mejora el rendimiento académico de adolescentes, pocos han contrastado resultados a partir de sus preferencias musicales o de composiciones de Mozart. Participaron en el estudio 185 adolescentes pertenecientes a los cursos de 1º a 4º de Educación Secundaria Obligatoria con edades comprendidas entre 12 y 17 años con una (EM = 13,63; DS = 1,26) de las cuales el 52,4% eran chicas. Se realizó una asignación aleatoria de los grupos a una de dos condiciones experimentales: escuchar su preferencia musical o composiciones de Mozart mientras desarrollaban una prueba matemática. Los resultados muestran que los chicos obtienen significativamente mejores resultados en matemáticas que las chicas. Asimismo, se aprecia una disminución en el tiempo de ejecución de tareas matemáticas y que los estudiantes con rendimiento más bajo obtienen mayor beneficio con música. Igualmente, en el grupo que escuchó su preferencia musical se produjo una mayor mejora en las chicas y en cambio, en el que escuchó música de Mozart esta se manifestó en los chicos. Se considera que la optimización de los niveles de excitación ha mejorado el enfoque atencional, lo que a su vez ha incrementado la velocidad de procesamiento haciendo que aumentara la eficiencia para seleccionar información y encontrar respuestas más acertadas, redundando, de este modo, en el rendimiento matemático. Asimismo, se presta especial atención a que la escucha de música durante el desempeño de tareas matemáticas ha ayudado en mayor medida al alumnado con un pobre rendimiento matemático. A través de este artículo se manifiesta, debido a su importancia, una posición en pro de un mayor reconocimiento y presencia musical a nivel curricular en Educación Secundaria Obligatoria.
View
... Further, the present study did not assess whether the outcomes examined had any impact on the academic performance of students who participated in the Brain Balance programme. However, the outcomes examined here (sensory motor skills, attention and cognitive performance) have been shown in previous studies to influence and be predictive of academic achievement, including in maths, reading comprehension and writing (Bull et al., 2008;Checa & Rueda, 2011;Geertsen et al., 2016;Hajovsky et al., 2018;Khng & Ng, 2021;Rennie et al., 2014;Schmidt et al., 2017;Taub et al., 2008;Worthen, 2010). It would be useful for future studies of the Brain Balance programme in a school setting to examine pre-and post-programme scores on standardized academic tests, in order to elucidate whether program-related improvements in sensory motor skills, VADTRS scores and CBS cognitive performance translate to improvements in academic outcomes. ...
... Además, el presente estudio no evaluó si los resultados examinados tuvieron algún impacto en el rendimiento académico de los estudiantes que participaron en el programa Brain Balance. Sin embargo, los resultados examinados aquí (habilidades motoras sensoriales, atención y rendimiento cognitivo) han demostrado en estudios anteriores que influyen y son predictivos del rendimiento académico, incluso en matemáticas, comprensión lectora y escritura (Bull et al., 2008;Checa & Rueda, 2011;Geertsen et al., 2016;Hajovsky et al., 2018;Khng & Ng, 2021;Rennie et al., 2014;Schmidt et al., 2017;Taub et al., 2008;Worthen, 2010). Sería útil para futuros estudios del programa Brain Balance en un entorno escolar examinar las puntuaciones antes y después del programa en pruebas académicas estandarizadas, con el fin de dilucidar si las mejoras relacionadas con el programa en las habilidades motoras sensoriales, las puntuaciones VADTRS y el rendimiento cognitivo CBS se traducen en mejoras en los resultados académicos. ...
View
... Furthermore, children's non-verbal ability is known to play a role in mathematics achievement (e.g. Taub et al., 2008), and this was controlled for by measuring children's non-verbal reasoning skills. ...
Grade one single-digit addition strategies as predictors of grade four achievement in mathematics
Article
Full-text available
  • Nov 2023
Early detection of and relevant information on children’s mathematical difficulties is important to initiate targeted teaching and intervention. This study investigated the extent to which strategy use in single-digit addition provides additional predictive information about 61 grade one children’s (6-year-old) mathematical achievement 3 years later that is not available from a standardised mathematics achievement test. Four predictors available in year one (arithmetic strategy use, mathematical achievement, non-verbal reasoning skills and sex) explained 54% of the variation in grade four mathematics achievement. Arithmetic strategy use was the most important single predictor of year four mathematics achievement ( R ² = 30%) and explained an additional 12% variation if added to a model comprised by the three other year one predictors. This result suggests that systematically obtained measures of how young children solve single-digit arithmetic problems might provide useful information about their foundational number knowledge, which in turn may reveal how well they achieve later in school.
View
... Numerous academic studies have investigated the relationship between grade level and general cognitive ability as well as academic achievement (Boulanger, 1981;Fleming & Malone, 1983;Steinkamp & Maehr, 1983). As grade levels progress, the accumulation of academic knowledge increases, leading intelligence to be considered the strongest predictor of academic success (Gottfredson, 2002;Kuncel et al., 2004;Rosander et al., 2011;Taub et al., 2008). Laidra et al. (2007) emphasized a causal relationship between intelligence and achievement, revealing that the most powerful predictor of success at all levels of students is their general cognitive ability. ...
The Impact of Gender and Grade Level on Students' General Intelligence, Verbal Potential, Visual Potential, and Memory Capacity
Article
Full-text available
  • Jan 2023
This study investigates the impact of gender and grade level on students' general intelligence, verbal potential, visual potential, and memory capacity. The participants of the study consist of 4063 students who applied Anadolu University Center for Research and Practice for High Ability Education (EPTS) for intelligence test administration between the years 2017 and 2021. Of the total sample 2250 were male, 1813 were female. On the other hand, of the sample 1224 were preschool students, 1879 were primary school students and 960 were secondary school students. To determine the students' general intelligence, verbal potential, visual potential and memory capacity, Anadolu Sak Intelligence Scale (ASIS) was used. ASIS is the first intelligence test developed, standardized and normed in Turkey. To examine the impact of gender and grade level on students' general intelligence index (GIQ), verbal potential index (VEPI), visual potential index (VIPI), and memory capacity index (MCI), 2x3 ANOVA was carried out. The results showed that the joint interaction of gender and grade level variables significantly impacts all index scores except for VIPI (p<.05). In other words, gender and grade level variables together are determinants of GIQ, VEPI, and MCI scores. In conclusion, this study reveals that males and females exhibit differences in specific cognitive abilities. Furthermore, it is noteworthy that the averages of primary school students are lower than the averages of preschool students in general intelligence and in each of the indices (VEPI, VIPI, MCI). As a result of this study, males and females in different grade have different advantages.
View
... In a large prospective study of 70,000 students, it was found that general intelligence could explain up to 58.6% of the variation in performance on national tests at the age of 16 years (Deary et al., 2007). Fluid intelligence is part of general intelligence and is recognized as a causal factor when experiencing non-familiar situations in general (Valentin Kvist & Gustafsson, 2008;Watkins et al., 2007) and solving mathematical tasks in particular (Floyd et al., 2003;Taub et al., 2008). Ravens Advanced Progressive Matrices (APM) (Raven & Raven, 1991), which is the most common test for fluid intelligence, consists of 48 regular test items and 12 practice items. ...
Shifts in student attention on algorithmic and creative practice tasks
Article
Full-text available
  • Aug 2023
In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior during repetitive practice, an eye-tracking study was conducted with 50 upper secondary and university students. Their eye movements were analyzed to study how the two groups shifted their gaze both within and across 10 task sets. The results show that when a solution method was present, the students reread this every time they solved the task, while only giving minute attention to the illustration that carried information supporting mathematical understanding. Students who practiced with tasks without a solution method seemed to construct a solution method by observing the illustration, which later could be retrieved from memory, making this method more efficient in the long run. We discuss the implications for teaching and how tasks without solution methods can increase student focus on important mathematical properties.
View
... Individual differences like the Intelligence Quotient level remain one of the most significant factors towards students' achievements. It is evident from the literature that individual student achievement is highly related to intelligence (from r=.3 to r=0.7) (Brody 1997;Gustafsson and Undheim 1996;Sattler and Ryan 2009;Chamorro-Premuzic, Quiroga, and Colom 2009;Colom and Flores-Mendoza 2007;Deary et al. 2007;Gottfredson 2002;Jensen 1998;Kuncel, Hezlett, and Ones 2004;Kyttälä and Lehto 2008;Laidra, Pullmann, and Allik 2007;Lemos et al. 2014;Neisser et al. 1996;Primi, Ferrão, and Almeida 2010;Rosander, Bäckström, and Stenberg 2011;Taub et al. 2008;Agarwal et al. 2021). (Agarwal et al. 2021) specifically targeted this fact and found that intelligence is significantly related to academic achievements. ...
Determinants of Percentage Achievements of Public Primary School Students in Northern Pakistan
Article
Full-text available
  • Jan 2023
This study probes the socioeconomic and school background factors that may affect students' marks in primary schools in northern Pakistan. The data was collected from four parts of the province. The result confirms that free lunch is an influential academic booster if provided to lower groups of students; in some cases, the school is away from students. Adequate staff and adequate funds, too, have elevating effects on marks. Male parents are a means of more academic gain for male students and less for females. Internet at home is a better option. Recommendations are delineated at the end.
View
View
Reliable change in developmental outcomes of Brain Balance® participants stratified by baseline severity
Article
Full-text available
  • Aug 2023
The effects of comprehensive multimodal programs on developmental outcomes have not been well-studied. Emerging evidence suggests a possible role for the Brain Balance ® (BB) program, a multimodal training program, in serving as a nonpharmacologic approach to addressing cognitive, attentional, and emotional issues in youth. In this analysis, we examined the effects of 3 months of participation in the BB program on the outcomes of children and adolescents with developmental difficulties ( N = 4,041; aged 4–18 years; 69.7% male). Parent-rated scores on the Brain Balance–Multidomain Developmental Survey (BB-MDS) were used to assess six areas at baseline and post-program: (1) negative emotionality; (2) reading/writing difficulties; (3) hyperactive/disruptive behavior; (4) academic disengagement; (5) motor/coordination problems; and (6) social communication problems. To estimate change from pre- to post-program, we calculated effect size (Cohen’s d ) and the Reliable Change Index (RCI) for groups stratified by baseline severity. There was a very large effect size for the moderate/high severity ( d = 1.63) and extreme severity ( d = 2.08) groups, and a large effect size for the mild severity group ( d = 0.87). The average percentage of participants who observed reliable change over all BB-MDS domains was 60.1% (RCI CTT ) for extreme severity, 46.6% (RCI CTT ) for moderate/high severity, and 21.1% (RCI CTT ) for baseline mild severity. In additional assessments of primitive reflexes and sensory motor activity, students demonstrated significantly diminished primitive reflexes from pre- to post-participation and significant improvements in sensory motor skills including fine motor skills, gait and aerobic ability, proprioception, rhythm and timing, and eye-gaze stability. Overall, these results demonstrate improvements in primitive reflex integration and sensory motor skills, as well as statistically significant reliable change in emotionality, reading/writing, behavior, academic engagement, motor skills, and social communication in BB participants from pre- to post-program, with the probability and degree of change increasing as the participants’ baseline severity increases. These results contribute to the growing literature on the need for evidence-based nonpharmacologic approaches to addressing developmental issues. Future research with well-controlled designs, longitudinal follow-up, implementation across settings, and participant groups in which diagnoses are known, will help to more fully characterize the effects of the BB program.
View
Vliv kognitivních schopností na rozvoj přírodovědné gramotnosti u žáků prvního stupně základní školy
Thesis
Full-text available
  • May 2023
Tématem disertační práce je vliv kognitivních schopností na rozvoj přírodovědé gramotnosti u žáků prvního stupně základní školy. V teoretické části je proveden rozbor odborné literatury s akcentem na problematiku kognitivních schopností a přírodovědné gramotnosti u žáků mladšího školního věku. Praktickou část tvoří výsledky šetření standardizovaným Testem kognitivních schopností-TKS (Thorndike & Hagen, 1998) a didaktickým testem zaměřeným na zjištění úrovně přírodovědné gramotnosti u žáků čtvrtých ročníků základních škol, který je inspirovaný uvolněnými úlohami mezinárodního šetření TIMSS (Trends in International Mathematics and Science Study). Cílem výzkumného šetření je rozponat odlišnosti v kognitivních schopnostech u vybraných respondentů ve vztahu k míře jejich přírodovědné gramotnosti. Součástí práce je širší polemika zjištěných závěrů, formulace relevantních závěrů a doporučení pro praxi primárního přírodovědného vzdělávání. Celkový počet respondentů výzkumného šetření je 393, z toho 211 chlapců (54 %) a 182 dívek (46 %). Z výsledků byla zjištěna středně silná korelace vlivu kognitivních schopností na výsledky žáků v didaktickém testu přírodovědné gramotnosti.
View
The Effect of Developers’ General Intelligence on the Understandability of Domain Models: An Empirical Study
Article
Full-text available
  • Jan 2023
The discipline of software engineering has long studied the understandability of domain models, but always focusing on the semantic and notational characteristics of these models. However, as some authors point out, understandability is a cognitive process, where many human factors of the developers themselves are involved. In this sense, one of the human factors most studied by cognitive psychology is the Intelligence, considered as a set of skills that give each person abilities among which stand out comprehensibility and problem solving, both associated with the understandability process. In this paper we focus on Spearman’s Bifactorial Theory that proposes the use of D48 test, to obtain the so-called General Intelligence that represents a factor underlying specific mental abilities. This work proposes a theoretical model that has guided an empirical study with 102 subjects from the University of Alicante, we measure their general intelligence using the D48 test, and then these subjects perform a set of UML domain model understandability tasks, both in comprehensibility and problem solving. At this point, we also study the impact that the model understandability performance has on the final intention to adopt the model, based on the UMAM-Q test. Once the data were obtained, we applied a two-way analysis of variance, and the study obtained statistically significant results confirming that: 1) subjects with higher intelligence perform obtain better results on model understandability performance, and 2) subjects with higher model understandability also have higher compatibility and intention to adopt the model.
View
Mathematical Disabilities: Cognitive, Neuropsychological, and Genetic Components
Article
Full-text available
  • Sep 1993
Cognitive, neuropsychological, and genetic correlates of mathematical achievement and mathematical disability (MD) are reviewed in an attempt to identify the core deficits underlying MD. Three types of distinct cognitive, neuropsychological, or cognitive and neuropsychological deficits associated with MD are identified. The first deficit is manifested by difficulties in the representation or retrieval of arithmetic facts from semantic memory. The second type of deficit is manifested by problems in the execution of arithmetical procedures. The third type involves problems in the visuospatial representation of numerical information. Potential cognitive, neuropsychological, and genetic factors contributing to these deficits, and the relationship between MD and reading disabilities, are discussed. Finally, suggestions for the subtyping of mathematical disorders are offered.
View
What does the Cognitive Assessment System (CAS) measure? Joint confirmatory factor analysis of the CAS and the Woodcock-Johnson Tests of Cognitive Ability
Article
Full-text available
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.
View
View
View
View
View
View
View
Just Say No to Subtest Analysis: A Critique on Wechsler Theory and Practice
Article
  • Sep 1990
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.
View
Predictive Validity of the Cattell-Horn Gf-Gc Constructs to Achievement
Article
  • Mar 1996
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.
View