Sex Differences and Similarities in Relations Between Mathematics Achievement, Attitudes, and Anxiety: A Seventh-to-Ninth Grade Longitudinal Study.

There are consistent correlations between mathematics achievement, attitudes, and anxiety, but the longitudinal relations among these constructs are not well understood nor are sex differences in these relations. To address this gap, mathematics achievement, attitudes, and anxiety were longitudinally assessed for 342 (169 boys) adolescents from 7th to 9th grade, inclusive, and Latent Growth Curve Models were used to assess the relations among these traits and developmental change in them. Spatial abilities (7th, 8th grade) and trait anxiety (8th, 9th grade) were also assessed and used for control for sex differences in these traits.

Sex Differences in Developmental Pathways to Mathematical Competence.

The study tested the hypothesis that there are sex differences in the pathways to mathematical development. Three hundred forty-two adolescents (169 boys) were assessed in various mathematics areas from arithmetic fluency to algebra across 6 to 9 grade, inclusive, and completed a battery of working memory, spatial, and intelligence measures in middle school. Their middle school and 9 grade teachers reported on their in-class attentive behavior.

Boys' advantage in solving algebra word problems is mediated by spatial abilities and mathematics anxiety.

Adolescents' ( = 342, 169 boys) general algebra and algebra word problems performance were assessed in 9th grade as were intelligence, academic achievement, working memory, and spatial abilities in prior grades. The adolescents reported on their academic attitudes and anxiety and their teachers reported on their in-class attentive behavior in 7th to 9th grade. There were no sex differences on the general algebra measure or for mathematics achievement, but boys had an advantage on the algebra word problems measure ( = .

Mathematics Clusters Reveal Strengths and Weaknesses in Adolescents' Mathematical Competencies, Spatial Abilities, and Mathematics Attitudes.

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders ( = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of pre-algebra strengths and weaknesses and if variation between clusters was related to mathematics attitudes, anxiety, or for a subsample ( = 342) some combination of intelligence, working memory, or spatial abilities. Critically, strengths and weaknesses were not uniform across the three identified clusters.

Boys' visuospatial abilities compensate for their relatively poor in-class attentive behavior in learning mathematics.

The mathematics and reading achievement of 322 adolescents (159 boys) was assessed in seventh and eighth grades, as were their intelligence, working memory, and spatial abilities. Their seventh- and eighth-grade mathematics and English language arts teachers reported on their in-class attentive behavior. The latter emerged as an important predictor of achievement, but more so for mathematics than for reading.

In-Class Attention, Spatial Ability, and Mathematics Anxiety Predict Across-Grade Gains in Adolescents' Mathematics Achievement.

Identifying meaningful cognitive and non-cognitive predictors of mathematical competence is critical for developing targeted interventions for students struggling with mathematics. Here, 317 students' short-term verbal memory, verbal and visuospatial working memory, complex spatial abilities, intelligence, and mathematics attitudes and anxiety were assessed, and their teachers reported on their attentive-behavior in seventh-grade mathematics classrooms. Bayesian regression models revealed that complex spatial abilities and in-class attention were the most plausible predictors of seventh-grade mathematics, but not word reading, achievement, controlling for prior achievement.

Comorbid Learning Difficulties in Reading and Mathematics: The Role of Intelligence and In-Class Attentive Behavior.

The goal was to identify the domain-general cognitive abilities and academic attitudes that are common and unique to reading and mathematics learning difficulties that in turn will have implications for intervention development. Across seventh and eighth grade, 315 (155 boys) adolescents ( age = 12.75 years) were administered intelligence, verbal short-term and working memory, and visuospatial memory, attention, and ability measures, along with measures of English and mathematics attitudes and mathematics anxiety.

Boys' advantage on the fractions number line is mediated by visuospatial attention: Evidence for a parietal-spatial contribution to number line learning.

The study tested the hypotheses that boys will have an advantage learning the fractions number line and this advantage will be mediated by spatial abilities. Fractions number line and, as a contrast, fractions arithmetic performance were assessed for 342 adolescents, as was their intelligence, working memory, and various spatial abilities. Boys showed smaller placement errors on the fractions number line (d = -0.

Sex Differences in Mathematics Anxiety and Attitudes: Concurrent and Longitudinal Relations to Mathematical Competence.

Sex differences in the strength of the relations between mathematics anxiety, mathematics attitudes and mathematics achievement were assessed concurrently in sixth grade ( = 1,091, 545 boys) and longitudinally from sixth- to seventh-grade ( = 190, 97 boys). Mathematics anxiety was composed of two facets, one associated with evaluations and the other for learning more generally. Girls had higher mathematics anxiety for evaluations than did boys (s = -.

Preschool deficits in cardinal knowledge and executive function contribute to longer-term mathematical learning disability.

In a preschool through first grade longitudinal study, we identified groups of children with persistently low mathematics achievement (n = 14) and children with low achievement in preschool but average achievement in first grade (n = 23). The preschool quantitative developments of these respective groups of children with mathematical learning disability (MLD) and recovered children and a group of typically achieving peers (n = 35) were contrasted, as were their intelligence, executive function, and parental education levels. The core characteristics of the children with MLD were poor executive function and delayed understanding of the cardinal value of number words throughout preschool.

Predicting Age of Becoming a Cardinal Principle Knower.

Children's first mathematics concept is their understanding of the quantities represented by number words (cardinal value), and the age at which they achieve this insight predicts their readiness for mathematics learning in school. We provide the first exploration of the factors that influence the age of becoming a cardinal principle knower (CPK), with a longitudinal study of 197 (94 boys) children from the beginning to the end of two years of preschool. Core symbolic and non-symbolic quantitative competencies at the beginning of preschool, as well as measures of intelligence, executive function, preliteracy skills, and parental education were used to predict timing of CPK status.

Early Conceptual Understanding of Cardinality Predicts Superior School-Entry Number-System Knowledge.

We demonstrate a link between preschoolers' quantitative competencies and their school-entry knowledge of the relations among numbers (number-system knowledge). The quantitative competencies of 141 children (69 boys) were assessed at the beginning of preschool and throughout the next 2 years of preschool, as was their mathematics and reading achievement at the end of kindergarten and their number-system knowledge at the beginning of first grade. A combination of Bayes analyses and standard regressions revealed that the age at which the children had the conceptual insight that number words represent specific quantities (cardinal value) was strongly related to their later number-system knowledge and was more consistently related to broader mathematics than to reading achievement, controlling for intelligence, executive function, and parental education levels.

Developmental Foundations of Children's Fraction Magnitude Knowledge.

The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children's mathematical development, and the knowledge of fraction magnitudes influences children's later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8 and 9 graders' (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9 grade algebra achievement.

Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems.

The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory.

Adolescents' functional numeracy is predicted by their school entry number system knowledge.

One in five adults in the United States is functionally innumerate; they do not possess the mathematical competencies needed for many modern jobs. We administered functional numeracy measures used in studies of young adults' employability and wages to 180 thirteen-year-olds. The adolescents began the study in kindergarten and participated in multiple assessments of intelligence, working memory, mathematical cognition, achievement, and in-class attentive behavior.

Competence with fractions predicts gains in mathematics achievement.

Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.

Independent contributions of the central executive, intelligence, and in-class attentive behavior to developmental change in the strategies used to solve addition problems.

Children's (N=275) use of retrieval, decomposition (e.g., 7=4+3 and thus 6+7=6+4+3), and counting to solve additional problems was longitudinally assessed from first grade to fourth grade, and intelligence, working memory, and in-class attentive behavior was assessed in one or several grades.

Mathematical Cognition Deficits in Children With Learning Disabilities and Persistent Low Achievement: A Five-Year Prospective Study.

First- to fifth-grade mathematics and word reading achievement were assessed for children with mathematical learning disability (MLD, = 16), persistent low achievement (LA, = 29), and typical achievement ( = 132). Intelligence, working memory, processing speed, and in-class attention were assessed in 2 or more grades, and mathematical cognition was assessed with experimental tasks in all grades. The MLD group was characterized by low school-entry mathematics achievement and poor word reading skills.

First-Grade Predictors of Mathematical Learning Disability: A Latent Class Trajectory Analysis.

Kindergarten to 3(rd) grade mathematics achievement scores from a prospective study of mathematical development were subjected to latent growth trajectory analyses (n = 306). The four corresponding classes included children with mathematical learning disability (MLD, 6% of sample), and low (LA, 50%), typically (TA, 39%) and high (HA, 5%) achieving children. The groups were administered a battery of intelligence (IQ), working memory, and mathematical-cognition measures in 1(st) grade.

Development of number line representations in children with mathematical learning disability.

Children with a mathematical learning disability (MLD, n = 19) and low achieving (LA, n = 43) children were identified using mathematics achievement scores below the 11th percentile and between the 11th and 25th percentiles, respectively. A control group of typically achieving (TA, n = 50) children was also identified. Number line and speed of processing tasks were administered in 1st and 2nd grade and a working memory battery in 1st grade.

Mathematical cognition in intellectually precocious first graders.

Forty-six intellectually precocious (M age = 74 months) and 250 intellectually typical (M age = 75 months) children were administered a standardized working memory battery, speed of processing measures, and tasks that assessed skill at number line estimation and strategies used to solve simple and complex addition problems. Precocious children had an advantage over same-age peers for all components of working memory, and used a more mature mix of strategies to solve addition problems and to make number line estimates; there were no group differences for speed of processing. Many of the advantages of the precocious children on the number line and addition strategy tasks were significantly reduced or eliminated when group differences in working memory were controlled.

Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability.

Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n=15) and low achieving (LA, n=44) were identified. These groups and a group of typically achieving (TA, n=46) children were administered a battery of mathematical cognition, working memory, and speed of processing measures (M=6 years). The children with MLD showed deficits across all math cognition tasks, many of which were partially or fully mediated by working memory or speed of processing.

Rethinking speed theories of cognitive development. Increasing the rate of recall without affecting accuracy.

Researchers have suggested that developmental improvements in immediate recall stem from increases in the speed of mental processes. However, that inference has depended on evidence from correlation, regression, and structural equation modeling. We provide counter-examples in two experiments in which the speed of spoken recall was manipulated.