Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 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 (n = 342) some combination of intelligence, working memory, or spatial abilities. Critically, strengths and weaknesses were not uniform across the three identified clusters. Lower-performing students had pronounced deficits in their understanding of mathematical equality, fractions magnitudes, and the fractions number line. Higher-performing students had particular advantages in whole number and fractions arithmetic, and the fractions number line. Students could be reliably placed into clusters based on their mathematics self-efficacy and a combination of intelligence and spatial abilities. The results contribute to our understanding of key aspects of students' mathematical development, highlight areas in need of intervention for at-risk students, and identify cognitive areas in which scaffolds might be incorporated into these interventions.

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 = -0.22) and correctly solved more fractions arithmetic problems (d = 0.23) than girls. Working memory and intelligence predicted performance on both fractions measures, and a measure of visuospatial attention uniquely predicted number line performance and fully mediated the sex difference. Visuospatial working memory uniquely predicted fractions arithmetic performance and fully mediated the sex difference. The results help to clarify the nuanced relations between spatial abilities and formal mathematics learning and the sex differences that often emerge in mathematical domains that have a visuospatial component.

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 (M 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. Teachers reported on students' in-class attentive behavior. A combination of Bayesian and multi-level models revealed that intelligence and in-class attentive behavior were common predictors of reading accuracy, reading fluency, and mathematics achievement. Verbal short-term memory was more critical for reading accuracy and fluency, whereas spatial ability and mathematics self-efficacy were more critical for mathematics achievement. The combination of intelligence and in-class attentive behavior discriminated typically achieving students from students with comorbid (D = 2.44) or mathematics (D = 1.59) learning difficulties, whereas intelligence, visuospatial attention, and verbal short-term memory discriminated typically achieving students from students with reading disability (D = 1.08). The combination of in-class attentive behavior, verbal short-term memory, and mathematics self-efficacy discriminated students with mathematics difficulties from their peers with reading difficulties (D = 1.16). Given the consistent importance of in-class attentive behavior, we conducted post hoc follow-up analyses. The results suggested that students with poor in-class attentive behavior were disengaging from academic learning which in turn contributed to their risk of learning difficulties.

Sex differences in the strength of the relations between mathematics anxiety, mathematics attitudes, and mathematics achievement were assessed concurrently in sixth grade (n = 1,091, 545 boys) and longitudinally from sixth to seventh grade (n = 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 (ds = -.30 to -.52), but not for mathematics learning. In sixth grade, the negative correlation between mathematical competence and mathematics anxiety for evaluations was stronger in girls than in boys. Longitudinally, higher mathematical competence in sixth grade was associated with lower mathematics anxiety for evaluations and better mathematics attitudes in seventh grade for girls but not for boys. The key finding is that adolescent girls' mathematics anxiety and their attitudes toward mathematics are more reflective of their actual mathematical competence than they are for boys. One implication is that relative to boys with low mathematics achievement, girls with low achievement are at higher risk of developing mathematics anxiety and poor attitudes toward mathematics.