The Relation Between Attention and Memory.

The relation between attention and memory has long been deemed important for understanding cognition, and it was heavily researched even in the first experimental psychology laboratory by Wilhelm Wundt and his colleagues. Since then, the importance of the relation between attention and memory has been explored in myriad subdisciplines of psychology, and we incorporate a wide range of these diverse fields. Here, we examine some of the practical consequences of this relation and summarize work with various methodologies relating attention to memory in the fields of working memory, long-term memory, individual differences, life-span development, typical brain function, and neuropsychological conditions. We point out strengths and unanswered questions for our own embedded processes view of information processing, which is used to organize a large body of evidence. Last, we briefly consider the relation of the evidence to a range of other theoretical views before drawing conclusions about the state of the field.

The relation between number line performance and mathematics outcomes: Two meta-analyses.

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be overestimated because general cognitive ability has not been fully controlled in prior studies. The first of two meta-analyses (162 studies, 33,101 participants) confirmed a relation between performance on whole number (r = 0.33) and fractions number (r = 0.41) lines and overall mathematics performance. These relations were generally consistent across content domains (e.g., algebra and computation) and other moderators. The second (71 studies, 14,543 participants) used meta-analytic structural equation modeling to confirm these relations while controlling general cognitive ability (defined by IQ and working memory measures) and, in one analysis, general mathematics competence. The relation between number line performance and general mathematics competence remained significant but reduced (ß = 0.13). Controlling general cognitive ability, whole number line performance consistently predicted competence with fractions but not performance on numeracy or computations measures. The results suggest an understanding of the magnitudes represented by whole numbers might be particularly important for students' fractions learning. RESEARCH HIGHLIGHTS: Two meta-analyses examined the link between the number line and mathematics performance. The first revealed significant relations across domains (e.g., algebra and computation). The second controlled for general cognitive ability and resulted in reduced but still significant relations. The relation between number line and fractions performance was stronger than relations to other domains.

Relative Contributions of g and Basic Domain-Specific Mathematics Skills to Complex Mathematics Competencies.

Meta-analytic structural equation modeling was used to estimate the relative contributions of general cognitive ability or g (defined by executive functions, short-term memory, and intelligence) and basic domain-specific mathematical abilities to performance in more complex mathematics domains. The domain-specific abilities included mathematics fluency (e.g., speed of retrieving basic facts), computational skills (i.e., accuracy at solving multi-step arithmetic, algebra, or geometry problems), and word problems (i.e., mathematics problems presented in narrative form). The core analysis included 448 independent samples and 431,344 participants and revealed that g predicted performance in all three mathematics domains. Mathematics fluency contributed to the prediction of computational skills, and both mathematics fluency and computational skills predicted word problem performance, controlling g. The relative contribution of g was consistently larger than basic domain-specific abilities, although the latter may be underestimated. The patterns were similar across younger and older individuals, individuals with and without a disability (e.g., learning disability), concurrent and longitudinal assessments, and family socioeconomic status, and have implications for fostering mathematical development.

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 6th to 9th grade, inclusive, and completed a battery of working memory, spatial, and intelligence measures in middle school. Their middle school and 9th grade teachers reported on their in-class attentive behavior. There were no sex differences in overall mathematics performance, but boys had advantages on all spatial measures (ds = .29 to .58) and girls were more attentive in classroom settings (ds = -.28 to -.37). A series of structural equation models indicated that 6th- to 9th-grade mathematical competence was influenced by a combination of general cognitive ability, spatial abilities, and in-class attention. General cognitive ability was important for both sexes but the spatial pathway to mathematical competence was relatively more important for boys and the in-class attention pathway for girls.

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. Overall, boys had stronger spatial abilities and more positive mathematics attitudes and were less anxious than girls, but there were no sex differences in mathematics achievement. Across grades, mathematics achievement improved, attitudes became less positive, and anxiety increased for both boys and girls. Higher than average cross-grade growth in mathematics achievement mitigated boys' developmental declines in mathematics attitudes and increases in anxiety. Girls with strong spatial abilities had lower mathematics anxiety, but girls overall maintained higher mathematics anxiety and less positive mathematics attitudes relative to boys, even when they showed strong cross-grade gains in mathematics achievement. The study demonstrated that longitudinal gains in mathematics are associated with cross-grade changes in attitudes and anxiety but with several different developmental patterns for boys and girls.

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 (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.