Mary K. Hoard

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. In both grades, the MLD children were less accurate in their number line placements and more reliant on a natural number-magnitude representational system to make these placements than were TA children. The TA children were more reliant on the school-taught linear system in both grades. The performance of the LA children was similar to that of the MLD children in first grade and to the TA children in second. The central executive component of working memory contributed to across-grade improvements in number line performance and to group differences in this performance.

Numerical and arithmetical deficits in learning-disabled children: Relation to dyscalculia and dyslexia

Cognitive research on the number, counting, and arithmetic competencies of children with a learning disability in arithmetic (AD) is reviewed, and similarities between the associated deficits of AD children and the deficits of individuals afflicted with dyscalculia are highlighted. It is concluded that the defining features of AD and most dyscalculias are difficulties with the procedural features associated with the solving of complex arithmetic problems and difficulties in remembering basic arithmetic facts. The procedural deficits and one form of retrieval deficit appear to be associated with functioning of the prefrontal cortex, while a second form of retrieval deficit appears to be associated with the functioning of the left parieto-occipito-temporal areas and several subcortical structures. The review ends with a discussion of the potential relation between this second form of retrieval deficit and dyslexia.

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. Their number system knowledge at the beginning of first grade was defined by measures that assessed knowledge of the systematic relations among Arabic numerals and skill at using this knowledge to solve arithmetic problems. Early number system knowledge predicted functional numeracy more than six years later (ß = 0.195, p = .0014) controlling for intelligence, working memory, in-class attentive behavior, mathematical achievement, demographic and other factors, but skill at using counting procedures to solve arithmetic problems did not. In all, we identified specific beginning of schooling numerical knowledge that contributes to individual differences in adolescents’ functional numeracy and demonstrated that performance on mathematical achievement tests underestimates the importance of this early knowledge.

Sexual Jealousy as a Facultative Trait: Evidence From the Pattern of Sex Differences in Adults From China and the United States

Abstract Across two studies, 716 and 308 undergraduate students from the United States and mainland China, respectively, were administered a series of measures on jealousy, emotional responses to partner infidelity, family background, and personality. Across both studies for the U.S. and Chinese samples, a higher proportion of males than females reported more distress to a partners imagined sexual infidelity than to emotional infidelity, whereas a higher proportion of females than males reported more distress to a partners emotional infidelity than to sexual infidelity, consistent with theoretical expectations and previous empirical research. However, a much higher proportion of U.S. males and females reported more distress to sexual infidelity than their same-sex Chinese peers, suggesting that the tendency toward sexual jealousy might be facultatively influenced by sexual permissiveness in the general culture. The overall pattern of results is considered in terms of individual and contextual differences in the expression of jealousy, as well as in terms of the emotional and behavioral responses associated with jealousy reactions.

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=.14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement.

Fact Retrieval Deficits in Low Achieving Children and Children With Mathematical Learning Disability

Using 4 years of mathematics achievement scores, groups of typically achieving children (n = 101) and low achieving children with mild (LA–mild fact retrieval; n = 97) and severe (LA–severe fact retrieval; n = 18) fact retrieval deficits and mathematically learning disabled children (MLD; n = 15) were identified. Multilevel models contrasted developing retrieval competence from second to fourth grade with developing competence in executing arithmetic procedures, in fluency of processing quantities represented by Arabic numerals and sets of objects, and in representing quantity on a number line. The retrieval deficits of LA–severe fact retrieval children were at least as debilitating as those of the children with MLD and showed less across-grade improvement. The deficits were characterized by the retrieval of counting string associates while attempting to remember addition facts, suggesting poor inhibition of irrelevant information during the retrieval process. This suggests a very specific form of working memory deficit, one that is not captured by many typically used working memory tasks. Moreover, these deficits were not related to procedural competence or performance on the other mathematical tasks, nor were they related to verbal or nonverbal intelligence, reading ability, or speed of processing, nor would they be identifiable with standard untimed mathematics achievement tests.

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

Childrens (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. The goal was to assess the relation between capacity of the central executive component of working memory, controlling for intelligence and in-class attentive behavior, and grade-related changes in childrens use of these strategies. The predictor on intercept effects from multilevel models revealed that children with higher central executive capacity correctly retrieved more facts and used the most sophisticated counting procedure more frequently and accurately than their lower capacity peers at the beginning of first grade, but the predictor on slope effects indicated that this advantage disappeared (retrieval) or declined in importance (counting) from first grade to fourth grade. The predictor on slope effects also revealed that from first grade to fourth grade, children with higher capacity adopted the decomposition strategy more quickly than other children. The results remained robust with controls for childrens sex, race, school site, speed of encoding Arabic numerals and articulating number words, and mathematics achievement in kindergarten. The results also revealed that intelligence and in-class attentive behavior independently contributed to childrens strategy development.

Estrogens and relationship jealousy

The relation between sex hormones and responses to partner infidelity was explored in two studies reported here. The first confirmed the standard sex difference in relationship jealousy, that males (n=133) are relatively more distressed by a partner’s sexual infidelity and females (n=159) by a partner’s emotional infidelity. The study also revealed that females using hormone-based birth control (n=61) tended more toward sexual jealousy than did other females, and reported more intense affective responses to partner infidelity (n=77). In study two, 47 females were assessed four times across one month. Patterns of response to partner infidelity did not vary by week of menstrual cycle, but significant relations between salivary estradiol level and jealousy responses were obtained during the time of rising and high fertility risk. The implications, at least for females, are that any evolved psychological, affective, or behavioral dispositions regarding reproduction-related relationships are potentially moderated by estradiol, and that the use of synthetic hormones may disrupt this relation.

Numerical and Arithmetical Cognition: Performance of Low- and Average-IQ Children

Neuropsychological and developmental models of number, counting, and arithmetical skills, as well as the supporting working memory and speed of articulation systems, were used as the theoretical framework for comparing groups of low- and average-IQ children. The low-IQ children, in relation to their average-IQ peers, showed an array of deficits, including difficulties in retaining information in working memory while counting, more problem solving errors, shorter memory spans, and slower articulation speeds. At the same time, the low-IQ childrens conceptual understanding of counting did not differ from that of their higher-IQ peers. Implications for the relation between IQ and mathematics achievement are discussed.

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. Individual differences analyses revealed that each of the three components of working memory contributed to different aspects of skilled performance on the mathematics tasks.