How does a child solve 7 + 8? Decoding brain activity patterns associated with counting and retrieval strategies

Cognitive development and learning are characterized by diminished reliance on effortful procedures and increased use of memory-based problem solving. Here we identify the neural correlates of this strategy shift in 7-9-year-old children at an important developmental period for arithmetic skill acquisition. Univariate and multivariate approaches were used to contrast brain responses between two groups of children who relied primarily on either retrieval or procedural counting strategies. Children who used retrieval strategies showed greater responses in the left ventrolateral prefrontal cortex; notably, this was the only brain region which showed univariate differences in signal intensity between the two groups. In contrast, multivariate analysis revealed distinct multivoxel activity patterns in bilateral hippocampus, posterior parietal cortex and left ventrolateral prefrontal cortex regions between the two groups. These results demonstrate that retrieval and counting strategies during early learning are characterized by distinct patterns of activity in a distributed network of brain regions involved in arithmetic problem solving and controlled retrieval of arithmetic facts. Our findings suggest that the reorganization and refinement of neural activity patterns in multiple brain regions plays a dominant role in the transition to memory-based arithmetic problem solving. Our findings further demonstrate how multivariate approaches can provide novel insights into fine-scale developmental changes in the brain. More generally, our study illustrates how brain imaging and developmental research can be integrated to investigate fundamental aspects of neurocognitive development.     

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. 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 children's 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 children's 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 children's strategy development.     

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.     

Sex differences in in-group cooperation vary dynamically with competitive conditions and outcomes

Men's but not women's investment in a public goods game varied dynamically with the presence or absence of a perceived out-group. Three hundred fifty-four (167 male) young adults participated in multiple iterations of a public goods game under intergroup and individual competition conditions. Participants received feedback about whether their investments in the group were sufficient to earn a bonus to be shared among all in-group members. Results for the first trial confirm previous research in which men's but not women's investments were higher when there was a competing out-group. We extended these findings by showing that men's investment in the in-group varied dynamically by condition depending on the outcome of the previous trial: In the group condition, men, but not women, decreased spending following a win (i.e., earning an in-group bonus). In the individual condition, men, but not women, increased spending following a win. We hypothesize that these patterns reflect a male bias to calibrate their level of in-group investment such that they sacrifice only what is necessary for their group to successfully compete against a rival group.     

Helping or Hovering? The Effects of Helicopter Parenting on College Students’ Well-Being

Parental involvement is related to many positive child outcomes, but if not developmentally appropriate, it can be associated with higher levels of child anxiety and depression. Few studies have examined the effects of over-controlling parenting, or “helicopter parenting,” in college students. Some studies have found that college students of over-controlling parents report feeling less satisfied with family life and have lower levels of psychological well-being. This study examined self-determination theory as the potential underlying mechanism explaining this relationship. College students (N = 297) completed measures of helicopter parenting, autonomy supportive parenting, depression, anxiety, satisfaction with life, and basic psychological needs satisfaction. Students who reported having over-controlling parents reported significantly higher levels of depression and less satisfaction with life. Furthermore, the negative effects of helicopter parenting on college students’ well-being were largely explained by the perceived violation of students’ basic psychological needs for autonomy and competence.     

Acuity of the approximate number system and preschoolers’ quantitative development

The study assessed the relations among acuity of the inherent approximate number system (ANS), performance on measures of symbolic quantitative knowledge, and mathematics achievement for a sample of 138 (64 boys) preschoolers. The Weber fraction (a measure of ANS acuity) and associated task accuracy were significantly correlated with mathematics achievement following one year of preschool, and predicted performance on measures of children's explicit knowledge of Arabic numerals, number words, and cardinal value, controlling for age, sex, parental education, intelligence, executive control, and preliteracy knowledge. The relation between ANS acuity, as measured by the Weber fraction and task accuracy, and mathematics achievement was fully mediated by children's performance on the symbolic quantitative tasks, with knowledge of cardinal value emerging as a particularly important mediator. The overall pattern suggests that ANS acuity facilitates the early learning of symbolic quantitative knowledge and indirectly influences mathematics achievement through this knowledge.     

Modelling decisions to undergo genetic testing for susceptibility to common health conditions: An ancillary study of the Multiplex Initiative

New genetic tests reveal risks for multiple conditions simultaneously, although little is understood about the psychological factors that affect testing uptake. We assessed a conceptual model called the multiplex genetic testing model (MGTM) using structural equation modelling. The MGTM delineates worry, perceived severity, perceived risk, response efficacy and attitudes towards testing as predictors of intentions and behaviour. Participants were 270 healthy insured adults aged 25–40 from the Multiplex Initiative conducted within a health care system in Detroit, MI, USA. Participants were offered a genetic test that assessed risk for eight common health conditions. Confirmatory factor analysis revealed that worry, perceived risk and severity clustered into two disease domains: cancer or metabolic conditions. Only perceived severity of metabolic conditions was correlated with general response efficacy (β?=?0.13, p<0.05), which predicted general attitudes towards testing (β?=?0.24, p<0.01). Consistent with our hypothesised model, attitudes towards testing were the strongest predictors of intentions to undergo testing (β?=?0.49, p<0.01), which in turn predicted testing uptake (OR 17.7, β?=?0.97, p<0.01). The MGTM explained a striking 48% of the variance in intentions and 94% of the variation in uptake. These findings support use of the MGTM to explain psychological predictors of testing for multiple health conditions.     

Fertility cycle patterns in motives for sexual behavior

Three studies examined the relationship between fertility, as indexed by day in cycle or salivary estradiol levels, and reported motives for sexual intercourse. Data from university and community samples in both cross-sectional and repeated-measures designs showed that sex-for-intimacy motives are endorsed significantly less by women who are relatively more fertile or show higher salivary estrogen levels. Sex for enhancement, self-affirmation, and partner approval also declined, although the data were less consistent. The remaining motives (coping and power) showed no consistent patterns across fertility status. Results suggest that sexual motives are rooted partly in woman's biology and are discussed in terms of plausible evolutionary mechanisms that might promote female "choosiness" at midcycle.     

Second to fourth digit ratio and numerical competence in children

The ratio between the 2nd and 4th fingers (2D:4D)-a potential proxy for prenatal testosterone (T) exposure-shows a sex difference, with males usually having lower mean values; the latter potentially indicates higher prenatal T exposure. We studied relations between 2D:4D and competencies in the domains of counting, number knowledge, and visual-number representation in 73 children aged 6-11 years. Significant negative correlations between numerical performance in all of these areas and right and left hand 2D:4D ratios were found for boys but not girls. To the extent that 2D:4D ratios reflects prenatal exposure to T, the implications are (i) high prenatal T may be associated with better performance on some basic numerical measures for boys, and (ii) prenatal exposure to T may affect boys and girls differently with respect to some numerical competencies.     

Brain and cognitive evolution: forms of modularity and functions of mind

Genetic and neurobiological research is reviewed as related to controversy over the extent to which neocortical organization and associated cognitive functions are genetically constrained or emerge through patterns of developmental experience. An evolutionary framework that accommodates genetic constraint and experiential modification of brain organization and cognitive function is then proposed. The authors argue that 4 forms of modularity and 3 forms of neural and cognitive plasticity define the relation between genetic constraint and the influence of developmental experience. For humans, the result is the ontogenetic emergence of functional modules in the domains of folk psychology, folk biology, and folk physics. The authors present a taxonomy of these modules and review associated research relating to brain and cognitive plasticity in these domains.