A structural equation modeling of executive functions,IQ and mathematical skills in primary students: Differential effects on number production,mental calculus and arithmetical problems

Though the relationship between executive functions (EFs) and mathematical skills has been well documented, little is known about how both EFs and IQ differentially support diverse math domains in primary students. Inconsistency of results may be due to the statistical techniques employed, specifically, if the analysis is conducted with observed variables, i.e., regression analysis, or at the latent level, i.e., structural equation modeling (SEM). The current study explores the contribution of both EFs and IQ in mathematics through an SEM approach. A total of 118 8- to 12-year-olds were administered measures of EFs, crystallized (Gc) and fluid (Gf) intelligence, and math abilities (i.e., number production, mental calculus and arithmetical problem-solving). Confirmatory factor analysis (CFA) offered support for the three-factor solution of EFs: (1) working memory (WM), (2) shifting, and (3) inhibition. Regarding the relationship among EFs, IQ and math abilities, the results of the SEM analysis showed that (i) WM and age predict number production and mental calculus, and (ii) shifting and sex predict arithmetical problem-solving. In all of the SEM models, EFs partially or totally mediated the relationship between IQ, age and math achievement. These results suggest that EFs differentially supports math abilities in primary-school children and is a more significant predictor of math achievement than IQ level.     

Changing stereotypes,changing grades: a longitudinal study of stereotyping during a college math course

Previous research has illuminated an important connection between stereotypes and the performance of those targeted by a stereotype. This body of work suggests that even implicit (i.e., nonconscious and unintended) math-gender stereotyping is related to poor math performance among women. Our longitudinal study sought to measure students’ math-gender stereotyping during a college math course and examine the relationship between changes in implicit stereotyping and course performance. Results showed that, for both male and female students, stereotypes increased during the course. Importantly, there was a significant interaction between gender and changes in implicit stereotyping when predicting course performance. Female students showed a negative relationship between changes in implicit stereotypes and course performance, while male students showed no relationship between changes in implicit stereotyping and course performance. This suggests that only for women, who are stereotyped as poor math performers, did the observed increases in stereotyping over time predict poorer math performance.     

Mental Set Shifting in Childhood: The Role of Working Memory and Inhibitory Control

The role of working memory (WM) and inhibition in mental set shifting was examined from an individual difference perspective in children aged 5–14 years (N = 117). Using the Hearts and Flowers task the rationale of the present study was to directly test the theoretical assumption that mental set shifiting in childhood primarily builds on WM and inhibitory processes. Theoretical predictions about WM and inhibitory demands in the congruent and incongruent conditions of the Hearts and Flowers task were also considered because these blocks underlie relevant measures of set shifting. The findings show that both WM and inhibition (extracted as factors in confirmatory factor analysis) are important for set shifting but that this general association is driven by the link between these executive functions (EFs) and the goal‐representation aspect (i.e. global switch costs) of shifting, rather than to the actual switch‐implementation process (i.e. local switch costs). In addition, our findings are novel in showing that, despite a substantial correlation between the two EF components, it was the variance specific to WM and inhibition that was important for mental set shifting. Copyright © 2014 John Wiley & Sons, Ltd.     

Language counts: Early language mediates the relationship between parent education and children's math ability

Children's early math skills have been hailed as a powerful predictor of academic success. Disparities in socioeconomic context, however, also have dramatic consequences on children's learning. It is therefore critical to investigate both of these distinct contributors in order to better understand the early foundations of children's academic outcomes. This study tests an integrated model of children's developing math ability so as to (1) identify the specific skills and abilities most clearly linked to early math achievement and (2) measure the influence of children's socioeconomic context on each of these skills. We first evaluated the early vocabulary, number word knowledge (knower level), and Approximate Number System (ANS) acuity of a diverse group of preschoolers. Then, approximately 1 year later as they entered Kindergarten, we administered a test of early math achievement. We find that children's early language (general vocabulary and number word knowledge) fully mediates the relationship between parent education and math ability. Additionally, number word knowledge mediates the relationship between ANS acuity and early math. We argue that increased focus on number word knowledge, as well as general vocabulary, may help to minimize disparities in math ability as children enter kindergarten. We also highlight the role of parent education on children's learning and note that this may be an important locus for intervention.     

Magnitude processing and complex calculation is negatively impacted by mathematics anxiety while retrieval‐based simple calculation is not

Mathematics anxiety (MA) refers to the experience of negative affect when engaging in mathematical activity. According to Ashcraft and Kirk (2001), MA selectively affects calculation with high working memory (WM) demand. On the other hand, Maloney, Ansari, and Fugelsang (2011) claim that MA affects all mathematical activities, including even the most basic ones such as magnitude comparison. The two theories make opposing predictions on the negative effect of MA on magnitude processing and simple calculation that make minimal demands on WM. We propose that MA has a selective impact on mathematical problem solving that likely involves processing of magnitude representations. Based on our hypothesis, MA will impinge upon magnitude processing even though it makes minimal demand on WM, but will spare retrieval‐based, simple calculation, because it does not require magnitude processing. Our hypothesis can reconcile opposing predictions on the negative effect of MA on magnitude processing and simple calculation. In the present study, we observed a negative relationship between MA and performance on magnitude comparison and calculation with high but not low WM demand. These results demonstrate that MA has an impact on a wide range of mathematical performance, which depends on one's sense of magnitude, but spares over‐practiced, retrieval‐based calculation.     

Making gender matter: the role of gender-based expectancies and gender identification on women's and men's math performance in Sweden

It is well established that an emphasis on gender differences may have a negative effect on women's math performance in USA, Germany and the Netherlands. It has further been found that an individual's identification with the stereotyped group may moderate effects of negative stereotypes. The present study investigated how gender-based expectancies affected the math performance of women and men in Sweden, a nation with a smaller gender gap than in other countries, and a strong cultural emphasis on gender equality. Participants, 112 female and 74 male undergraduate math students from Swedish universities, completed a difficult math test in which their gender was either linked to their test performance or not. Men performed better than women when gender was made relevant among participants who did not see their gender as an important aspect of their identity, while participants high in gender identification were unaffected by gender identity relevance. Moreover, the gender relevance manipulation affected men's performance more than women's. The results deviate from findings on US samples, indicating that the role of group identification as a moderator of stereotype-based expectancy effects is complex, and that factors in the cultural context may interact with individual differences in identification to determine the impact of negative stereotypes.     

Developmental dynamics between reading and math in elementary school

Reading and math attainment develop during elementary grades. Questions remain, though, about the co‐developmental nature of the relation between reading and math. This study examined dynamic, longitudinal pathways between reading and math in first through fourth grades. Participants of the study were 554 academically at‐risk children (M_age at the first assessment point = 6.57 years; SD = 0.38) from Texas Project Achieve. Children were assessed utilizing the Woodcock‐Johnson–III reading and math measures. Results from dynamic bivariate latent change score models indicated unidirectional longitudinal coupling effects from reading to math. Specifically, average and high levels of reading performance were associated with subsequent gains in math growth, in particular for below average performing children in math. In contrast, low levels of reading performance had negligible or no amplifying influences on change in math growth. The nature of the dynamics was replicated even when controlling for nonverbal cognitive abilities. Results demonstrated that good reading skills pave the way for children to develop their math skills. Such findings underscore the importance of considering reading performance in treating math difficulties.     

How is anxiety related to math performance in young students? A longitudinal study of Grade 2 to Grade 3 children

Both general and math-specific anxiety are related to proficiency in mathematics. However, it is not clear when math anxiety arises in young children, nor how it relates to early math performance. This study therefore investigated the early association between math anxiety and math performance in Grades 2 and 3, by accounting for general anxiety and by further inspecting the prevalent directionality of the anxiety–performance link. Results revealed that this link was significant in Grade 3, with a prevalent direction from math anxiety to performance, rather than the reverse. Longitudinal analyses also showed an indirect effect of math anxiety in Grade 2 on subsequent math performance in Grade 3. Overall, these findings highlight the importance of monitoring anxiety from the early stages of schooling in order to promote proficient academic performance.     

The relationship between executive functions,episodic feeling-of-knowing and confidence judgements

Metamemory processes and executive control may be related, given that both are frontally mediated. However, previous behavioural research has been limited in identifying common processes driving this somewhat weak relationship partly because they mostly relied upon global executive measures and composite scores of executive function (EF). The present study investigated the relationship between specific EFs (task shifting, interference resolution), working memory capacity and feeling-of-knowing (FOK) and confidence judgements (CONF) in an episodic memory task. We found that, of the EFs, only task-switching performance was correlated with FOK accuracy and proposed a shared mechanism that may be at play in both task-switching and FOK judgements. We also demonstrated that interference resolution and episodic memory measures were related, suggesting strategic influences on memory retrieval. Finally, we found a strong consistency in the strength and accuracy of FOK and CONF judgements, possibly due to retrieval-based mechanisms in both types of judgements.     

Choke or thrive? The relation between salivary cortisol and math performance depends on individual differences in working memory and math-anxiety

In the current study, we explored how a person's physiological arousal relates to their performance in a challenging math situation as a function of individual differences in working memory (WM) capacity and math-anxiety. Participants completed demanding math problems before and after which salivary cortisol, an index of arousal, was measured. The performance of lower WM individuals did not depend on cortisol concentration or math-anxiety. For higher WM individuals high in math-anxiety, the higher their concentration of salivary cortisol following the math task, the worse their performance. In contrast, for higher WM individuals lower in math-anxiety, the higher their salivary cortisol concentrations, the better their performance. For individuals who have the capacity to perform at a high-level (higher WMs), whether physiological arousal will lead an individual to choke or thrive depends on math-anxiety.     

Avoidance temperament and social-evaluative threat in college students' math performance: a mediation model of math and test anxiety

Background and Objectives: Standardized testing has become a common form of student evaluation with high stakes, and limited research exists on understanding the roles of students' personality traits and social-evaluative threat on their academic performance. This study examined the roles of avoidance temperament (i.e., fear and behavioral inhibition) and evaluative threat (i.e., fear of failure and being viewed as unintelligent) in standardized math test and course grades in college students. Design and Methods: Undergraduate students (N = 184) from a large public university were assessed on temperamental fear and behavioral inhibition. They were then given 15 minutes to complete a standardized math test. After the test, students provided data on evaluative threat and their math performance (scores on standardized college entrance exam and average grades in college math courses). Results: Results indicate that avoidance temperament was linked to social-evaluative threat and low standardized math test scores. Furthermore, evaluative threat mediated the influence of avoidance temperament on both types of math performance. Conclusions: Results have educational and clinical implications, particularly for students at risk for test anxiety and underperformance. Interventions targeting emotion regulation and stress management skills may help individuals reduce their math and test anxieties.     

From poor performance to success under stress: working memory, strategy selection, and mathematical problem solving under pressure

Two experiments demonstrate how individual differences in working memory (WM) impact the strategies used to solve complex math problems and how consequential testing situations alter strategy use. In Experiment 1, individuals performed multistep math problems under low- or high-pressure conditions and reported their problem-solving strategies. Under low-pressure conditions, the higher individuals' WM, the more likely they were to use computationally demanding algorithms (vs. simpler shortcuts) to solve the problems, and the more accurate their math performance. Under high-pressure conditions, higher WM individuals used simpler (and less efficacious) problem-solving strategies, and their performance accuracy suffered. Experiment 2 turned the tables by using a math task for which a simpler strategy was optimal (produced accurate performance in few problem steps). Now, under low-pressure conditions, the lower individuals' WM, the better their performance (the more likely they relied on a simple, but accurate, problem strategy). And, under pressure, higher WM individuals performed optimally by using the simpler strategies lower WM individuals employed. WM availability influences how individuals approach math problems, with the nature of the task performed and the performance environment dictating skill success or failure.     

The benefits of emotional expression for math performance

This study investigated the effects of emotional expression on actual and perceived math performance. Female participants were either asked to express their emotions or given no special instructions before taking a math test under stereotype threat or no stereotype threat conditions. Participants in the emotional expression condition performed better on the math test than participants in the control condition. Under stereotype threat, participants in the emotional expression condition believed they performed better on the math test. Emotional expression appears not only to have health benefits (e.g., Pennebaker, 1997), but academic benefits as well, including for stereotyped threatened individuals.     

Executive function and weight status in children: A one-year longitudinal perspective

There is considerable evidence for an association between obesity and impaired executive function (EF) in adolescents and adults. However, little research has examined EF in overweight or obese children. Furthermore, data on EF in underweight individuals is lacking. In addition, there is no consensus on the directionality of the relationship between Body Mass Index (BMI) and EF, and longitudinal studies are rare. Thus, the present study examined whether children differ in their performance on a battery of EF tasks depending on their weight status (underweight, normal-weight, overweight), and investigated the longitudinal cross-lagged associations between EF and BMI. Hot EF (delay of gratification, affective decision-making), cool EF (attention shifting, inhibition, working memory [WM] updating), and BMI were assessed in 1,657 German elementary-school children at two time points, approximately one year apart. Overweight children exhibited slightly poorer attention shifting, WM updating, and affective decision-making abilities as compared to normal-weight children. Unexpectedly, they did not show any deficits in inhibition or delay of gratification. EF levels of underweight children did not differ significantly from those of normal-weight children. Furthermore, poor attention shifting and enhanced affective decision-making predicted a slightly higher BMI one year later, and a higher BMI also predicted poorer attention shifting and WM updating one year later. The latter association between BMI and subsequent EF scores, however, diminished when controlling for socioeconomic status. Results indicate that hot and cool EF plays a role in the weight development of children, and might be a promising factor to address in preventive interventions.     

The relation between teachers' math talk and the acquisition of number sense within kindergarten classrooms

The aim of the present study was to investigate the relation between teachers' math talk and the acquisition of number sense within kindergarten classrooms. The mathematical language input provided by 35 kindergarten teachers was examined with 9 different input categories. The results of this study indicate that the role of each of these math talk categories is not as straightforward as was hypothesized. Although significant positive relations were found for math talk categories such as cardinality and conventional nominatives, the relations between the categories' calculation and number symbols and children's score on specific number sense tasks were negative. Moreover, a large diversity in math talk was negatively related to kindergartners' number sense acquisition. These results suggest that teachers should be careful and selective with the amount of math talk that they offer to young children.     

工作记忆对小学三年级学生解决比较问题的影响

研究工作记忆与小学生解决比较问题成绩之间的关系。实验1运用双任务作业研究一致问题和不一致问题的工作记忆负荷是否有显著差别,被试为34名小学三年级学生。实验2运用工作记忆测验研究成功解题者与不成功解题者的工作记忆容量是否有显著差别,被试为37名小学三年级学生。结果表明;(1)小学生解决比较问题的成绩受问题类型的影响,他们在一致问题上的成绩显著优于不一致问题。(2)一致问题和不一致问题的工作记忆负荷水平不同,不一致问题的工作记忆负荷大于一致问题。(3)成功解题者的工作记忆容量大于不成功解题者的工作记忆容量。本研究结果说明工作记忆对小学生解决比较问题有重要影响。     

Working Memory in Children Predicts Performance on a Gambling Task

ABSTRACT. The authors investigated whether working memory (WM) plays a significant role in the development of decision making in children, operationalized by the Children's Gambling Task (CGT). A total of 105 children aged 6–7, 8–9, and 10–11 years old carried out the CGT. Children aged 6–7 years old were found to have a lower performance than older children, which shows that the CGT is sensitive to participant's age. The hypothesis that WM plays a significant role in decision making was then tested following two approaches: (a) an experimental approach, comparing between groups the performance on the CGT in a control condition (the CGT only was administered) to that in a double task condition (participants had to carry out a recall task in addition to the CGT); (b) an interindividual approach, probing the relationship between CGT performance and performance on tasks measuring WM efficiency. The between-groups approach evidenced a better performance in the control group. Moreover, the interindividual approach showed that the higher the participants’ WM efficiency was, the higher their performance in the CGT was. Taken together, these two approaches yield converging results that support the hypothesis that WM plays a significant role in decision making in children.     

Short-term retention of a single word relies on retrieval from long-term memory when both rehearsal and refreshing are disrupted

Many working memory (WM) models propose that the focus of attention (or primary memory) has a capacity limit of one to four items, and therefore, that performance on WM tasks involves retrieving some items from long-term (or secondary) memory (LTM). In the present study, we present evidence suggesting that recall of even one item on a WM task can involve retrieving it from LTM. The WM task required participants to make a deep (living/nonliving) or shallow (“e”/no “e”) level-of-processing (LOP) judgment on one word and to recall the word after a 10-s delay on each trial. During the delay, participants either rehearsed the word or performed an easy or a hard math task. When the to-be-remembered item could be rehearsed, recall was fast and accurate. When it was followed by a math task, recall was slower, error-prone, and benefited from a deeper LOP at encoding, especially for the hard math condition. The authors suggest that a covert-retrieval mechanism may have refreshed the item during easy math, and that the hard math condition shows that even a single item cannot be reliably held in WM during a sufficiently distracting task—therefore, recalling the item involved retrieving it from LTM. Additionally, performance on a final free recall (LTM) test was better for items recalled following math than following rehearsal, suggesting that initial recall following math involved elaborative retrieval from LTM, whereas rehearsal did not. The authors suggest that the extent to which performance on WM tasks involves retrieval from LTM depends on the amounts of disruption to both rehearsal and covert-retrieval/refreshing maintenance mechanisms.     

Lasting effects of alcohol: Subliminal alcohol cues,impairment expectancies,and math performance

Many people believe that drinking alcohol reduces cognitive performance, and prior research has shown such expectancy‐related impairment even when people merely thought that the (non‐alcoholic) drink they consumed contained alcohol. This study tested whether subliminal priming with alcohol‐related cues would similarly result in expectancy‐consistent cognitive performance decrements. Additionally, the moderating role of alcohol use was examined. After assessing participants' baseline math performance, participants were primed with alcohol‐related or neutral words and then completed a post‐treatment math task. Whereas impairment expectancies had no influence on math performance in control participants, expectancies predicted math performance for participants primed with alcohol‐related words. As hypothesized, expectancy‐consistent impairment in performance was only observed among high alcohol users. The current findings suggest that, in the presence of alcohol‐related cues in the environment, some people may perform less on cognitive tasks even in the absence of actual or assumed alcohol consumption and without being aware of it. Copyright © 2011 John Wiley & Sons, Ltd.     

Not all executive functions are related to intelligence

Accumulating evidence suggests that executive functions (EFs) are related to intelligence, despite neuropsychological results initially considered evidence of no such relation. However, findings that EFs are not unitary raise the issue of how intelligence relates to different EFs. This study examined the relations of fluid and crystallized intelligence and Wechsler Adult Intelligence Scale IQ to three separable EFs--inhibiting prepotent responses (inhibiting), shifting mental sets (shifting), and updating working memory (updating)--in young adults. Updating was highly correlated with the intelligence measures, but inhibiting and shifting were not. Furthermore, in structural equation models controlling for the inter-EF correlations, updating remained strongly related to intelligence, but the relations of inhibiting and shifting to intelligence were small and not significant. The results indicate that intelligence measures differentially relate to these three EFs, suggesting that current intelligence measures do not equally assess a wide range of executive control abilities likely required for many "intelligent" behaviors.