A Longitudinal Assessment of Executive Function Skills and Their Association with Math Performance

The present study was designed to examine both concurrent and predictive associations between scores on a measure of executive function (EF) skills, the Contingency Naming Test (CNT), during the early school-age years. A secondary aim of the study was to examine the association between EF skills and mathematics performance. We administered tests of mathematics ability, and the CNT, to 178 children at ages 6 to 7, 8 to 9, and 10 to 11 years. From the CNT we obtained measures of response fluency/efficiency, working memory, and inhibition. The results demonstrate main effects of age on all CNT measures of EF, as anticipated, and inconsistent main effects of gender or mathematics learning disability status. Rates of improvement in EF varied as a function of the working memory demands present during a given task. There were differences in concurrent and predictive correlations for different CNT performance measures. EF scores obtained during the first assessment were as strongly associated with each other as they were with EF scores obtained four years later, suggesting a moderately stable source of individual differences on cognitive performance. EF scores at age 6 to 7 years were associated with concurrent and later mathematics scores, and most of these correlations were stronger than the significant associations found between response fluency on a baseline task (with no working memory demand) and mathematics performance. These findings have implications for the stability of EF skills during the school-age years, and the role of EF in early and later elementary school mathematics performance.     

A longitudinal assessment of executive function skills and their association with math performance.

The present study was designed to examine both concurrent and predictive associations between scores on a measure of executive function (EF) skills, the Contingency Naming Test (CNT), during the early school-age years. A secondary aim of the study was to examine the association between EF skills and mathematics performance. We administered tests of mathematics ability, and the CNT, to 178 children at ages 6 to 7, 8 to 9, and 10 to 11 years. From the CNT we obtained measures of response fluency/efficiency, working memory, and inhibition. The results demonstrate main effects of age on all CNT measures of EF, as anticipated, and inconsistent main effects of gender or mathematics learning disability status. Rates of improvement in EF varied as a function of the working memory demands present during a given task. There were differences in concurrent and predictive correlations for different CNT performance measures. EF scores obtained during the first assessment were as strongly associated with each other as they were with EF scores obtained four years later, suggesting a moderately stable source of individual differences on cognitive performance. EF scores at age 6 to 7 years were associated with concurrent and later mathematics scores, and most of these correlations were stronger than the significant associations found between response fluency on a baseline task (with no working memory demand) and mathematics performance. These findings have implications for the stability of EF skills during the school-age years, and the role of EF in early and later elementary school mathematics performance.     

A causal model of mathematics performance in early adolescence: the role of sex

Using path analysis, the present investigation was done to clarify possible causal linkages among general scholastic aptitude, academic achievement in mathematics, self-concept of ability, and performance on a mathematics examination. Subjects were 122 eighth-grade students who completed a mathematics examination as well as a measure of self-concept of ability. Aptitude and achievement measures were obtained from school records. Analysis showed sex differences in prediction of performance on the mathematics examination. For boys, this performance could be predicted from scholastic aptitude and previous achievement in mathematics. For girls, performance only could be predicted from previous achievement in mathematics. These results indicate that the direction, strength, and magnitude of relations among these variables differed for boys and girls, while mean levels of performance did not.     

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.     

Differences in Mathematical Performance,Creativity Potential,and Need for Cognitive Closure between Chinese and Australian Students

Research has shown that Chinese students outperform students from several Western countries on mathematics performance while some evidence has suggested that Western students perform more strongly on tests of creativity. One potential mechanism for these differences may be a higher need for cognitive closure among Chinese students. The current research compared performance on tests of mathematics and creativity among 50 students of Chinese background and 49 Australian students of Anglo‐Saxon background. As predicted, Chinese students performed better on mathematics while Australian students performed better on the measure of creativity. Australian students also had a lower score on one subscale of the need for cognitive closure, preference for predictability. Across the sample, preference for predictability showed small but significant negative correlations with several measures of creativity and positive correlations with several measures of mathematics. These findings were interpreted with respect to characteristic educational practices in both nations.     

Parent-report and performance-based measures of executive function assess different constructs

A total of 405 children of 5–18 years of age were administered performance-based and parent-report measures of executive function (EF), and measures of motor, attention, reading, and mathematics performance. Attention, reading, and mathematics abilities were associated with a parent-report measure of EF. Reading and mathematics abilities were also associated with performance-based measures of EF, including the Animal Sorting, Inhibition, and Response Set subtests of the Developmental NEuroPSYchological Assessment-II. In contrast, motor functioning was only associated with performance-based measures of EF. Findings suggest that different constructs of EF are measured by parent-report versus performance-based measures, and that these different constructs of EF are associated with different neurodevelopmental processes.     

印尼留学生汉语句子产生中的跨语言句法启动

采用图片描述范式探讨了不同年级印尼留学生汉语句子产生中的跨语言句法启动效应。结果发现,印尼语主动句启动条件下中年级印尼留学生没有产生跨语言句法启动,而高年级印尼留学生产生了跨语言句法启动;印尼语被动句启动条件下中、高年级印尼留学生均产生明显的跨语言句法启动。本研究结果初步表明,印尼留学生印尼语－汉语间跨语言句法启动与词序无关而与汉语水平有关。即使启动句为词序不同的印尼语被动句时,也能产生印尼语－汉语间跨语言句法启动。中年级印尼留学生句法表征中母语句法特征占优势,高年级印尼留学生句法表征中母语和汉语两种句法     

The role of planning in different mathematical skills

Despite the fact that planning has been found to be a significant predictor of reading (particularly of reading comprehension), much less is known about its contribution to mathematics. The purpose of this study was to examine the role of two levels of planning (operation planning and action planning) in three mathematical skills (calculation fluency, math problem-solving, and math reasoning). Eighty Grade 2 children from Shanghai, China were assessed on measures of nonverbal cognitive ability (nonverbal matrices), working memory (digit span backwards and N-back), operation planning (matching numbers, planned codes, and planned search), action planning (crack the code), and mathematics (calculation fluency, math problem-solving, and math reasoning). The results of regression analyses showed that both levels of planning accounted for unique variance in mathematics over and above the effects of nonverbal cognitive ability and working memory. The effects of action planning were particularly strong in math problem-solving. These findings suggest that measures of planning could be used along with measures of working memory to detect children at-risk for mathematics disabilities and that intervention programmes targeting planning could be developed to boost children's mathematics performance.     

ASSESSING PERCEIVED SELF EFFICACY IN RELATION TO MATHEMATICS TASKS: A STUDY OF THE RELIABILITY AND VALIDITY OF ASSESSMENT

Summary . This study investigated aspects of the reliability and validity of assessing perceived self efficacy in relation to mathematics tasks. Perceived self efficacy was assessed in two modes, a direct and generalised mode for two mathematics tasks. Self efficacy assessment was conducted over five trials in a repeated measures design with 72 children, age 9–10 years. Performance accuracy at the tasks was assessed after the first and fourth self efficacy assessment. Results showed moderate to high test-retest and inter-interviewer reliability for the self efficacy measures. Results also indicated discriminant validity for self efficacy judgments for different tasks. There was evidence for the association between self efficacy and task performance and mathematics self concept. The study confirms some limited aspects of reliability and validity of self efficacy assessment, but not for the construct in its assumed causal influence on performance attainment.     

The Effectiveness of a REBT Training Program in Increasing the Performance of High School Students in Mathematics

The efficacy of an REBT-based skill training program on the mathematics performance of disadvantaged black eleventh graders enrolled in Upward Bound was examined. Fifty-six students (18 males and 37 females) were randomly assigned to Perception Analysis Training (PAT) or an attention control group (ACG). The two groups met at the same hour each week for eight-weeks. PAT consisted of instruction in the application of RET strategies to the management of emotions that interfere with the development of proficiency in mathematics. ACG group members discussed films pertaining to career and personal development. Pre-test results confirmed a relationship between beliefs and mathematics achievement. Three measures of problematic beliefs concerning mathematics were significantly correlated (p>.01) with high school math grades and performance on the California Achievement Test-Math (CAT). At post-test PAT participants were less committed to self-defeating beliefs regarding mathematics than AGC members. ANCOVAs showed that PAT students made significantly greater pre- to post-test gains in their mathematical performance than control group members. PAT group members out performed AGC subjects in terms of Upward Bound math grades (ES=0.61; p >.0008), high school math grades (ES = 1.09; p>.0001), and scores on the CAT (ES=0.40; p >.02).     

Using student-managed interventions to increase homework completion and accuracy

We examined the effectiveness of self-managed individual and group contingency procedures in improving the completion and accuracy rates of daily mathematics homework assignments. A group of sixth-grade students having homework difficulties in mathematics were selected for the study. There was substantial improvement in the amount of homework completed over baseline for a majority of the students, whereas the results for accuracy were mixed. Students who participated in the self-management training made significant gains on standardized measures of academic achievement and curriculum-based measures of classroom performance. Parents also reported significantly fewer problems associated with homework completion following the intervention. Students who were allowed to select their own performance goals made superior improvements in the number of homework assignments returned compared to students who were given a specified goal by the classroom teacher. Parents, subjects, and the classroom teacher responded positively on consumer satisfaction measures following termination of the study.     

Working memory and individual differences in mathematics achievement: A longitudinal study from first grade to second grade

This longitudinal study examined the relationship between working memory and individual differences in mathematics. Working memory measures, comprising the phonological loop, the visuospatial sketchpad, and the central executive, were administered at the start of first grade. Mathematics achievement was assessed 4 months later (at the middle of first grade) and 1 year later (at the start of second grade). Working memory was significantly related to mathematics achievement in both grades, showing that working memory clearly predicts later mathematics achievement. The central executive was a unique predictor of both first- and second-grade mathematics achievement. There were age-related differences with regard to the contribution of the slave systems to mathematics performance; the visuospatial sketchpad was a unique predictor of first-grade, but not second-grade, mathematics achievement, whereas the phonological loop emerged as a unique predictor of second-grade, but not first-grade, mathematics achievement.     

The relationship between visuospatial sketchpad capacity and children's mathematical skills

This study examined the association between visuospatial sketchpad (VSSP) capacity and children's mathematics attainment. The aim of the study was to explore age-related differences in the relationship between the visual and spatial memory subcomponents of the VSSP (Logie, 1995) and a range of mathematical skills. Fifty-one 7- to 8-year-old and fifty-six 9- to 10-year-old primary schoolchildren participated in the study. The Visual Patterns Test and the Block Recall task were employed as VSSP measures. The results revealed a differential pattern of associations between children's visual and spatial working memory abilities and their mathematical skills. In younger children, the Block Recall task predicted mathematics performance, whereas, in the older children, the Visual Patterns Test was a significant predictor of mathematics performance.     

Athletic self-concept and mathematics achievement in girls

Several researchers have suggested that girls' mathematics performance may be mediated by an assertive sex role or "masculine interest." The present study made the assumption that girls' athletic self-confidence reflects "masculine interest" so girls' test scores for perceived athletic competence would be related to their mathematics achievement scores. A total of 207 boys and girls in Grades 4, 5, and 6 were tested for their perceived athletic ability using the Athletic Competence subscale of Harter's 1985 Self-perception Profile, and these scores were correlated with their mathematics achievement as measured on the Metropolitan Achievement Test and term grades. A low but significant correlation with Athletic Competence scores was found for girls on both measures of mathematics achievement. Although boys scored higher on the Athletic Competence subscale, there were no sex differences on either measure of mathematics achievement. Results are discussed in terms of both sex-role theory and cognitive development.     

Relationship between students' self-assessment of their capabilities and their teachers' judgments of students' capabilities in mathematics problem-solving

The study examined the judgments made by four seventh-grade mathematics teachers of their 107 students' competence in solving mathematics problems. Simultaneously, the 107 students made self-efficacy judgments about their capability in solving mathematics problems. The two sets of judgments were tested for predicting students' mathematics performance. Also, students' prior mathematics achievement was studied for its influence on both teachers' and students' judgments and students' mathematics performance. Teachers were asked to make judgments of each student for every mathematics problem solved. Results were consistent with prior research indicating that students' mathematics self-efficacy beliefs were highly predictive of their performance. Path analysis indicated that the mathematics teachers' judgments were also highly predictive of students' performance and self-efficacy. In turn, these variables predicted students' postperformance judgments. Combining students' self-efficacy judgments and teachers' judgments of students increased predictiveness for students' mathematics performance. Educational implications were also discussed.     

The developmental relations between spatial cognition and mathematics in primary school children

Spatial thinking is an important predictor of mathematics. However, existing data do not determine whether all spatial sub‐domains are equally important for mathematics outcomes nor whether mathematics–spatial associations vary through development. This study addresses these questions by exploring the developmental relations between mathematics and spatial skills in children aged 6–10 years (N = 155). We extend previous findings by assessing and comparing performance across Uttal et al.'s (2013), four spatial sub‐domains. Overall spatial skills explained 5%–14% of the variation across three mathematics performance measures (standardized mathematics skills, approximate number sense and number line estimation skills), beyond other known predictors of mathematics including vocabulary and gender. Spatial scaling (extrinsic‐static sub‐domain) was a significant predictor of all mathematics outcomes, across all ages, highlighting its importance for mathematics in middle childhood. Other spatial sub‐domains were differentially associated with mathematics in a task‐ and age‐dependent manner. Mental rotation (intrinsic‐dynamic skills) was a significant predictor of mathematics at 6 and 7 years only which suggests that at approximately 8 years of age there is a transition period regarding the spatial skills that are important for mathematics. Taken together, the results support the investigation of spatial training, particularly targeting spatial scaling, as a means of improving both spatial and mathematical thinking.     

Association between basic numerical abilities and mathematics achievement

Various measures have been used to investigate number processing in children, including a number comparison or a number line estimation task. The present study aimed to examine whether and to which extent these different measures of number representation are related to performance on a curriculum‐based standardized mathematics achievement test in kindergarteners, first, second, and sixth graders. Children completed a number comparison task and a number line estimation task with a balanced set of symbolic (Arabic digits) and non‐symbolic (dot patterns) stimuli. Associations with mathematics achievement were observed for the symbolic measures. Although the association with number line estimation was consistent over grades, the association with number comparison was much stronger in kindergarten compared to the other grades. The current data indicate that a good knowledge of the numerical meaning of Arabic digits is important for children's mathematical development and that particularly the access to the numerical meaning of symbolic digits rather than the representation of number per se is important.     

The effects of assertive training on performance in highly anxious adolescents

The effects of assertive training on measures of assertiveness, state anxiety, and mathematics performance in highly anxious adolescents were investigated. A group of 96 highly anxious 9th graders was assigned to one of four treatment groups. Pretest and posttest assessment included the Adolescent Self-Expression Scale (a measure of assertiveness), the State-Trait Anxiety Inventory, and the Mathematics Problems and Concepts subtests of the California Achievement Test. Experimental treatment consisted of four assertive training sessions, while placebo treatment for the control groups consisted of four career development training sessions. Posttest was administered to all four groups. A MANOVA was used to analyze all of the data on the students who took the pre- and posttest and attended two or more training sessions. Assertive training resulted in increased assertiveness and decreased state anxiety, with no significant effect on mathematics performance, and no significant effect due to sex. It was concluded that assertive training is a counseling technique which can be used effectively with 9th graders.     

Experiential and Affective Correlates of Math Anxiety in Adult Women

Mathematics anxiety has been discussed as one of the factors contributing to poor mathematics performance, especially among women. Although many programs have been developed for its treatment, little research has been conducted concerning its correlates. The present study examines correlates of mathematics anxiety among the 69 female participants in a program designed to help individuals overcome their fears and become more competent in mathematics. Results indicate the following: (a) that mathematics anxiety in program participants is highly correlated with other academically relevant anxiety scales, (b) that test anxiety and self-estimated mathematics ability are the most important variables in the prediction of mathematics anxiety, and (c) that mathematics anxiety and high school mathematics preparation are the most important variables in the prediction of arithmetic performance.     

Cognitive correlates of performance in advanced mathematics

Background. Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). Aims. To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. Samples. We recruited 80 undergraduates from four universities in Beijing. Methods. The current study investigated the associations between students’ performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. Results. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Conclusions. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications.