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.     

Learning potential and anxious tendency: Test anxiety as a bias factor in educational testing

Abstract

Contrary to conventional educational testing, in so-called dynamic assessment subjects are allowed to consult help during testing or are offered prior training. The differential results of both testing procedures are sometimes ascribed to the idea that dynamic tests reflect the breadth of the zone of proximal development on top of independent achievement. Alternative explanations claim that conventional tests are more strongly biased towards various characteristics of persons, which have a negative influence on performance, when compared to dynamic tests. In this study, it was hypothesised that static as well as dynamic assessment is biased towards anxious tendencies of subjects, but the former more strongly than the latter. In order to investigate this supposition, the performance of subjects on dynamic and static tests was systematically compared and related to measures of test anxiety in a longitudinal experiment. In the experiment, repeated measures of independent mathematics achievement as well as mathematics learning potential were gathered among students of secondary education in the Netherlands. Prior to every mathematics test, subjects filled out a test anxiety questionnaire. After every mathematics test, subjects filled out a general state anxiety questionnaire. The participating subjects were students from secondary education, either preparing for higher vocational training or university, aged approximately 15 years on average.

The results of the experiment showed that lack of self-confidence is an important constituent factor of test anxiety, apart from worry and emotionality. The data supported the assumption that such testing procedures are less biased towards anxiety than conventional tests, but it was not established that dynamic testing procedures render results that are not biased by test anxious tendencies.     

Changes in self‐perceptions of competence and intrinsic motivation among elementary schoolchildren

Background: Children's perceived competence and intrinsic motivation are assumed to be very high at the outset of schooling. However, how they change and how they relate to each other and to academic achievement across early schooling years remain open to question. Aims: This 3‐year longitudinal study was aimed at examining the following questions. Do children's perceived competence and intrinsic motivation about reading and mathematics change across the first 3 years of schooling? Do their perceived competence and intrinsic motivation differ according to academic domains? Do their perceived competence and intrinsic motivation relate to their academic achievement in each academic domain? Sample: A total of 115 elementary schoolchildren (63 boys and 52 girls) were examined in first grade (mean age = 84,5 months, SD = .67) and for the next 2 years. Method: Children responded to questionnaires about their perceived competence and intrinsic motivation in reading and mathematics. Year‐end grades in these two subjects were used as a measure of performance. Results: Changes in perceived competence and intrinsic motivation, and between‐year intercorrelations, were observed to differ according to academic domains and gender. Intrinsic motivation did not make a significant contribution to academic achievement at either school grade or in any academic domain, whereas perceived competence was significantly related to achievement at each school grade in both reading and mathematics. Conclusions: Differences between boys and girls observed in this study were not linked to a specific domain and cannot be attributed to gender‐role stereotypes. Girls appeared to be more precocious in differentiating their competence and intrinsic motivation according to academic domain, as well as in being able to process and integrate information about their ability from past performances in a domain to judge their competence in the same domain.     

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.     

Relations between social comparison orientation and adjustment in Chinese adolescents: Moderating effects of initial adjustment status

This 1‐year longitudinal study examined relations between social comparison orientation (SCO) and socioemotional adjustment and academic achievement. A sample of Grades 7 and 8 students (N = 336, initial M age = 14.08 years) in China participated in the study. Data were collected from self‐reports, peer assessments and school records. It was found that early SCO positively contributed to later academic achievement. Moreover, the relations between early SCO and later socioemotional adjustment were moderated by the initial status of adolescents. Specifically, SCO was positively associated with social competence and negatively associated with depression in initially competent and well‐adjusted adolescents, but the pattern of the associations was opposite in initially incompetent and poorly adjusted adolescents. The results indicate that whereas SCO may contribute directly to academic achievement, its contributions to socioemotional development might depend on adolescents' initial status in adjustment.     

Racing dragons and remembering aliens: Benefits of playing number and working memory games on kindergartners' numerical knowledge

Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet‐based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten‐age children. We hypothesized that playing a number‐based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; M_age = 71.87 months) were randomly assigned to either play a number‐based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain‐specific and domain‐general skills can benefit a broad range of kindergarten‐aged children.     

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.     

Behavioral Self‐Regulation,Early Academic Achievement,and the Effectiveness of Urban Schools for Low‐Income Ethnic Minority Children

The independent and joint associations between child behavioral self‐regulation ability and school effectiveness in relation to academic achievement were examined in a sample of low‐income African American (n = 132) and Latino (n = 198) children attending kindergarten and first grade across a large metropolitan area. Child behavioral self‐regulation and school effectiveness were positively associated with both reading and mathematics performance. School effectiveness moderated the effect of behavioral self‐regulation on reading but not math achievement. Lower child behavioral self‐regulation during early elementary school was associated with lower reading achievement the following year but only among children attending less effective schools. Behavioral self‐regulation was not related to reading achievement among children attending more effective schools. Implications of these findings for policies addressing disparities in early academic achievement are discussed.     

Early predictors of middle school fraction knowledge

Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning.     

The contribution of logical reasoning to the learning of mathematics in primary school

It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6‐year‐old children's logical abilities and their working memory predict mathematical achievement 16 months later; and (b) logical scores continued to predict mathematical levels after controls for working memory, whereas working memory scores failed to predict the same measure after controls for differences in logical ability. In our second study, we trained a group of children in logical reasoning and found that they made more progress in mathematics than a control group who were not given this training. These studies establish a causal link between logical reasoning and mathematical learning. Much of children's mathematical knowledge is based on their understanding of its underlying logic.     

Children’s mapping between symbolic and nonsymbolic representations of number

When children learn to count and acquire a symbolic system for representing numbers, they map these symbols onto a preexisting system involving approximate nonsymbolic representations of quantity. Little is known about this mapping process, how it develops, and its role in the performance of formal mathematics. Using a novel task to assess children’s mapping ability, we show that children can map in both directions between symbolic and nonsymbolic numerical representations and that this ability develops between 6 and 8 years of age. Moreover, we reveal that children’s mapping ability is related to their achievement on tests of school mathematics over and above the variance accounted for by standard symbolic and nonsymbolic numerical tasks. These findings support the proposal that underlying nonsymbolic representations play a role in children’s mathematical development.     

Early predictors of high school mathematics achievement

Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students' knowledge of fractions and of division uniquely predicts those students' knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.     

The relationship between executive functioning and self-regulated learning in Australian children

Executive functioning (EF) and self-regulated learning (SRL) are established predictors of academic achievement, both concurrent and future. Although it has been theorized that EF development enables SRL in early childhood, this directional model remains empirically untested against plausible alternatives. Thus, this study investigated the longitudinal relations between children’s EF and SRL during the transition from kindergarten to Year 1 in an Australian sample to determine the direction and strength of the association between EF and SRL. We compared four directional models and also tested whether EF and SRL can be construed as manifestations of a common factor. Children’s EF was assessed using a battery of tasks tapping working memory, inhibition, and shifting, and their SRL was assessed by teachers using the Checklist of Independent Learning Development. Cross-lagged structural equation modelling analyses were conducted on a longitudinal dataset of 176 children at the end of kindergarten (age M = 5 years, 8 months; SD = 4.02 months), and 1 year later (age M = 6 years, 5 months; SD = 3.65 months). EF predicted SRL longitudinally (β= .58, controlling for kindergarten SRL), consistent with common assumptions, whereas SRL did not predict EF. However, the common factor model also fit the data very well. We concluded that EF and SRL are indeed related concurrently and longitudinally but that further evidence is needed to disambiguate whether EF is best understood as a necessary antecedent of SRL development in early childhood, or whether they reflect the same general construct.     

Approximate number sense,symbolic number processing,or number–space mappings: What underlies mathematics achievement?

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children’s performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well children compared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.     

Who uses more strategies? Linking mathematics anxiety to adults’ strategy variability and performance on fraction magnitude tasks

Adults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude comparison and estimation. Adults with higher mathematics anxiety had lower accuracy on the comparison task and greater percentage absolute error (PAE) on the estimation task. Unexpectedly, mathematics anxiety was not related to variable strategy use. However, variable strategy use was linked to more accurate magnitude comparisons, especially among adults with lower working memory performance or those who use mathematics less frequently, as well as lower PAE on the estimation task. These findings shed light on the role of strategy variability in fraction problem solving and demonstrate a link between mathematics anxiety and fraction magnitude reasoning, a key predictor of general mathematics achievement.     

数学成就的性别差异

数学成就的性别差异是多年来广受关注的问题。长期以来人们多关注男性、女性数学成就水平的高低, 而近年来研究结果一方面揭示出总体上男性和女性数学成就的平均水平差异很小, 呈现出相似性多于差异性的特点; 同时也显示男性内部变异比女性更大, 男性在高数学成就者中占多数。数学成就性别差异的大小和方向受到评分系统、测验组织形式、测验内容和难度的影响。数学成就性别差异的形成是心理、生物、社会文化等方面多因素综合作用的结果。近期研究探讨了年龄、遗传和进化、激素和脑、刻板印象威胁、社会性别公平和时代等因素在数学成就性别差异的形成中的作用。未来对数学成就性别差异的研究应注意开展追踪研究, 关注低数学能力者, 进一步探讨复杂数学加工机制的性别差异, 建立数学成就性别差异形成机制的综合模型, 并在更广阔的社会文化背景下开展研究。     

Early antecedents of childhood impulsivity: The role of parent-child interaction,cognitive competence,and temperament

This prospective longitudinal investigation examined early mother-child interaction as a predictor of children's later self-control capabilities. Multimethod assessments of mother-child relationships, primarily focused on observed relationship qualities in the home, were conducted during the first 2 years and related to children's later impulse control capabilities. Child cognitive competence and temperament assessed during the 2nd year were also related to later impulsivity. Follow-up assessments of children's impulsivity were conducted at age 6 (N=79), using a variety of laboratory measures. Findings indicated that responsive, cognitively stimulating parenttoddler interactions in the 2nd year modestly predicted later measures of cognitive nonimpulsivity and ability to delay gratification. Security of mother-infant attachment predicted the same outcomes, but only for boys and not for girls. Child cognitive competence in the 2nd year also consistently predicted children's later impulse control capabilities, although this was not true for measures of child temperament. Overall, the findings support a multidimensional and developmental conceptualization of the early antecedents of childhood impulsivity.This research was supported by NIMH grants MH28018 to J. E. Bates and MH38605 to S. L. Olson. Portions of this research were presented at the biennial meeting of the Society for Research in Child Development, Baltimore, April 1987. The authors thank the families who participated, and others whose help was essential in data collection: Beth Ridge, Melinda Monroe, Jeff Harness, and Christine Maslin.     

ANS acuity and mathematics ability in preschoolers from low‐income homes: contributions of inhibitory control

Recent findings by Libertus, Feigenson, and Halberda (2011) suggest that there is an association between the acuity of young children's approximate number system (ANS) and their mathematics ability before exposure to instruction in formal schooling. The present study examined the generalizability and validity of these findings in a sample of preschoolers from low‐income homes. Children attending Head Start (N = 103) completed measures to assess ANS acuity, mathematics ability, receptive vocabulary, and inhibitory control. Results showed only a weak association between ANS acuity and mathematics ability that was reduced to non‐significance when controlling for a direct measure of receptive vocabulary. Results also revealed that inhibitory control plays an important role in the relation between ANS acuity and mathematics ability. Specifically, ANS acuity accounted for significant variance in mathematics ability over and above receptive vocabulary, but only for ANS acuity trials in which surface area conflicted with numerosity. Moreover, this association became non‐significant when controlling for inhibitory control. These results suggest that early mathematical experiences prior to formal schooling may influence the strength of the association between ANS acuity and mathematics ability and that inhibitory control may drive that association in young children.     

Social support,physical functioning,and cognitive functioning among older African American adults

ABSTRACT

Social support and functional ability are related to a number of outcomes in later life among African Americans, including cognitive performance. This study examined how providing and receiving social support was related to fluid and crystallized cognitive abilities among aging African American adults after accounting for functional limitations, age, education, sex, income, and self-reported health. Data from 602 African American adults (M?=?69.08, SD?=?9.74; 25% male) were analyzed using latent variable modeling. Fluid ability was a second-order factor indicated by measures that assessed verbal memory, working memory, perceptual speed, and inductive reasoning. Crystallized ability was a first-order factor indicated by three measures that assessed vocabulary (Shipley Verbal Meaning Test and parts A and B of the ETS Vocabulary Test). Results indicated that the receipt of social support was negatively related to both fluid and crystallized abilities, while the provision of support was positively related to fluid and crystallized ability. Follow-up tests found that the receipt of support was more strongly related to fluid ability than crystallized ability. There was no significant difference regarding the relationship of provision of support with fluid ability compared to crystallized ability. Results discuss the importance of considering the social context of older adults when examining cognitive ability.     

Can we predict mathematical learning disabilities from symbolic and non‐symbolic comparison tasks in kindergarten? Findings from a longitudinal study

Background. The ability to compare numbers, as the most basic form of number sense, has been related to arithmetical achievement. Aims. The current study addressed the predictive value of non‐symbolic and symbolic (number word (NW) and Arabic number (AN)) comparison for arithmetics by means of a longitudinal design. Sample. Sixteen children with mathematical disabilities (MD), 64 low achievers (LA), and 315 typical achieving (TA) children were followed from kindergarten till grade 2. Method. The association of comparison skills with arithmetical skills in grades l and 2 was studied. The performances of MD, LA and TA children were compared. Results. Regression analyses showed that non‐symbolic skills in kindergarten were predictively related to arithmetical achievement 1 year later and fact retrieval 2 years later. AN comparison was predictively related to procedural calculation 2 years later. In grade 2, there was an association between both symbolic tasks and arithmetical achievement. Children with MD already had deficits in non‐symbolic and symbolic AN comparison in kindergarten, whereas in grade 2 the deficits in processing symbolic information remained. Conclusions. The combination of non‐symbolic and symbolic deficits represents a risk of developing MD.