儿童早期工作记忆与数学学习的关系

以往研究认为工作记忆对数学学习很重要,但是以往工作记忆和早期数学学习的关系研究结果并不一致。本研究运用元分析的方法回顾了33篇独立研究,含307项相关系数作为效应值,总被试量为42423名平均年龄3~8岁的儿童,旨在探讨工作记忆的3个主成分PL(语音回路)、VSSP(视觉空间画板)、CE(中央执行)与数学学习不同方面之间的关系,以及样本年龄对工作记忆和数学学习相关程度的调节作用。结果显示:工作记忆与数学学习确实存在强相关,工作记忆子成分中,CE与数学学习平均相关的程度最强。并且,CE与数学学习不同方面之间的相关程度不存在显著差异,PL、VSSP与数运算的相关程度比数概念更强,存在显著差异。样本年龄对CE、PL与数学学习之间相关关系存在显著调节作用,对VSSP与数学学习之间的相关关系不存在显著调节作用。文献梳理还发现,以往研究对数学学习的考察,大都聚焦数概念、数运算的内容,未来研究需要关注几何与空间、测量等方面内容。     

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.     

Working memory dependence of spatial contextual cueing for visual search

When spatial stimulus configurations repeat in visual search, a search facilitation, resulting in shorter search times, can be observed that is due to incidental learning. This contextual cueing effect appears to be rather implicit, uncorrelated with observers’ explicit memory of display configurations. Nevertheless, as I review here, this search facilitation due to contextual cueing depends on visuospatial working memory resources, and it disappears when visuospatial working memory is loaded by a concurrent delayed match to sample task. However, the search facilitation immediately recovers for displays learnt under visuospatial working memory load when this load is removed in a subsequent test phase. Thus, latent learning of visuospatial configurations does not depend on visuospatial working memory, but the expression of learning, as memory‐guided search in repeated displays, does. This working memory dependence has also consequences for visual search with foveal vision loss, where top‐down controlled visual exploration strategies pose high demands on visuospatial working memory, in this way interfering with memory‐guided search in repeated displays. Converging evidence for the contribution of working memory to contextual cueing comes from neuroimaging data demonstrating that distinct cortical areas along the intraparietal sulcus as well as more ventral parieto‐occipital cortex are jointly activated by visual working memory and contextual cueing.     

The differential effect of background music on memory for verbal and visuospatial information

Background music is a part of our everyday activities. Considerable evidence suggests that listening to music while performing cognitive tasks may negatively influence performance. However, other studies have shown that it can benefit memory when the music played during the encoding of information is also provided during the retrieval of that information, in the so-called context dependent memory effect. Since controversial results may be attributed to the nature of the material to be memorized, the aim of the present study is to compare the potential effect of consistent background music on the immediate and long-term recall of verbal and visuospatial information. Experiment 1 showed that instrumental background music does not benefit nor decrease recall of a list of unrelated words, both at the immediate and the 48-hours-delayed tests. By contrast, Experiment 2 revealed that the same background music can impair immediate and therefore long-term memory for visuospatial information. Results are interpreted in terms of competition for neurocognitive resources, with tasks mostly relying on the same brain hemisphere competing for a limited set of resources. Hence, background music might impair visuospatial memory to a greater extent than verbal memory, in the context of limited capacity cognitive system. In conclusion, the nature of the material to be learnt must be considered to fully understand the effect of background music on memory.     

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.     

Vocabulary learning in primary school children: Working memory and long-term memory components

The goal of this study was to investigate which working memory and long-term memory components predict vocabulary learning. We used a nonword learning paradigm in which 8- to 10-year-olds learned picture-nonword pairs. The nonwords varied in length (two vs. four syllables) and phonology (native sounding vs. including one Russian phoneme). Short, phonologically native nonwords were learned best, whereas learning long nonwords leveled off after a few presentation cycles. Linear structural equation analyses showed an influence of three constructs—phonological sensitivity, vocabulary knowledge, and central attentional resources (M capacity)—on nonword learning, but the extent of their contributions depended on specific characteristics of the nonwords to be learned. Phonological sensitivity predicted learning of all nonword types except short native nonwords, vocabulary predicted learning of only short native nonwords, and M capacity predicted learning of short nonwords but not long nonwords. The discussion considers three learning processes—effortful activation of phonological representations, lexical mediation, and passive associative learning—that use different cognitive resources and could be involved in learning different nonword types.     

Working memory and response inhibition in children and adolescents: age and organization issues

The aim of the present study was to examine the role of age in the organization of verbal working memory, visuospatial working memory and inhibition; specifically whether these constructs could be considered unitary or separate in children aged 7 to 12 years (n = 164) and in adolescents aged 13 to 16 years (n = 75) using a multi-group confirmatory factor analysis. Results suggested that verbal working memory, visuospatial working memory and inhibition improved from childhood to adolescence. However, improvement was not followed by a change in the organization of these components. Verbal working memory, visuospatial working memory and inhibition constituted separable but associated constructs in children and in adolescents.     

Action-control beliefs and behaviors as predictors of change in adjustment across the transition to middle school

Abstract

We examined longitudinal changes in young adolescents’ (N=368) action-control beliefs, coping behaviors, and adjustment (i.e., positive and negative affect, depression, aggression) across the transition from elementary school to middle school. Results indicated greater inter-individual instability in adjustment during this transition than during the previous school year. Using ordinary least-squares (OLS) growth models to extract intra-individual change scores for each variable (i.e., slopes and intercepts), we conducted a series of stepwise regressions to determine which features of control beliefs and coping behaviors best predicted changes in adjustment across the transition to middle school. We found that negative coping behaviors (i.e., antisocial coping) consistently predicted negative changes in the adjustment variables (e.g., greater depression, more aggression), whereas positive beliefs and behaviors did not consistently predict changes in the adjustment variables.     

小学儿童数学焦虑的潜在类别转变及其父母教育卷入效应：3年纵向考察

研究采用潜在转变分析考察小学儿童数学焦虑的类别转变以及父母教育卷入在小学儿童数学焦虑类别转变中的作用。以1720名三、四年级儿童为被试, 对其数学焦虑和感知到的父母教育卷入进行3次追踪, 每次间隔1年。结果表明：(1)小学儿童数学焦虑存在低数学焦虑组、高数学评估焦虑组和高数学获得焦虑组3种不同类别; (2)随时间的推移, 高数学评估焦虑组倾向于向低数学焦虑组转变, 高数学获得焦虑组倾向于向高数学评估焦虑组转变, 而低数学焦虑组稳定性较强; (3)父亲/母亲教育卷入对儿童数学焦虑类别转变的预测作用, 因不同的数学焦虑类别而异。上述发现为深入理解数学焦虑的形成机制以及干预措施的制定提供了重要参考。     

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.     

Working memory and vocabulary development in Greek preschool and primary school children

The present research investigated the relative contributions of verbal short-term memory (STM) and working memory (WM) to vocabulary development in the early years among Greek-speaking children. Participants were 5.5-, 7.5-, 8.5- and 9.5-year-old (N = 216) native speakers of Greek, a language differing from English in which most investigations have been conducted. Children were assessed with a receptive vocabulary task, four verbal STM measures (word, digit, and non-word list recall, as well as word list matching), and three verbal WM tasks (listening, counting, and backward digit recall). Results offer support to the view that both STM and WM influence vocabulary development in early stages. Vocabulary was associated with verbal STM at 7.5 and 8.5 years, but only with verbal WM at 5.5 years. Associations declined with age (by 9.5 years), earlier than in English-speaking children. Findings are discussed in relation to Greek language characteristics, demonstrating the importance of cross-cultural investigations.     

Working memory and inhibition across the adult life-span

Research has shown that age-related changes in cognitive performance are due mostly to the decline of general factors such as working memory and inhibition. The present study is aimed at investigating age-related changes in these mechanisms across the adult life-span from 20 to 86 years of age. Results indicate a linear relationship between each working memory measure and age, independently of the nature of the task, and a quadratic relationship between the single inhibitory measures and age. Moreover, hierarchical regression analyses show that inhibition accounts for a significant, but modest, part of the age-related variance in working memory. Taken together, these results suggest that inhibition is not as crucial a contributor of age-related changes in the functional capacity of working memory across the adult life-span as previously thought.     

Working memory and phonological awareness as predictors of progress towards early learning goals at school entry

This study investigates whether working memory skills of children are related to teacher ratings of their progress towards learning goals at the time of school entry, at 4 or 5 years of age. A sample of 194 children was tested on measures of working memory, phonological awareness, and non‐verbal ability, in addition to the school‐based baseline assessments in the areas of reading, writing, mathematics, speaking and listening, and personal and social development. Various aspects of cognitive functioning formed unique associations with baseline assessments; for example complex memory span with rated writing skills, phonological short‐term memory with both reading and speaking and listening skills, and sentence repetition scores with both mathematics and personal and social skills. Rated reading skills were also uniquely associated with phonological awareness scores. The findings indicate that the capacity to store and process material over short periods of time, referred to as working memory, and also the awareness of phonological structure, may play a crucial role in key learning areas for children at the beginning of formal education.     

Behavioral fluency and mathematics intervention research: A review of the last 20 years

Behavioral fluency refers to the relationship between the achievement of performance standards, or frequency ranges of behavior, and critical learning outcomes. Over the past 20 years, Precision Teaching and related research have contributed a number of studies examining behavioral fluency. The subsequent review investigates the empirical evidence from mathematics intervention research. Several studies suggest numerical markers that best support behavioral fluency. Results indicate that fluency interventions set to performance standards increased behavioral fluency and associated critical learning outcomes; however, more research is warranted to operationalize and standardize each outcome to the principles of behavior and numerical markers that constitute behavioral fluency.     

Long-term autobiographical memory across middle childhood: patterns,predictors, and implications for conceptualizations of childhood amnesia

ABSTRACT

We examined recall of events by children 4–11 years to inform patterns of retention of autobiographical memories as well as factors that predict their survival. 101 children participated in a 4-year prospective study. At study inception, children were 4, 6, and 8 years. They were tested annually for three more years for a total of four waves of data collection. At each wave, we obtained narrative reports of recent (all waves) and distant (Waves 2–4) events, resulting in virtually continuous sampling of memories formed by 4- to 11-year-olds and recalled after 1–3-year delays. We also measured children's language, and domain-general and memory-specific cognitive skills. Multi-level modelling revealed age-related increases in the likelihood of survival of memories over the delays. Critically, the rate of increase in retention of individual memories was the same across the cohorts. In addition to age, thematic coherence of original memory reports predicted memory survivability. Other factors were not predictive. The dense sampling and prospective tracking of memories across the 4–11-year age period permitted an especially strong test for continuity versus discontinuity in autobiographical memory across the second half of the first decade of life. The data are strongly indicative of continuity and gradual change.     

Stable same‐sex friendships with higher achieving partners promote mathematical reasoning in lower achieving primary school children

This study was designed to investigate friend influence over mathematical reasoning in a sample of 374 children in 187 same‐sex friend dyads (184 girls in 92 friendships; 190 boys in 95 friendships). Participants completed surveys that measured mathematical reasoning in the 3rd grade (approximately 9 years old) and 1 year later in the 4th grade (approximately 10 years old). Analyses designed for dyadic data (i.e., longitudinal actor‐partner interdependence model) indicated that higher achieving friends influenced the mathematical reasoning of lower achieving friends, but not the reverse. Specifically, greater initial levels of mathematical reasoning among higher achieving partners in the 3rd grade predicted greater increases in mathematical reasoning from 3rd grade to 4th grade among lower achieving partners. These effects held after controlling for peer acceptance and rejection, task avoidance, interest in mathematics, maternal support for homework, parental education, length of the friendship, and friendship group norms on mathematical reasoning.     

Preschool language and visuospatial skills respectively predict multiplication and addition/subtraction skills in middle school children

A converging body of evidence from neuroimaging, behavioral, and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in a longitudinal study measuring language and visuospatial skills in 358 preschoolers, and testing their mental calculation skills at the beginning of middle school. Language skills at 5.5 years significantly predicted multiplication, but not addition nor subtraction scores at 11.5 years. Conversely, early visuospatial skills predicted addition and subtraction, but not multiplication scores. These results provide strong support for the existence of a double dissociation in mental arithmetic operations, and demonstrate the existence of long-lasting links between language/visuospatial skills and specific calculation abilities.     

Successive teacher expectation effects across the early school years

The capacity for teacher expectation effects to interact and compound across a child's schooling offers a largely untested mechanism for magnifying or minimizing effects. This study examined four types of long-term teacher expectation effects: within-year effects of single teachers, cross-year effects of single teachers, mediated effects of single and multiple teachers, and compounded effects of multiple teachers. Participants were 110 students tracked from preschool through Grade 4 on measures of achievement and teacher expectations. Evidence was found for within-year but not direct cross-year effects. However, path models demonstrated enduring indirect effects of teacher expectations on cross-year achievement. Multiple years of teacher expectation effects were additive in predicting student achievement at fourth grade, with similar effects for teachers' over- and underestimates of student ability. The study extends understanding of longer-term teacher expectation effects.     

数学学习困难与工作记忆关系研究的现状与前瞻

工作记忆是一种对信息进行暂时加工和贮存的能量有限的记忆系统,在许多复杂的认知活动中起重要作用,工作记忆缺陷是造成数学学习困难的根本原因。数学学习困难儿童都存在视觉空间模板、语音回路以及中央执行器功能等方面的缺陷,工作记忆的各成分对数学困难者的影响不同。今后研究将以整体的、发展的视角,不断改进研究方法,将行为研究和神经加工机制研究相结合。