ISSN 1671-3710
CN 11-4766/R
主办:中国科学院心理研究所
出版:科学出版社

心理科学进展, 2018, 26(9): 1661-1669 doi: 10.3724/SP.J.1042.2018.01661

研究前沿

早期儿童数学学习与执行功能的关系

康丹,1, 曾莉2

1湖南师范大学, 认知与人类行为湖南省重点实验室, 长沙 410081

2成都大学师范学院, 成都 610106

The relationship between early childhood mathematics learning and executive function

KANG Dan,1, ZENG Li2

1 Cognition and Human Behavior Key Laboratory of Hunan Province, Hunan Normal University, Changsha 410081, China

2 Normal College, Chengdu University, Chengdu 610106, China

通讯作者: * 康丹, E-mail:kangdankang@163.com

收稿日期: 2017-07-10   网络出版日期: 2018-09-15

基金资助: 教育部人文社会科学研究青年基金项目(16YJC880025)

Received: 2017-07-10   Online: 2018-09-15

Fund supported: (16YJC880025)

摘要

执行功能是个体对复杂的认知活动的自我调节和以明确目标为导向的活动过程, 对早期儿童的数学学习起着重要的作用。早期儿童数学学习与执行功能呈显著正相关, 执行功能是儿童数学学习的重要认知加工机制。早期儿童执行功能和数学学习之间存在着相互预测的关系, 执行功能可以预测数学成绩, 数学成绩可以预测执行功能。高质量的早期数学教育可能具有发展儿童执行功能和数学能力的双重价值。未来研究可以明确执行功能的界定和统一测量工具, 提供更可靠的证据证明早期儿童执行功能与数学能力的因果关系, 以及进一步探究语言、数学以及执行功能三者之间的关系。

关键词: 早期儿童; 数学学习; 执行功能; 数学能力

Abstract

Executive function is the self-regulation of complex cognitive activities and a clear goal-oriented process, playing an important role in mathematics learning in early childhood. Executive function offers an important cognitive processing mechanism for the childhood mathematics learning. There is a mutual prediction relationship between executive function and mathematics learning. Executive function can be used to estimate mathematics achievement, and vice versa. Therefore, high quality mathematics education in early childhood may contribute to both developing children’s executive function and mathematical ability. Further research can help for clarifying the definition of executive function and unifying measurement tools. More reliable evidences are needed to prove the causal relationship between early childhood mathematics ability and executive function and further explore their relationships with languages.

Keywords: early childhood; mathematical learning; executive function; mathematical ability

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本文引用格式

康丹, 曾莉. 早期儿童数学学习与执行功能的关系 . 心理科学进展, 2018, 26(9): 1661-1669 doi:10.3724/SP.J.1042.2018.01661

KANG Dan, ZENG Li. The relationship between early childhood mathematics learning and executive function. Advances in Psychological Science, 2018, 26(9): 1661-1669 doi:10.3724/SP.J.1042.2018.01661

1 引言

执行功能在儿童的数学学习中起着非常重要的作用。从理论上看, 执行功能影响儿童的数学学习表现在两个方面。第一, 执行功能是支持儿童数学学习的必要认知过程, 是儿童数学能力和推理能力发展的前提条件和基础。至少, 工作记忆对儿童过程性数学学习是必不可少的(Geary, Hoard,& Nugent, 2012)。例如, 儿童用倒数策略解决减法问题的时候, 就需要记住整体和部分的关系, 以及已经数过的数字。此外, 工作记忆可以帮助儿童将学习策略和问题情境建立起联系, 并且建构数学结构和问题解决技巧(van der Ven, Kroesbergen, Boom, & Leseman, 2012)。第二, 执行功能可以提高儿童的自我调节能力, 影响他们与其他人的互动, 从而直接或间接地影响儿童的数学学习(Montroy, Bowles, Skibbe, & Foster, 2014)。

目前, 学界对执行功能的定义尚未达成共识。一般认为, 执行功能(Executive Function)是个体对复杂认知活动的自我调节和以明确目标为导向的活动过程, 对输入的信息进行存储和加工, 灵活处理各种有效信息, 并控制无关信息对认知加工过程的干扰, 使行为变得有目的性、有序(Isquith, Gioia, & Espy, 2004)。执行功能可以在功能上看成是一个整体, 也可以分为刷新工作记忆, 认知灵活性和抑制控制三个成分(Miyake & Friedman,2012; Schoemaker, Bunte, Espy, Deković, & Matthys, 2014)。工作记忆是一个负责短期持有和信息处理的系统, 具体指在处理新信息时更新旧的工作记忆, 即在参与另一个认知需求较高的任务时, 维护、操纵和使用相关的信息; 认知灵活性是个体根据不同的规则要求, 在不同的任务或心理定势之间进行转换, 克服心理定势效应的影响并保持思维和动作灵活性的过程; 抑制控制是对个体认知过程或认知内容进行抑制控制, 对认知过程中的优势或自动化反应进行有意识的抑制控制(Miller, Müller, Giesbrecht, Carpendale, & Kerns, 2013)。

执行功能作为一般认知能力, 不仅支持着早期儿童的数学能力发展, 也对儿童的语言发展起着重要的作用。最近研究发现, 6岁儿童的词汇、空间和执行功能与阅读、数学相关显著(Zhang, Hu, Ren, & Fan, 2017)。早期儿童的执行功能可以预测语言能力的发展(White, Alexander, & Greenfield, 2017)。但是, 数学与执行功能的相关程度比语言等其他学科相关的程度更高(Cragg & Gilmore, 2014)。早期儿童的数学技能(例如基数理解, 计数技能和基本计算等)和执行功能, 都是儿童未来数学能力的重要预测因子(Clark, Sheffield, Wiebe, & Espy, 2013)。迄今, 研究者已经对执行功能和数学学习的关系进行了大量的探讨。梳理早期儿童数学学习和执行功能的关系可以为教育者设计课程提供依据。例如, 如果执行功能与数学之间的相关程度比阅读强, 那么将执行功能与数学课程组合在一起, 可以提高教育的有效性。如果抑制控制与数学学习之间的关系比认知灵活性或工作记忆更密切, 那么教育者在设计课程的时候就可以更关注培养儿童的抑制控制能力。如果执行功能在儿童年龄较小的时候更具有可塑性, 或者随着儿童年龄的增长, 执行功能与数学成绩之间的相关程度下降。那么, 在学前教育和早期小学阶段的课程中包含更多的执行功能的训练会更有意义。本研究集中探讨早期儿童(3~8岁)的执行功能和数学学习的关系, 以更好地理解如何促进两种能力的发展。首先, 总结了儿童数学学习的执行功能加工机制; 其次, 探讨了早期儿童数学能力与执行功能是否存在因果关系; 最后, 就已有的研究进行了总结并对今后的相关领域研究作出一定的展望。

2 早期儿童数学学习的执行功能加工机制

2.1 工作记忆机制

工作记忆在儿童数学学习中不仅起到保持信息的关键作用, 也起到操作和更新信息的作用(Cragg & Gilmore, 2014)。工作记忆是数学学习的关键机制, 可以预测儿童不同年龄阶段的数学技能(van der Ven et al., 2012)。工作记忆和数学各个方面呈显著正相关, 可以解释不同年龄组儿童在书面、口头运算、数学应用题等各方面的差异, 而且这种差异不能用年龄、智商、数学能力、处理速度、阅读和语言技能等其他因素来解释(Agostino, Johnson, & Pascual-Leone, 2010)。国内学者陈英和等研究发现, 儿童算术认知策略表现受到其工作记忆广度的限制, 不同工作记忆广度的儿童在出声、手动、心里数数、竖式、分解、凑整、猜测、算术认知策略的执行上有显著性差异(王明怡, 陈英和, 2005; 陈英和, 王明怡, 2006)。

纵向追踪研究发现, 学前班儿童的工作记忆能够预测三年级的数学成绩(Bull, Espy, & Wiebe, 2008)。而且, 工作记忆比抑制控制和认知灵活性更能预测早期儿童的数字线, 工作记忆更好的儿童在数字线方面提高更快(Kolkman, Hoijtink, Kroesbergen,& Leseman, 2013)。另外一项追踪研究发现, 从幼儿园到5年级, 儿童的工作记忆与阅读的相关程度随着年龄增长会减弱, 而数学与工作记忆的相关程度却随年龄的增长会增强(Geary,2011)。这表明, 虽然工作记忆对数学以外的学术成就也很重要, 但工作记忆与不同学科领域的相关程度在不同的年龄阶段有所不同。为了进一步检测儿童数学学习所涉及的机制, 研究者用功能性磁共振成像技术(fMRI)研究成年人和儿童在完成数字比较任务和简单加法任务中的脑成像, 结果发现成年人的大脑后顶叶区域比儿童显示出更强的活动性, 而儿童在额叶区域显示更大的活动, 例如额叶内侧和额下回。研究者认为随着年龄的增长, 儿童的数学学习对工作记忆和注意力依赖的逐渐减少, 支持其数学学习的大脑区域功能上逐渐专门化(Cantlon et al., 2009)。

工作记忆对数学的重要性还体现在数学学习困难儿童的数学学习中。研究者认为工作记忆的缺陷是导致儿童数学成绩差的一个重要原因, 而且工作记忆的缺陷导致儿童在抑制控制、认知灵活性方面的困难, 从而间接地影响儿童的数学成绩(Bull & Scerif, 2001)。元分析研究进一步表明, 有数学学习困难的儿童在工作记忆方面尤其困难, 特别是当涉及到数字信息的时候, 如数字倒背广度任务(David, 2012)。工作记忆影响儿童的数量加工、问题解决以及数学成绩, 数学学习困难儿童在工作记忆方面表现出不足(Xenidou-Dervou, De Smedt, van der Schoot, & van Lieshout, 2013)。即使使用非数字刺激任务(例如字母或单词), 工作记忆仍然能够预测数学成绩和数学学习困难, 甚至超过数学能力的预测价值(Toll, van der Ven, Kroesbergen, & van Luit, 2011)。工作记忆可以作为鉴别早期数学学习困难儿童的指标之一。

2.2 认知灵活性机制

学前儿童的认知灵活性可以预测数学能力, 一年级儿童的模式学习与认知的灵活度有关(Bock et al., 2015)。Bull等人采用威斯康星卡片分类测验、双任务测验、斯特鲁普(stroop)任务以及数字广度任务评价学前儿童的执行功能。结果表明, 除了双重任务外, 其他任务测量都与儿童的数学能力呈显著正相关; 排除了阅读能力和智商的影响后, 不同数学能力的儿童在威斯康星卡片分类任务(测量认知灵活性任务)有显著性差异; 认知灵活性不佳的儿童, 其主要困难在于从一种分类转换到另一种分类, 以及由此产生的多种连续性反应错误(Bull et al., 2008)。McLean和Rusconi (2014)的研究对认知灵活性影响儿童数学学习的机制做了初步解释, 认知灵活性是通过对数学问题解决中多个策略和方法之间的交替支持来影响数学学习的。例如, 如果7岁儿童如果认知灵活性差, 就可能表现出数学学习困难, 主要体现在他们解决新的数学问题时比正常儿童差, 因为完成这些新的数学学习任务需要他们从常用的策略转换到用新的策略(Bull & Scerif, 2001)。然而, 有的研究却发现了认知灵活性与学前儿童的数学能力相关不显著。艾普森等人对2~5岁儿童的研究也发现, 认知灵活性不能预测儿童的数学能力(Espy et al., 2004)。Blair和Razza (2007)的研究也发现, 3~5岁儿童的认知灵活性与数学能力相关不显著, 但是抑制控制与数学能力呈显著正相关。可见, 目前的研究对早期儿童的认知灵活性与数学之间的关系的结论并不一致, 还需要更多的研究证实两者之间的关系。

2.3 抑制控制机制

抑制控制也是执行功能的一个重要组成部分, 对儿童数学学习很重要。儿童在解决数学问题的时候, 需要抑制占优势的自动化反应, 采取正确的策略解决问题。如, “现在有3块积木, 之前拿走了2块。原来有多少块积木?”儿童要抑制住“拿走”这一词所产生的采用减法的想法, 而是通过其他策略计算总和。此外, 早期儿童数学学习中需要抑制控制无关信息的干扰, 从而将注意力集中于解决问题的关键信息。例如, 儿童在解决加法问题的时候就需要抑制大量关于问题背景或者无关信息的干扰。“小明有3块糖果, 妈妈再给了他2块, 现在一共有几块糖果?”在解决这类问题的时候, 儿童要抑制住对“糖果”信息的关注, 主要关注问题中的数量关系。研究发现, 学前儿童的抑制控制是数学能力的一个重要预测因子(Bull & Scerif, 2001;Steele, Karmiloff-Smith, Cornish, & Scerif, 2012)。对2~5岁儿童的纵向追踪研究发现, 控制了年龄、母亲教育背景和儿童语言词汇能力等因素后, 抑制控制和工作记忆能预测数学能力(Espy et al., 2004)。国内的研究发现, 注意和抑制控制可以影响儿童在数字比较任务中的许多认知加工效应, 例如数字距离效应、SNARC效应(spatial numerical association of response codes)、符号效应(刘超, 买晓琴, 傅小兰, 2004; 隋光远, 吴燕, 曹晓华, 2006)。近年的研究进一步证实了抑制控制对数学学习的重要性, 当考虑到抑制控制因子后, 近似值数字比较任务不再是数学能力的预测因子(Ng, Tamis-Lemonda, Yoshikawa, & Sze, 2015)。这说明领域一般性的抑制控制任务比领域特殊性的近似值数字比较任务更能预测儿童的数学成绩。此外, 数学学习困难儿童在抑制控制方面存在缺陷, 抑制控制差是造成儿童解决计算问题困难的最基本原因之一(Geary, Hoard, Byrd- Craven, & DeSoto, 2004)。

3 早期儿童执行功能与数学能力的相互预测关系

早期儿童的执行功能可以预测未来的数学成绩(Clark, Pritchard, & Woodward, 2010; Monette, Bigras, & Guay, 2011)。执行功能在数学学习中的作用与任务的难度有关系, 特别是数学学习任务需要复杂的执行功能参与的时候, 执行功能的作用更加重要(LeFevre et al., 2013)。同时, 数学能力也可以预测执行功能(van der Ven et al., 2012)。也就是说, 早期儿童执行功能与数学能力存在着相互预测的关系。

3.1 早期儿童的执行功能可以预测数学能力

Bull等使用曲线增长模型发现儿童4岁时的执行功能得分与5~7岁时的数学能力呈显著正相关, 执行功能可以预测数学能力的高低(Bull et al., 2008)。Clark等人的研究发现3岁时候的执行功能与6岁时候的数学能力呈显著正相关, 在控制了早期非正式数学能力、社会经济地位、语言和速度加工等因素后, 两者仍然呈显著正相关(Clark et al., 2010)。当考虑到加工速度的因素, 执行功能虽然不能预测3岁儿童的数学能力, 但是可以预测4~5岁儿童的数学能力(Clark et al., 2014)。最近的研究表明, 学前儿童的执行功能可以预测一年级的数学成绩(Davidse, de Jong, & Bus, 2015)。在控制了早期儿童数学技能和其他背景因素(例如年龄, 性别, 英语学习者状况)后, 执行功能独立地预测了一年级的数学分数, 尤其对“应用题”子测验的预测效应最大(Hassinger-Das, Jordan, Glutting, Irwin, & Dyson, 2014)。

早期儿童的执行功能发展与数学和阅读都呈显著正相关,一年级阅读能力差的儿童执行功能技能也较差(Dombek & Connor, 2012)。在控制了性别和智商等因子后, 抑制控制和认知灵活性能预测幼儿的数学和读写能力(Blair & Razza, 2007)。这表明执行功能可能是早期儿童的语言和数学学习过程中共同的重要认知机制。在探讨执行功能和数学学习的关系的时候, 也需要考虑语言这个变量。尽管执行功能可以预测之后的数学能力的研究成果较多, 但是学者们对有的研究结果的执行功能与数学能力之间关系的线性解释存在一些质疑。例如, Clark等人(2010)的研究中发现早期儿童的执行功能可以预测数学技能, 但是这个研究中并没有对儿童的数学技能进行前测和对执行功能进行后测, 研究结果只能作为两者之间因果关系的可能解释。

3.2 早期儿童的数学能力可以预测执行功能

已有研究非常注重执行功能对儿童数学能力发展的重要性, 甚至认为执行功能是确保其未来学业发展的重要基础(McClelland et al., 2007)。那么, 数学能力是否可以预测儿童执行功能的发展呢?一项追踪研究表明执行功能与数学能力是可以相互预测的。研究者发现, 初入学前班儿童的工作记忆和注意力控制预测了一年的早期读写能力和认数能力的增长。认数能力也预测了学前班儿童这一年的执行功能的增长(van der Ven et al., 2012)。幼儿园大班入学时的工作记忆和注意力预测了大班末的早期读写能力和数学能力的增长, 计算能力预测了之后的执行功能(Welsh, Nix, Blair, Bierman, & Nelson, 2010)。还有研究发现了儿童早期和之后的数学成绩之间呈显著正相关, 执行功能在其中起到了中介作用; 早期数学能力预测了执行功能的所有任务(Watts et al., 2015)。早期儿童读写能力与执行功能之间不存在双向预测关系(Fuhs, Nesbitt, Farran, & Dong, 2014)。儿童进入学前班时的执行功能显著预测了在学前班结束时的词汇技能, 但词汇技能并不能预测执行功能的发展(Weiland, Barata, & Yoshikawa, 2014)。

以上研究结果表明, 早期儿童的执行功能与数学能力可以相互预测, 但是这些结果并不一定代表二者之间是因果关系。为了评估执行功能与数学成绩是否具有因果关系, 需要更严格的实验设计。研究设计需要符合两个基本条件。第一, 设计旨在提高儿童执行功能或者数学能力的干预措施, 但不会影响任何其他因素, 再探讨儿童的数学成绩或者执行功能是否因干预而得到提高。第二, 随机分配被试, 并在干预前后评估儿童的执行功能和数学成绩。

4 早期儿童执行功能和数学能力的干预研究

4.1 执行功能干预对执行功能和数学能力的影响

执行功能可以通过训练或干预提高(Zelazo & Carlson, 2012)。有研究者认为, 提高早期儿童的执行功能是预防以后学业失败(包括数学学习)的一个重要方法。如果可以通过提高儿童的执行功能来影响数学成绩, 那么执行功能的干预就具有双重价值。因此, 较多学者和实践者十分关注早期儿童执行功能干预研究。

“心灵的工具” (Tools of the Mind)是一个旨在提高儿童执行功能的学前教育课程, 这个课程是依据维果斯基的观点设计的。研究者将147名儿童随机分成实施“心灵工具”课程的实验组和实施传统早期识字课程的控制组。教师每天花费80%的时间来提升儿童的执行功能。结果发现参与“心灵的工具”课程组的儿童在简单和复杂的执行功能任务中表现明显优于控制组儿童。然而, 由于这个研究没有执行功能的前测数据, 也没有严格控制儿童的类别, 使得研究结果的解释存在分歧。后续的研究结果也没有强有力的证据表明“心灵的工具”对执行功能和学业成绩产生积极影响(Barnett et al., 2008)。但是, 当执行功能嵌入到学前儿童的识字、数学和科学学习活动中时, 对儿童的学业成绩产生了一些积极的影响(Clements, Sarama, & Germeroth, 2016)。

另外一个著名的项目是芝加哥入学准备项目(Chicago School Readiness Project, 简称CSRP), 是一个旨在通过训练儿童的自我控制能力来提高执行功能和学业成绩的项目。结果发现, 实验组儿童的执行功能、数学技能、字母命名有显著的提高; 其中对早期数学技能的干预效应值为0.54; 儿童的执行功能对字母命名和数学的干预效应起到中介作用(Raver et al., 2011)。这项研究为使用课程干预执行功能可行性和可塑性提供了证据, 但是这个研究旨在同时提高儿童的执行功能和数学能力, 并不关心两者是否有因果关系。

还有一个称为“红灯, 紫灯(Red Light, Purple Light)”的旨在训练学前儿童执行功能的游戏课程。这个游戏类似于传统的“红灯停、绿灯行”游戏, 儿童必须记住哪种颜色的灯意味着“停止”, 哪种颜色的灯意味着“走”; 规则会周期性地改变, 所以有时候紫灯表示“停止”, 有时候意味着“走”。这种类型的游戏有6种不同的形式。随机分配被试进行实验研究, 实验组儿童每周参加2次, 每次30分钟, 总共8周。采用“头、脚、膝盖、肩膀”任务(Head-Toes-Knees-Shoulders, 简称HTKS)来评估儿童的执行功能。研究结果发现, 整个样本的儿童的执行功能没有提高, 但是执行功能差的儿童的执行功能提高了; 干预对儿童字母识别的影响显著, 对数学成绩的影响不显著(Tominey & McClelland,2011)。这项干预研究似乎影响了执行功能, 但并没有影响到整个样本的执行功能。

产生以上结果的可能原因有两个。第一, 干预实际上也可能影响了儿童的执行功能, 但是在单一的测查任务(如HTKS)中没有表现出来。如果有更多的测量来评估执行功能, 研究的结果可能更加具有说服力。第二, 干预措施也可能对执行功能以外的其他因素产生影响, 如自信心, 这些被影响的因素可能影响了学习成绩。然而, 有的研究者却认为执行功能和成绩之间可能没有因果关系, 因为考虑到儿童背景特征和智商的时候, 执行功能与儿童成绩之间减少了2/3以上的相关(Jacob & Parkinson, 2015)。总之, 目前的研究还不够强有力地证明干预执行功能可以提高数学成绩, 未来需要更多的研究证明执行功能干预对数学成绩产生的影响。

4.2 数学干预对数学和执行功能发展的影响

有研究发现, 高质量的数学教学活动不仅可以提高早期儿童的数学能力, 也可能促进执行功能的发展。例如, 以提高儿童数学能力为目标的积木建构数学课程(Building Blocks mathematics curriculum), 在提高儿童数学能力的同时, 也促进了儿童的执行功能的发展(Weiland & Yoshikawa, 2013)。研究者把学前儿童分成了三个组:积木建构数学课程+心灵工具组, 心灵工具组, 控制组。他们提出了两个实验假设:第一, “心灵工具”组儿童的执行功能增长会显著高于“积木建构数学课程+心灵工具”组; 第二, “心灵工具”组和“积木建构数学课程+心灵工具”组儿童的数学能力增长都会显著高于控制组。研究结果发现, “积木组”的数学分数比其他两组的分数更高, 但是没有达到统计学显著水平。“积木组”在执行功能的“头、脚、膝盖、肩膀”任务(HTKS)的得分显著高于控制组; “积木组”在执行功能的数字倒背任务的得分显著高于“积木建构数学课程+心灵工具” (Clements et al., 2016)。这个研究说明儿童的数学学习可能在一定程度对数学能力和执行功能都产生了积极的影响。以往的研究中研究者认为, 领域一般认知能力(包括执行功能)对儿童数学能力的发展起单向的支持作用(Östergren & Träff, 2013), 而数学学习影响一般认知能力的研究较少涉及。这项研究可以启发学者和教育者重新认识早期儿童数学学习的价值。在实践教学中, 教师对数学的关注越多, 儿童在数学和执行功能方面的收获就越大(King, Lancaster, DeFrance, Melin, & Cleveland, 2013)。这是因为儿童数学学习为执行功能的发展提供了可能和支架, 数学学习过程本身就需要运用工作记忆、认知灵活性和抑制控制等一般认知能力。例如, 与儿童解决应用题的时候可能会把问题情境与自己熟悉的现实世界体验结合起来, 这种建构的方式能够指导儿童把现实情境转化为逻辑和系统的数学结构。这样的活动不仅促进了数学能力发展, 而且也提高了执行功能, 特别是工作记忆和抑制控制。当然, 这一结论还需要更多研究来证实。

5 小结和展望

本研究试图系统地分析文献中早期儿童的执行功能与数学能力的关系。已有的研究证明了执行功能与幼儿的数学能力之间呈显著正相关, 执行功能是儿童数学学习的重要认知加工机制(Ng et al., 2015)。学前儿童的执行功能是数学能力的预测因子。相比于语言, 执行功能与数学之间的关系更加密切(Fuhs et al., 2014)。其次, 执行功能各成分对数学能力的贡献并非是一致的。有的研究者认为抑制对数学的影响最大(Blair & Razza, 2007), 有的研究者却认为工作记忆对数学能力的影响最大(Geary et al., 2012), 尚无定论。再次, 执行功能与数学的不同方面相关。小学儿童的工作记忆与更高级的数学策略之间呈显著正相关, 一年级儿童的模式与认知灵活性密切相关(Bock et al., 2015)。工作记忆能预测加法能力, 即使控制了加工速度和短时记忆, 工作记忆仍然可以预测3~6年级儿童的计算能力(Berg, 2008)。已有研究的相关研究结果的相关系数比预测关系系数大, 这可能是因为已有的研究在分析相关关系的时候往往较少控制干扰变量, 而分析预测关系的时候控制的干扰变量要严格一些。

已有的研究具有重要的实践意义。早期优质的数学教育可能具有发展儿童数学能力和执行功能的双重价值(Watts et al., 2015)。神经心理学的研究也提供了证据, 儿童学习算术组合时, 他们首先使用的是他们的大脑的前额区域(执行功能), 接着使用颞区(陈述性记忆)和顶叶区域(数距判断和数学事实提取)和后枕区域(符号形式运算) (Butterworth, Varma, & Laurillard, 2011)。这说明数学是大脑思维的“体操”, 学习过程中儿童运用了执行功能, 可能促进了执行功能的进一步发展。数学可以对儿童的执行功能起到唤起、启动和锻炼的作用(Clements et al., 2016)。执行功能和数学能力可能是共同发展和相互支持的。儿童早期的数学能力为以后儿童数学能力和执行功能的发展提供了资源。提供优质的数学活动可以为发展儿童的执行功能提供支持。还需要更多设计更为严谨、高质量的数学项目, 进一步证明数学学习不仅可以提高儿童的数学能力, 也能促进执行功能发展。未来的研究还可以从以下几个方面完善。

首先, 需要更加明确、统一的执行功能定义、结构和测量任务。如果没有明确的执行功能界定和统一的测量工具, 很难得出可以比较的研究结论和进行有利于儿童发展的干预。例如, 已有的研究中大部分采用的经典研究任务的直接得分作为该执行功能成分的指标。然而,近年的验证性因子分析研究发现, 在学前阶段儿童的执行功能的各个成份并没有明确区分, 而是作为单一因素模型对数学技能产生影响, 执行功能作为一个潜在的变量预测了当前的和以后的数学技能; 小学低年级儿童的执行功能可以划分为工作记忆因子以及抑制、认知灵活性联合的因子(Bull & Lee, 2014)。那么, 是否可以假设在不同的年龄阶段, 儿童的执行功能成分可能存在差异?需要进一步验证在不同的年龄阶段儿童的执行功能的成分。

其次, 未来的研究可以对儿童背景特征进行强有力的控制的前提下, 进一步探究执行功能干预与数学学习之间是否存在因果关系。已有研究分析了有关背景特征和智商测量的数据, 但在很多回归分析中并没有控制这两个因素。大多数干预研究结果只是对执行功能和数学成绩之间的因果关系提供有限的支持。此外, 执行功能发展在什么时候, 在何种程度上影响数学学习, 也仍然是一个悬而未决的问题。未来需要更严格的研究设计来更好地了解执行功能与数学成绩之间关系的性质。

最后, 需要更多的研究进一步探究语言、数学和执行功能三者之间的关系。语言与早期儿童的数学成绩相关, 并且能够预测数学成绩。小学儿童的语言技能与应用题关系密切, 但是与运算不相关(Fuchs et al., 2010)。这是因为这两类数学问题对儿童的语言要求不同。如在解决数学应用题的过程中, 既要求儿童能够理解一系列数学词汇, 还要能够在词汇与符号之间相互转化(例如, “加上” “一共”)。语言技能与理解其数学概念的意义有关, 与数学运算过程却是无关的(Vukovic & Lesaux, 2013)。也有研究发现, 语言可以预测学前儿童的非正式数学技能, 但无法预测正式的数学运算技能(Purpura, Hume, Sims, & Lonigan, 2011)。这可能是因为早期儿童的数学学习中要将数学知识与词汇、符号联系起来, 或者要理解早期数学概念的意义。儿童还需要了解语言中一些概念(或术语), 比如“更多”和“更少”, 并且区分它们。学前儿童语言流畅性和加工速度对数学能力有预测作用, 执行功能在两者之间起中介作用(Clark et al., 2014)。但是, 总体看来现有研究中进一步揭示语言、数学以及执行功能三者关系的研究相对比较少, 进一步开展这些方面的研究, 并且验证其预防未来学习困难的有效性, 可以为教育者提供更多有益的启示。

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Journal of Cognitive Neuroscience, 21( 11), 2217-2229.

DOI:10.1162/jocn.2008.21159      URL     PMID:2745480      [本文引用: 1]

As literate adults, we appreciate numerical values as abstract entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notation-independent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance imaging, we examine the brain mechanisms that 6- and 7-year-old children and adults recruit to solve numerical comparisons across different notation systems. The data reveal that when young children compare numerical values in symbolic and nonsymbolic notations, they invoke the same network of brain regions as adults including occipito-temporal and parietal cortex. However, children also recruit inferior frontal cortex during these numerical tasks to a much greater degree than adults. Our data lend additional support to an emerging consensus from adult neuroimaging, nonhuman primate neurophysiology, and computational modeling studies that a core neural system integrates notation-independent numerical representations throughout development but, early in development, higher-order brain mechanisms mediate this process.

Clark C. A. C., Pritchard V. E., & Woodward L. J. ( 2010).

Preschool executive functioning abilities predict early mathematics achievement

Developmental Psychology, 46( 5), 1176-1191.

DOI:10.1037/a0019672      URL     [本文引用: 3]

Clark C. A. C., Sheffield T. D., Wiebe S. A., & Espy K. A. ( 2013).

Longitudinal associations between executive control and developing mathematical competence in preschool boys and girls

Child Development, 84( 2), 662-677.

DOI:10.1111/cdev.2013.84.issue-2      URL     [本文引用: 1]

Clark C. A. C., Nelson J. M., Garza J., Sheffield T. D., Wiebe S. A., & Espy K. A. ( 2014).

Gaining control: Changing relations between executive control and processing speed and their relevance for mathematics achievement over course of the preschool period

Frontiers in Psychology, 5, 107.

[本文引用: 2]

Clements D. H., Sarama J., & Germeroth C. ( 2016).

Learning executive function and early mathematics: Directions of causal relations

Early Childhood Research Quarterly, 36( 9), 79-90.

DOI:10.1016/j.ecresq.2015.12.009      URL     [本文引用: 3]

Although there has been much recent attention to young children's development of executive function and early mathematics, few studies have integrated the two. Here we review the evidence regarding executive function and mathematic achievement in the early years. After defining the executive function processes we consider, we briefly address the question of whether executive function can be taught in schools. We then turn to the relations between executive function and achievement. We begin with a review of the larger literature on correlations between the two, both concurrent and predictive. This leads to the fewer but more directly educationally-relevant causal studies. We conclude that developing both executive function processes and mathematical proficiencies is essential for young children and suggest that high-quality mathematics education may have the dual benefit of teaching this important content area and developing executive function processes.

Cragg, L., & Gilmore, C. ( 2014).

Skills underlying mathematics: The role of executive function in the development of mathematics proficiency

Trends in Neuroscience & Education, 3( 2), 63-68.

[本文引用: 2]

David, C. V. ( 2012).

Working memory deficits in math learning difficulties: A meta-analysis

International Journal of Developmental Disabilities, 58( 2), 67-84.

DOI:10.1179/2047387711Y.0000000007      URL     [本文引用: 1]

ABSTRACT In the present study, we made a quantitative synthesis of the literature comparing children with Math learning difficulties to average-achieving, age-matched children on measures of working memory in view of Baddeley and Hitch’s multicomponential working memory model. Our meta-analytic investigation drew from the literature a number of 18 studies that matched the inclusion criteria. We hypothesized that all three components of Baddeley and Hitch’s model should contribute to the poor Math performance displayed by children with Math learning difficulties, and that this relation varies as a function of age. Also, we hypothesized that children with Math learning difficulties would present more accentuated working memory deficits for numerical material and/or processing. Based upon Cohen’s criteria, the results indicate a large effect size, in favor of the controls for the relationship between Math performance and central executive component, as well as Math performance and the visual–spatial sketchpad, more accentuated in younger ages. Only a moderate effect size emerged in the case of Math performance and the phonological loop (PL). With respect to numerical versus non-numerical working memory deficits, a large effect size emerged for numerical central executive measures, along with a moderate effect size for the PL numerical measures, and a weak effect size for non-numerical PL. The results indicate that Math difficulties are attributable to a central executive deficit or delay, more accentuated for numerical stimuli and/or processing and to a visual–spatial working memory deficit.

Davidse N. J., de Jong M. T., & Bus A. G. ( 2015).

Causal relations among executive functions and academic skills from preschool to end of first grade

English Linguistics Research, 4( 1), 49-60.

[本文引用: 1]

Dombek, J. L., & Connor, C. M. ( 2012).

Preventing retention: First grade classroom instruction and student characteristics

Psychology in the Schools, 49( 6), 568-588.

DOI:10.1002/pits.21618      URL     [本文引用: 1]

Retention is a frequently used strategy to support children who are struggling academically. However, the strategy is costly, and research findings with regard to positive outcomes are mixed. This study examined whether efficacious reading instruction might reduce rates of retention in first grade. We also evaluated the reading instruction the students received compared with children with similar reading and vocabulary skills who were not retained. Additionally, we examined the impact students' self-regulation may have on grade retention. Findings reveal that it was significantly less likely for students to be retained at the end of first grade if their teacher was implementing more efficacious reading instruction. Moreover, there were substantial differences in the literacy instruction provided for children who were and were not retained. Finally, students in the efficacious reading condition who were retained exhibited significantly weaker self-regulation skills than did their matched-promoted peers. 2012 Wiley Periodicals, Inc.

Espy K. A., McDiarmid M. M., Cwik M. F., Stalets M. M., Hamby A., & Senn T. E. ( 2004).

The contribution of executive functions to emergent mathematic skills in preschool children

Developmental Neuropsychology, 26( 1), 465-486.

DOI:10.1207/s15326942dn2601_6      URL     PMID:15276905      [本文引用: 2]

Mathematical ability is related to both activation of the prefrontal cortex in neuroimaging studies of adults and to executive functions in school-age children. The purpose of this study was to determine whether executive functions were related to emergent mathematical proficiency in preschool children. Preschool children (N = 96) were administered an executive function battery that was reduced empirically to working memory (WM), inhibitory control (IC), and shifting abilities by calculating composite scores derived from principal component analysis. Both WM and IC predicted early arithmetic competency, with the observed relations robust after controlling statistically for child age, maternal education, and child vocabulary. Only IC accounted for unique variance in mathematical skills, after the contribution of other executive functions were controlled statistically as well. Specific executive functions are related to emergent mathematical proficiency in this age range. Longitudinal studies using structural equation modeling are necessary to better characterize these ontogenetic relations.

Fuchs L. S., Geary D. C., Compton D. L., Fuchs D., Hamlett C. L., Seethaler P. M., .. Schatschneider C. ( 2010).

Do different types of school mathematics development depend on different constellations of numerical versus general cognitive abilities?

Developmental Psychology, 46( 6), 1731-1746.

DOI:10.1037/a0020662      URL     [本文引用: 1]

Fuhs M. W., Nesbitt K. T., Farran D. C., & Dong N. ( 2014).

Longitudinal associations between executive functioning and academic skills across content areas

Developmental Psychology, 50( 6), 1698-1709.

DOI:10.1037/a0036633      URL     [本文引用: 2]

Geary D. C., Hoard M. K., Byrd-Craven J., & DeSoto M. C. ( 2004).

Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability

Journal of Experimental Child Psychology, 88( 2), 121-151.

DOI:10.1016/j.jecp.2004.03.002      URL     [本文引用: 1]

Geary, D. C. ( 2011).

Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study

Developmental Psychology, 47( 6), 1539-1552.

DOI:10.1037/a0025510      URL     PMID:3210883      [本文引用: 1]

Abstract The study's goal was to identify the beginning of 1st grade quantitative competencies that predict mathematics achievement start point and growth through 5th grade. Measures of number, counting, and arithmetic competencies were administered in early 1st grade and used to predict mathematics achievement through 5th (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence and processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning.

Geary D. C., Hoard M. K., & Nugent L. ( 2012).

Independent contributions of the central executive, intelligence, and in-class attentive behavior to developmental change in the strategies used to solve addition problems

Journal of Experimental Child Psychology, 113( 1), 49-65.

DOI:10.1016/j.jecp.2012.03.003      URL     [本文引用: 2]

Hassinger-Das B., Jordan N. C., Glutting J., Irwin C., & Dyson N. ( 2014).

Domain-general mediators of the relation between kindergarten number sense and first- grade mathematics achievement

Journal of Experimental Child Psychology, 118, 78-92.

DOI:10.1016/j.jecp.2013.09.008      URL     [本文引用: 1]

Isquith P. K., Gioia G. A., & Espy K. A. ( 2004).

Executive function in preschool children: Examination through everyday behavior

Developmental Neuropsychology, 26( 1), 403-422.

DOI:10.1207/s15326942dn2601_3      URL     PMID:15276902      [本文引用: 1]

Clinical assessment of executive function in preschool-age children is challenging given limited availability of standardized tasks and preschoolers' variable ability to participate in lengthy formal evaluation procedures. Given the benefits of ecological validity of measuring behavior by rating scales, the Behavior Rating Inventory of Executive Function (Gioia, Isquith, Guy, & Kenworthy, 2000) was modified for use with children ages 2 through 5 years to assess executive functions in an everyday context. The scale development process, based on samples of 460 parents and 302 teachers, yielded a single 63-item measure with 5 related, but nonoverlapping, scales, with good internal consistency and temporal stability. Exploratory factor analyses identified 3 consistent factors: Emergent Metacognition, Flexibility, and Inhibitory Self-Control across parent and teacher samples. In a second study with a mixed sample of preschool children with various developmental disorders, parents and teachers rated these preschool children as having greater executive difficulties in most domains than matched controls. Such rating-scale methodology may be a useful complementary tool by which to reliably assess executive functions in preschool children via everyday behaviors in the natural environment.

Jacob, R., & Parkinson, J. ( 2015).

The potential for school-based interventions that target executive function to improve academic achievement: A review

Review of Educational Research, 85( 4), 512-552.

DOI:10.3102/0034654314561338      URL     [本文引用: 1]

King C. M., Lancaster P. E., DeFrance N. L., Melin J. A., & Cleveland R. ( 2013).

Curricular and pedagogical imperatives for fostering effective stem teacher preparation

Teacher Education & Practice, 26, 706-720.

URL     [本文引用: 1]

This article describes a unique approach to developing and delivering the curriculum for an experimental program that prepares STEM (science, technology, engineering, and mathematics) graduates for teaching in high-needs secondary schools. The context for the collaborative design–including the charge, personnel, and purpose of the program–is briefly described, followed by the process used to determine the program's conceptual framework. A brief description of the curriculum and its delivery is explained, including the "rotations" aspect of each course, which plays a significant role in STEM teacher preparation. The objectives for each rotation are identified, and the settings in which rotations occurred are described. The article concludes with a discussion of the STEM graduates' views about the extent to which rotations foster pedagogical content knowledge in novice teacher candidates.

Kolkman M. E., Hoijtink H. J. A., Kroesbergen E. H., & Leseman, P. P. M. ( 2013).

The role of executive functions in numerical magnitude skills

Learning & Individual Differences, 24, 145-151.

DOI:10.1016/j.lindif.2013.01.004      URL     [本文引用: 1]

78 Executive functions are examined in relation to numerical skills. 78 Updating skills were the most important predictors of numerical skills. 78 Shifting and inhibition were to a lesser extent related to numerical skills.

LeFevre J. A., Berrigan L., Vendetti C., Kamawar D., Bisanz J., Skwarchuk S. L., .. Smith-Chant B. L. ( 2013).

The role of executive attention in the acquisition of mathematical skills for children in grades 2 through 4

Journal of Experimental Child Psychology, 114( 2), 243-261.

DOI:10.1016/j.jecp.2012.10.005      URL     [本文引用: 1]

McClelland M. M., Cameron C. E., Connor C. M., Farris C. L., Jewkes A. M., & Morrison F. J. ( 2007).

Links between behavioral regulation and preschoolers' literacy, vocabulary, and math skills

Developmental Psychology, 43( 4), 947-959.

DOI:10.1037/0012-1649.43.4.947      URL     PMID:17605527      [本文引用: 1]

This study investigated predictive relations between preschoolers' (N=310) behavioral regulation and emergent literacy, vocabulary, and math skills. Behavioral regulation was assessed using a direct measure called the Head-to-Toes Task, which taps inhibitory control, attention, and working memory, and requires children to perform the opposite of what is instructed verbally. Hierarchical linear modeling (HLM) was utilized because children were nested in 54 classrooms at 2 geographical sites. Results revealed that behavioral regulation significantly and positively predicted fall and spring emergent literacy, vocabulary, and math skills on the Woodcock Johnson Tests of Achievement (all ps<.05). Moreover, growth in behavioral regulation predicted growth in emergent literacy, vocabulary, and math skills over the prekindergarten year (all ps<.05), after controlling for site, child gender, and other background variables. Discussion focuses on the role of behavioral regulation in early academic achievement and preparedness for kindergarten.

McLean, J. F., & Rusconi, E. ( 2014).

Mathematical difficulties as decoupling of expectation and developmental trajectories

Frontiers in Human Neuroscience, 8, 44.

DOI:10.3389/fnhum.2014.00044      URL     PMID:3915105      [本文引用: 1]

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science.

Miller M. R., Müller U., Giesbrecht G. F., Carpendale J. I., & Kerns K. A. ( 2013).

The contribution of executive function and social understanding to preschoolers’ letter and math skills

Cognitive Development, 28( 4), 331-349.

DOI:10.1016/j.cogdev.2012.10.005      URL     [本文引用: 1]

Miyake, A., & Friedman, N. P. ( 2012).

The nature and organization of individual differences in executive functions: Four general conclusions

Current Directions in Psychological Science, 21( 1), 8-14.

DOI:10.1177/0963721411429458      URL     [本文引用: 1]

Monette S., Bigras M., & Guay M. C. ( 2011).

The role of the executive functions in school achievement at the end of grade

Journal of Experimental Child Psychology, 109( 2), 158-173.

DOI:10.1016/j.jecp.2011.01.008      URL     PMID:21349537      [本文引用: 1]

The aim of this study was to determine the role of executive functions (EFs) in early school achievement when a variety of potential confounding factors were controlled. Measures of EF (inhibition, flexibility, and working memory) and school readiness were administered to a sample of 85 kindergartners (39 boys and 46 girls, 5–6 years old). School achievement was then assessed at the end of Grade 1. Results show math and reading/writing skills at the end of Grade 1 to be associated with kindergarten EFs. Only working memory contributed uniquely to the variance in school achievement after all covariates (preacademic abilities, affective variables, and family variables) were controlled and, even then, only with respect to math skills. On the other hand, working memory and inhibition had an indirect effect on reading/writing skills via anger–aggression. EF implication in school achievement is discussed in terms of task demands and child age.

Montroy J. J., Bowles R. P., Skibbe L. E., & Foster T. D. ( 2014).

Social skills and problem behaviors as mediators of the relationship between behavioral self-regulation and academic achievement

Early Childhood Research Quarterly, 29( 3), 298-309.

DOI:10.1016/j.ecresq.2014.03.002      URL     [本文引用: 1]

Ng F. F. Y., Tamis-Lemonda C., Yoshikawa H., & Sze, I. N. L. ( 2015).

Inhibitory control in preschool predicts early math skills in first grade: Evidence from an ethnically diverse sample

International Journal of Behavioral Development, 39( 2), 139-149.

DOI:10.1177/0165025414538558      URL     [本文引用: 2]

Östergren R, & Träff, U. ( 2013).

Early number knowledge and cognitive ability affect early arithmetic ability

Journal of Experimental Child Psychology, 115( 3), 405-421.

DOI:10.1016/j.jecp.2013.03.007      URL     PMID:23665177      [本文引用: 1]

Previous literature suggests that early number knowledge is important for the development of arithmetic calculation ability. The domain-general ability of verbal working memory also has an impact on arithmetic ability. This longitudinal study tested the impact of early number knowledge and verbal working memory on the arithmetic calculation ability of children in preschool (N=315) and then later in Grade 1 using structural equation modeling. Three models were used to test hypotheses drawn from previous literature. The current study demonstrates that both early number knowledge and the domain-general ability of verbal working memory affect preschool and Grade 1 arithmetic ability. Early number knowledge had a direct impact on the growth of arithmetic ability, whereas verbal working memory had only an indirect effect via number knowledge and preschool arithmetic ability. These results fit well with von Aster and Shalev鈥檚 developmental model of numerical cognition (Developmental Medicine & Child Neurology, 2007, Vol. 49, pp. 868 873) and highlight the importance of considering arithmetic ability as independent from early number knowledge. Results also emphasize the importance of training early number knowledge before school entry to promote the development of arithmetic ability.

Purpura D. J., Hume L. E., Sims D. M., & Lonigan C. J. ( 2011).

Early literacy and early numeracy: The value of including early literacy skills in the prediction of numeracy development

Journal of Experimental Child Psychology, 110( 4), 647-658.

[本文引用: 1]

Raver C. C., Jones S. M., Li-Grining C., Zhai F. H., Bub K., & Pressler E. ( 2011).

CSRP’s impact on low-income preschoolers’ preacademic skills: Self-regulation as a mediating mechanism

Child Development, 82( 1), 362-378.

DOI:10.1111/cdev.2011.82.issue-1      URL     [本文引用: 1]

Schoemaker K., Bunte T., Espy K. A., Deković M., & Matthys W. ( 2014).

Executive functions in preschool children with ADHD and DBD: An 18-month longitudinal study

Developmental Neuropsychology, 39( 4), 302-315.

DOI:10.1080/87565641.2014.911875      URL     PMID:24854774      [本文引用: 1]

In this longitudinal study, we examined the stability of the association between executive functions and externalizing behavior problems, and the developmental change of executive functions in a predominately clinically diagnosed preschool sample (N = 200). Inhibition and working memory performance were assessed three times in 18 months. Across time, poorer inhibition performance in young children was associated with attention deficit hyperactivity disorder (ADHD) and disruptive behavior disorders (DBD), and poorer working memory performance was associated with ADHD. Inhibition and working memory performance increased over time, especially in the early preschool period. The improvement of inhibition performance was more pronounced in the clinically diagnosed children compared to the TD children.

Steele A., Karmiloff-Smith A., Cornish K., & Scerif G. ( 2012).

The multiple subfunctions of attention: Differential developmental gateways to literacy and numeracy

Child Development, 83( 6), 2028-2041.

DOI:10.1111/cdev.2012.83.issue-6      URL     [本文引用: 1]

Toll S. W. M., van der Ven, S. H. G., Kroesbergen E. H., & van Luit, J. E. H. ( 2011).

Executive functions as predictors of math learning disabilities

Journal of Learning Disabilities, 44( 6), 521-532.

DOI:10.1177/0022219410387302      URL     PMID:21177978      [本文引用: 1]

In the past years, an increasing number of studies have investigated executive functions as predictors of individual differences in mathematical abilities. The present longitudinal study was designed to investigate whether the executive functions shifting, inhibition, and working memory differ between low achieving and typically achieving children and whether these executive functions can be seen as precursors to math learning disabilities in children. Furthermore, the predictive value of working memory ability compared to preparatory mathematical abilities was examined. Two classifications were made based on (persistent) mathematical ability in first and second grade. Repeated measures analyses and discriminant analyses were used to investigate which functions predicted group membership best. Group differences in performance were found on one inhibition and three working memory tasks. The working memory tasks predicted math learning disabilities, even over and above the predictive value of preparatory mathematical abilities.

Tominey, S. L., & McClelland, M. M. ( 2011).

Red light, purple light: Findings from a randomized trial using circle time games to improve behavioral self-regulation in preschool

Early Education & Development, 22( 3), 489-519.

[本文引用: 1]

van der ven, S. H. G., Kroesbergen, E. H., Boom J., & Leseman, P. P. M. ( 2012).

The development of executive functions and early mathematics: A dynamic relationship

British Journal of Educational Psychology, 82( 1), 100-119.

DOI:10.1111/j.2044-8279.2011.02035.x      URL     PMID:22429060      [本文引用: 4]

Background. The relationship between executive functions and mathematical skills has been studied extensively, but results are inconclusive, and how this relationship evolves longitudinally is largely unknown.Aim. The aim was to investigate the factor structure of executive functions in inhibition, shifting, and updating; the longitudinal development of executive functions and mathematics; and the relation between them.Sample. A total of 211 children in grade 2 (7 8 years old) from 10 schools in the Netherlands.Method. Children were followed in grade 1 and 2 of primary education. Executive functions and mathematics were measured four times. The test battery contained multiple tasks for each executive function: Animal stroop, local global, and Simon task for inhibition; Animal Shifting, Trail Making Test in Colours, and Sorting Task for shifting; and Digit Span Backwards, Odd One Out, and Keep Track for updating. The factor structure of executive functions was assessed and relations with mathematics were investigated using growth modelling.Results. Confirmatory factor analysis (CFA) showed that inhibition and shifting could not be distinguished from each other. Updating was a separate factor, and its development was strongly related to mathematical development while inhibition and shifting did not predict mathematics in the presence of the updating factor.Conclusions. The strong relationship between updating and mathematics suggest that updating skills play a key role in the maths learning process. This makes updating a promising target for future intervention studies.

Vukovic, R. K., & Lesaux, N. K. ( 2013).

The relationship between linguistic skills and arithmetic knowledge

Learning & Individual Differences, 23, 87-91.

DOI:10.1016/j.lindif.2012.10.007      URL     [本文引用: 1]

Although language is implicated in children's mathematical development, few studies have focused specifically on how different linguistic skills relate to children's mathematical performance. Building on the model proposed by LeFevre et al. (2010), this study examined how general verbal ability and phonological skills were differentially related to children's arithmetic knowledge. Third grade children (N = 287) were assessed on verbal analogies, phonological decoding, symbolic number skill, procedural arithmetic, and arithmetic word problems. Using mediation analyses, the results indicated that verbal analogies were indirectly related to arithmetic knowledge through symbolic number skill, whereas phonological decoding had a direct relationship with arithmetic performance. These results suggest that general verbal ability influences how children understand and reason with numbers, whereas phonological skills are involved in executing conventional arithmetic problems. (c) 2012 Elsevier Inc. All rights reserved.

Watts T. W., Duncan G. J., Chen M. C., Claessens A., Davis-Kean P. E., Duckworth K., .. Susperreguy M. I. ( 2015).

The role of mediators in the development of longitudinal mathematics achievement associations

Child Development, 86( 6), 1892-1907.

DOI:10.1111/cdev.12416      URL     PMID:4852708      [本文引用: 2]

Davis-Kean: Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this a...

Weiland C., Barata M. C., & Yoshikawa H. ( 2014).

The co-occurring development of executive function skills and receptive vocabulary in preschool-aged children: A look at the direction of the developmental pathways

Infant & Child Development, 23( 1), 4-21.

[本文引用: 1]

Weiland, C., & Yoshikawa, H. ( 2013).

Impacts of a prekindergarten program on children's mathematics, language, literacy, executive function, and emotional skills

Child Development, 84( 6), 2112-2130.

DOI:10.1111/cdev.2013.84.issue-6      URL     [本文引用: 1]

Welsh J. A., Nix R. L., Blair C., Bierman K. L., & Nelson K. E. ( 2010).

The development of cognitive skills and gains in academic school readiness for children from low-income families

Journal of Educational Psychology, 102( 1), 43-53.

DOI:10.1037/a0016738      URL     [本文引用: 1]

White L. J., Alexander A., & Greenfield D. B. ( 2017).

The relationship between executive functioning and language: Examining vocabulary, syntax, and language learning in preschoolers attending head start

Journal of Experimental Child Psychology, 164, 16-31.

DOI:10.1016/j.jecp.2017.06.010      URL     [本文引用: 1]

Xenidou-Dervou I., De Smedt B., van der Schoot M., & van Lieshout, E. C. D. M. ( 2013).

Individual differences in kindergarten math achievement: The integrative roles of approximation skills and working memory

Learning & Individual Differences, 28, 119-129.

[本文引用: 1]

Zelazo, P. D., & Carlson, S. M. ( 2012).

Hot and cool executive function in childhood and adolescence: Development and plasticity

Child Development Perspectives, 6( 4), 354-360.

DOI:10.1111/j.1750-8606.2012.00246.x      URL     [本文引用: 1]

Executive function (EF), which refers to the more deliberate, top-down neurocognitive processes involved in self-regulation, develops most rapidly during the preschool years, together with the growth of neural networks involving prefrontal cortex but continues to develop well into adulthood. Both EF and the neural systems supporting EF vary as a function of motivational significance, and this article discusses the distinction between the top-down processes that operate in motivationally and emotionally significant situations (“hot EF”) and the top-down processes that operate is more affectively neutral contexts (“cool EF”). Emerging evidence indicates that both hot and cool EF are surprisingly malleable, with implications for intervention and prevention.

Zhang X., Hu B. Y., Ren L. X., & Fan X. T. ( 2017).

Pathways to reading, mathematics, and science: Examining domain-general correlates in young Chinese children

Contemporary Educational Psychology, 51, 366-377.

DOI:10.1016/j.cedpsych.2017.09.004      URL     [本文引用: 1]

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