早期儿童数学学习与执行功能的关系

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。     

个体近似数量系统与其数学能力之间的关系：发展研究的证据

近似数量系统在个体数学能力的发展中起着重要的作用, 二者之间的关系受到年龄因素的影响。主要表现为, 随着年龄的增长, 相关程度逐渐减弱, 二者之间关系的作用机制可能由基数知识中介转变为多种中介变量的共同作用。未来可采用更严格的实验设计和多种研究方法考察各年龄段儿童近似数量系统与不同数学能力之间关系的发展趋势、因果方向、关键转折点和潜在机制, 以更好地理解近似数量系统在个体数学能力发展中所起的作用。     

心理理论的自发反应范式：方法、结果与解释

近30年来, 心理理论一直是认知发展领域关键而充满挑战的研究主题, 儿童理解他人错误信念的能力是心理理论发展的标志。诱导反应范式(elicited-response tasks)的研究结果表明4岁时儿童获得心理理论, 但是自发反应范式(spontaneous-response tasks)的研究结果表明婴儿15个月大时就已经具备心理理论。自发反应范式(spontaneous-response task) 是近些年来心理理论研究领域发展起来的研究范式。针对幼儿能通过自发反应范式却不能通过诱导反应范式这一问题, 已有三种相关的理论解释：早期能力掩盖说、内隐知识解释论和观点追踪解释论。未来心理理论研究应注意将自发反应范式运用于特殊儿童, 并进一步验证和研究心理理论的发展机制。     

核心知识系统及其对相关研究的启示

核心知识系统出现于人类个体发展和种系发展的早期,在人类复杂认知能力的发生发展中起着建构模块的作用。该文以表征物体和数量关系的两类核心知识系统的性质及二者在儿童的“数”概念形成和成人的数学思维中所起的作用为例,综述了以灵长类动物、婴儿、儿童和成人为被试的研究证据,并进而提出了核心知识系统给相关研究带来的若干启示。     

人类的近似数量系统

近似数量系统(Approximate Number System, ANS)指个体在不需要依赖于计算和数量符号的情况下, 对一组数量进行近似表征的系统。通过总结近十年来研究者们在ANS的遗传和神经基础、干预训练等方面取得的新进展, 指出未来应综合运用各种认知神经科学研究手段立足于ANS的基因和脑生理基础研究, 进一步揭示ANS的本质和内在发生发展机制, 并将有关研究发现运用到教育教学中, 对数学困难儿童进行干预, 以提高其数学能力和适应社会的能力。     

运算动量效应的理论解释及其发展性预测因素

了解运算偏差的形成与发展对探索算数运算系统的内在机制具有重要意义, 早期的算数运算能力是儿童理解和进行复杂数学运算的基础。运算动量偏差是指个体在进行基本数学运算时倾向于高估加法运算结果而低估减法运算结果的一种运算偏差, 主要包括三种理论解释, 即注意转移假说、启发式解释和压缩解释。鉴于运算动量效应在成年群体中相对稳定却在不同发展阶段儿童中存在不一致的证据, 数学能力的提高与空间注意的成熟可结合不同的理论解释来阐明儿童发展过程中运算动量效应的变化趋势。未来可以进一步整合多种研究任务以揭示运算动量效应的发展轨迹, 考察数量表征系统与运算动量效应间的关联, 探究运算动量效应在不同运算符号中的稳定性, 探讨不同因素共同作用对运算动量效应的影响, 并设计有关数学能力的干预措施以减少运算动量效应这一运算偏差。     

儿童早期空间非标准测量能力发展研究进展

测量是数学的主题之一。空间非标准测量能力的发展对儿童数学认知能力的发展有重要作用,对儿童思维抽象性、逻辑性、创造性的培养,问题解决能力的提高有重要影响。文章通过对近四十年来儿童空间非标准测量能力发展研究的成果进行概括分析,发现研究者主要对儿童空间非标准测量的认知加工线索,长度测量策略与工具的使用,空间非标准测量知识的获得顺序以及相关的测量教学顺序,空间非标准测量能力与守恒和推理能力的关系等问题进行了研究。并在此基础上提出了儿童空间非标准测量能力发展研究需进一步探讨的问题。     

认知需求和认知闭合需求对风险决策中外语效应的影响

外语效应指相比于母语背景,个体在外语背景下风险决策偏差会降低。针对影响外语效应的因素研究大多聚焦于外部因素和与个体外语水平相关的因素,少有研究探讨认知风格的作用。本研究通过524名成人被试,探索认知需求和认知闭合需求对外语效应的影响。结果表明:(1)风险决策中存在外语效应,相比于母语背景,外语背景下框架效应被削弱,且个体更偏向风险寻求。(2)对于认知需求和认知闭合需求都高或都低的个体,语言类型会影响风险决策,在母语环境下倾向于风险规避,在外语环境下倾向于风险寻求;而对于认知需求和认知闭合需求高低不一致的个体,语言类型对其风险决策倾向的影响不显著。本研究为认知风格如何综合影响风险决策提供了进一步的证据。     

手指的感知、运动以及数量表征对数字认知的促进作用

手指是儿童在习得数字符号之前最常使用的表征数量的工具,大量研究都表明手指在数字认知中具有促进作用。但是,目前仍不清楚手指在数字认知中的作用机制。综述从手指感知、手指运动以及手指数量表征三个方面总结了手指在数字认知中所起的作用。手指感知可能通过影响儿童的数量表征能力间接地影响其它数学能力;与表征量有关的手指运动可能促进了数量大小的加工。关于手指数量表征在数字认知中的作用存在两种有争议的观点：一种认为手指数量表征促进了儿童由非符号数量表征向符号数量表征的转化;另一种认为手指数量表征可能是一种数量语义表征方式。未来应该在发展、作用机制、性别差异等方向继续开展研究,进一步探讨手指在数字认知中所起的作用。     

儿童区分幻想和现实的发展特点及作用机制

幻想(Fantasy)是指向未来, 与个人愿望相联系的想象, 且不一定以客观规律为依据。现实(Reality)是存在于日常生活中, 或者与我们生活法则相一致的事物或现象。准确地区分幻想和现实有利于在保护儿童想象力的同时, 确保他们的人身安全。国内外研究发现, 儿童区分幻想和现实的能力随着年龄的增长而提高; 受外部(实验材料的情感色彩、人物和主题类型)和内部(个体情绪感知强度、经验)因素的影响; 语言、元认知、心理理论和认知神经等可能是儿童区分幻想和现实的作用机制。未来研究需探索各种作用机制在儿童年龄与区分幻想和现实能力之间可能的调节效应, 以及儿童混淆幻想和现实的认知神经。在此基础上, 进一步明确既保护儿童想象力又确保其人身安全的有效措施。     

Studies on spontaneous attention to number (SAN) are based on spontaneous focusing on numerosity (SFON)

Li and Baroody presented a study in which they investigate children’ spontaneous attention to exact quantity without acknowledging how previous studies of spontaneous focusing on numerosity (SFON) are related to their concept and methods. The authors’ reaction to our pointing this out makes it is clear that SFON research has had foundational role in the development of Baroody and his colleagues spontaneous attention to number (SAN) idea. Thus the authors must acknowledge the SFON literature as the substantial part of their theoretical and methodological construct. The latest definition of SAN states this undeniably. “SAN is the attentional process that underlies exact number recognition initiated by the mathematical thinking triggered by SFON (e.g., attention to “threeness” directed by conceptual knowledge of “three” activated by SFON).” Furthermore, in their response, Dr Baroody and Dr Li admit that “An awareness of the SFON literature did help us explicitly recognize that, given the ambiguous instructions that do not explicitly direct a child’s attention to number, both the nonverbal production and matching tasks were useful in assessing unguided or spontaneous attention to a number.” It is surprising that in their response to the European Journal of Educational Psychology, the authors maintain their claim that they have cited the SFON literature adequately in their study about SAN.     

Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills

The aim of this 2 year longitudinal study was to explore whether children’s individual differences in spontaneous focusing on numerosity (SFON) in kindergarten predict arithmetical and reading skills 2 years later in school. Moreover, we investigated whether the positive relationship between SFON and mathematical skills is explained by children’s individual differences in spontaneous focusing on a non-numerical aspect. The participants were 139 Finnish-speaking children. The results show that SFON tendency in kindergarten is a significant domain-specific predictor of arithmetical skills, but not reading skills, assessed at the end of Grade 2. In addition, the relationship between SFON and number sequence skills in kindergarten is not explained by children’s individual differences in their focusing on a non-numerical aspect that is, spatial locations.     

Is the study about spontaneous attention to exact quantity based on studies of spontaneous focusing on numerosity?

Li and Baroody present a study in which they investigate toddlers’ spontaneous attention to exact quantity without acknowledging how previous studies of spontaneous focusing on numerosity (SFON) are related to their concept and methods. In this commentary requested by the European Journal of Developmental Psychology, we argue that the concept and the methods of spontaneous attention to exact quantity in the study of Li and Baroody clearly arise from previous research on SFON, as the authors have previously noted in their paper published in 2008. It is highly questionable whether their approach can be theoretically or methodologically dissociated from the previous research on SFON tendency to the extent that it is necessary to use an alternative name for the concept in their study.     

The construct and measurement of spontaneous attention to a number

The Spontaneous Attention to a Number (SAN) construct serves a different purpose than Hannula-Sormunen and colleagues’ Spontaneous Focus on Number (SFON) construct. As an extension of Eleanor J. Gibson’s differentiation theory, the premise of SAN is that children’s step-wise construction of small number concepts enables them to perceptually differentiate among increasingly larger numbers—to distinguish reliably between “oneness” or “twoness” and larger numbers, then between “threeness” and “larger numbers,” and eventually between “fourness” and larger numbers. In contrast, SFON refers to the tendency to attend to numbers in general—an attentional process that, unlike SAN, is separate from enumeration skill. Not surprisingly, then, although the prototype for both the SAN and SFON tasks is Nancy C. Jordan and colleagues’ non-directive nonverbal number task, the independent development of the SAN and SFON tasks resulted in key differences in how they are administered and scored and to whom they are administered.     

儿童手势及其与学习的关系

手势是在交流或认知过程中产生的、不直接作用于物体的手部运动, 具有具体性和抽象性。其分类主要从手势的来源、手势的内容、手势的意图及手势和言语的匹配性等角度进行划分。不同类型手势在出现时间及发展趋势上存在差异。手势在儿童词汇学习、言语表达、数学问题解决、空间学习及记忆等方面起促进作用, 但对言语理解的影响未得出一致结论。未来可关注不同类型手势与儿童认知发展的关系及对比不同来源手势在各学习领域的优势情况。     

No intrinsic number bias: Evaluating the role of perceptual discriminability in magnitude categorization

Accumulating evidence suggests that there is a spontaneous preference for numerical, compared to non-numerical (e.g., cumulative surface area), information. However, given a paucity of research on the perception of non-numerical magnitudes, it is unclear whether this preference reflects a specific bias towards number, or a general bias towards the more perceptually discriminable dimension (i.e., number). Here, we found that when the number and area of visual dot displays were matched in mathematical ratio, number was more perceptually discriminable than area in both adults and children. Moreover, both adults and children preferentially categorized these ratio-matched stimuli based on number, consistent with previous work. However, when number and area were matched in perceptual discriminability, a different pattern of results emerged. In particular, children preferentially categorized stimuli based on area, suggesting that children's previously observed number bias may be due to a mismatch in the perceptual discriminability of number and area, not an intrinsic salience of number. Interestingly, adults continued to categorize the displays on the basis of number. Altogether, these findings suggest a dominant role for area during childhood, refuting the claim that number is inherently and uniquely salient. Yet they also reveal an increased salience of number that emerges over development. Potential explanations for this developmental shift are discussed.

Research Highlights

• Previous work found that children and adults spontaneously categorized dot array stimuli by number, over other magnitudes (e.g., area), suggesting number is uniquely salient.
• However, here we found that when number and area were matched by ratio, as in prior work, number was significantly more perceptually discriminable than area.
• When number and area were made equally discriminable (‘perceptually-matched’), children, contra adults, spontaneously categorized stimuli by area over number (and other non-numerical magnitudes).
• These findings suggest that area may be uniquely salient early in childhood, with the previously-observed number bias not emerging until later in development.

     

The development of race‐based perceptual categorization: skin color dominates early category judgments

Prior research on the development of race‐based categorization has concluded that children understand the perceptual basis of race categories from as early as age 4 (e.g. Aboud, 1988). However, such work has rarely separated the influence of skin color from other physiognomic features considered by adults to be diagnostic of race categories. In two studies focusing on Black–White race categorization judgments in children between the ages of 4 and 9, as well as in adults, we find that categorization decisions in early childhood are determined almost entirely by attention to skin color, with attention to other physiognomic features exerting only a small influence on judgments as late as middle childhood. We further find that when skin color cues are largely eliminated from the stimuli, adults readily shift almost entirely to focus on other physiognomic features. However, 6‐ and 8‐year‐old children show only a limited ability to shift attention to facial physiognomy and so perform poorly on the task. These results demonstrate that attention to ‘race’ in younger children is better conceptualized as attention to skin color, inviting a reinterpretation of past work focusing on children's race‐related cognition.     

Preschoolers doing arithmetic: the concepts are willing but the working memory is weak.

The study of early mathematical development provides important insights into young children's emerging academic competencies and, potentially, a basis for adapting instructional methods. We presented nonverbal forms of two- and three-term arithmetic problems to 4-year-olds to determine (a) the extent to which certain information-processing demands make some problems more difficult than others and (b) whether preschoolers use arithmetic concepts spontaneously when solving novel problems. Children's accuracy on simple arithmetic problems (a + b and a - b) was strongly related (r2 = .88) to representational set size, the maximum number of units that need to be held in working memory to solve a given problem. Some children also showed spontaneous use of procedures based on the arithmetic principle of inversion when solving problems of the form a + b - b. These results highlight the importance of identifying information-processing and conceptual characteristics in the early development of mathematical cognition.     

MORPHOLOGY MATTERS IN LEARNING TO READ: A COMMENTARY

This paper provides a review of current research on the relevance of morphological awareness to reading and reading instruction. On the assumption that many educators are relatively unfamiliar with morphology, children’s development of awareness of the morphemic structure of words is discussed, as is the need for children to learn strategies that will help them read, spell, and understand morphologically complex words. Educational practices and implications, based on theory and research findings, are presented. Results suggest that educators and educational researchers need to incorporate more word study into reading and spelling programs, focusing attention to both form and meaning. In addition, the value of instructional goals and programs in morphological awareness for children in the early elementary years needs to be explored.