幼儿及小学儿童数量表征的机制及作用

Magnitude representation is one of the basic numerical competences for individuals. It refers to the conceptual system of individuals to understand concepts of numbers and their relationships, and the processes of explaining, expressing and operating toward quantitative stimuli in brain. Magnitude representation contains non-symbolic and symbolic magnitude representations. Non-symbolic magnitude representation is widely presented by animals and humans, and after the emergence of the symbol system, it interacts with symbolic magnitude representation and both of them evolve into important foundations for the development of human's advanced numerical competences. Non-symbolic and symbolic magnitude representation have similar behavioral response characteristics and overlaps in activated brain regions, and they can converse into each other through the process of mapping..This research aims to investigate the mechanism and role of magnitude representation for children in kindergarten and primary school. To achieve the goals, two main studies will be carried. In study 1, behavioral experiments, event-related potential (ERP) analysis and near infrared reflectance spectroscopy (fNIRS) will be combined to systematically and comprehensively compare the relationships between non-symbolic and symbolic magnitude representation from the two perspectives of behavioral and neural mechanisms. Large magnitude representation and small magnitude representation will be examined respectively by presentations of stimuli through single-channel and cross-channel. In study 2, an aggregate cross-design will be used accompanied by cross-lag analysis to investigate the prediction of the magnitude representation ability to children's follow-up numerical competences. Besides, the prediction of magnitude representation to children's mathematical learning difficulties will also be examined. Furthermore, interventional programs targeted to improve calculating fluency will be developed according to the specific defects in magnitude representation of every child with mathematical learning difficulties. .This research has important theoretical significance and practical value. First, it will enrich and deepen the theories related on magnitude representation, and provide a more systematic understanding of the rules in humans' early development on quantity cognition. Upon these, this research will also make some contributions to the causations of magnitude representation developmental pattern. Second, this research will be conducive to further reveal the relationships between basic numerical competence and advanced numerical competence, thus provide theoretical bases for the settings of mathematics curriculums. Moreover, a new perspective will be introduced to the field of interventions toward children with mathematical learning difficulties. This will aid to provide deep insights into the causations of mathematical learning difficulties and improve children's mathematical literacy.

数量表征由非符号数量表征与符号数量表征组成，二者既有区别又有联系，且能通过映射过程在头脑中相互转换。本研究将结合行为实验与事件相关电位分析及近红外光谱分析技术，从行为机制及神经机制两个角度、单通道与跨通道两个方面及大数量和小数量两个范围全面、系统地对比分析幼儿及小学儿童两种数量表征的关系；并将在此基础上采用聚合交叉设计与交叉滞后分析技术，探讨数量表征对儿童后续数能力的预测作用，同时将考察数量表征对儿童数学学习困难的预测作用，并针对数困儿童的具体表征缺陷制定干预方案，提高其计算流畅度。本项目将有助于深化数量表征的相关理论，更系统地理解人类个体发展早期数量认知的规律，探究其成因；也有利于进一步揭示基本数能力与高级数能力的关系，为基础教育中数学课程的设置提供理论基础。此外，本研究将引入数困儿童干预研究的新视角，有助于深入了解数学学困的基础成因，并帮助数困儿童提高数学能力。

人类的数量表征是一个备受重视的科学问题。本课题从多感觉通道、多数量范围及多重注意资源负荷和工作记忆成分等综合角度考察了非符号和符号数量表征的发展特点、关系及心理与神经机制，同时进一步探明了儿童数量表征在数学运算能力中的作用以及数困儿童的数量表征特点，并对幼儿的数量表征能力进行了干预研究。. 研究发现，. 1.在数量表征特点上：（1）非符号和符号数量表征精确性均随年龄增长而逐渐提高；（2）非符号大、小数量表征均表现出近似表征特点，符号数量表征则具有精确性；（3）4岁以上儿童就能进行单通道和跨通道的数量表征，说明其能进行不受具体感觉通道限制的抽象数量表征。. 2.在两种数量表征映射特点上：儿童对非符号和符号数量表征的映射能力随年龄提高，儿童倾向于将非符号数量表征信息转化为符号数量表征信息进行操作，这种映射方向上的优势反应在6岁出现。. 3.在数量表征机制上：（1）小数量和大数量表征特点相似，可能存在于同一种表征系统中；（2）注意资源负荷和工作记忆对数量表征有重要影响；（3）对神经机制考察发现，单通道下视觉和听觉数量空间表征在额叶的N1波幅差异显著，跨通道下听觉干扰在额叶和顶叶能引起更大的N1波幅变化。. 4.在数量表征的作用及干预上：（1）非符号数量表征在儿童早期运算能力发展中起到基础作用，随着数学教育进行，符号表征逐渐起到主导作用，但符号表征的作用会随年龄增长而减弱；（2）正常儿童数量表征能力优于数困儿童，随着年龄增长，非符号数量表征能力对于数困儿童的影响逐渐减小，而符号数量表征能力对于数困儿童的影响随着年龄发展没有变化；（3）采用不同方式干预数量表征能力，效果不同。. 本课题为个体非符号和符号数量表征的发展特点、关系、影响因素、行为及神经机制提供了实证支持，为非符号和符号、大小数量表征机制等理论争议提供了新证据，为丰富这一领域的研究成果、发展数量表征的理论做出了积极的贡献。同时，也为儿童数学能力的培养提供了实践指导。