Development and Function of Nonverbal Number Approximation

描述(由申请人提供)：行为、神经心理学和脑成像研究指出了一种处理跨发育和跨物种共享的数字的专用系统(Dehaene，1998；Feigenson等人，2004)。这一基本的近似数系统(以下简称ANS)形成了场景中对象、声音或事件的数量的非标准表示。重要的是，它是不精确的，在这方面不同于精确的言语计数。这个系统是培养更复杂、更独特的人类数学能力的基础，涉及符号计算。虽然这个数值逼近系统的这些方面已经有了很好的记录，但它们也提出了一些重要的问题。首先，近数系统的敏锐度是如何在发展过程中发生变化的？有证据表明，婴儿的ANS表征不如成年人准确，但在婴儿期和成年期之间ANS的质量变化几乎完全无法描述。第二，ANS是在多早发育阶段参与的，其早期敏锐度是多少？目前，对6个月以下儿童的数值近似还一无所知。第三，在人的一生中，这个系统的敏锐度有哪些个体差异？尽管先前的研究表明，平均而言，成年人可以辨别出7：8的不同排列，但个别成年人的敏锐度可能会有很大差异。第四，儿童数值逼近能力的个体差异是什么？儿童个体ANS表征的精确度在发育过程中可能会保持稳定，也可能会随着年龄和经验的变化而波动。第五，ANS敏锐度的个体差异与符号数学能力测试成绩之间的关系是什么？确定ANS和数学成绩之间的关系对于确定数学缺陷的亚类和提高儿童的数学水平可能是至关重要的。第六，ANS发展进步的机制是什么？虽然成熟可能起到一定作用，但经验也可能有助于磨练人的敏锐度。目前的项目旨在通过检查婴儿、儿童和成人的数字能力来回答这些问题，并以此描述表示数字的基本机制的发展。最终，拟议的研究将有助于理解定量知识发展的连续性和间断性这一更广泛的目标。据估计，3%至7%的总人口(1/15)患有某种形式的数字加工缺陷(计算障碍)，该项目可能会对研究数字认知障碍产生重要影响。由于数字推理在日常生活和职业生活中的重要性，那些因疾病或中风而遭受ANS损伤的患者、那些有遗传媒介的计算障碍的患者，以及有数学特定缺陷的儿童，将受益于对近似数字系统的发展和功能的理解。公共卫生相关性：拟议的项目旨在通过调查正常发育的婴儿、儿童和成人的近似数字表示，为理解数字思维这一更大的目标做出贡献。在记录数值逼近的发展、数值逼近的个体差异以及数值逼近与数学成绩之间的关系方面，本项目可能会对理解数值处理的障碍和改进数学教育的策略产生影响。

DESCRIPTION (provided by applicant): Behavioral, neuropsychological, and brain imaging research points to a dedicated system for processing number that is shared across development and across species (Dehaene, 1998; Feigenson et al., 2004). This foundational Approximate Number System (henceforth, the ANS) forms amodal representations of the number of objects, sounds, or events in a scene. Importantly, it is imprecise, and in this way differs from exact verbal counting. This system serves as a basis for more sophisticated, uniquely human mathematical abilities involving symbolic calculation. While these aspects of this system for numerical approximation have been well documented, they also raise important questions. First, how does the acuity of the approximate number system change over the course of development? Evidence suggests that infants have less precise ANS representations than adults, yet qualitative changes in the ANS between infancy and adulthood remain almost entirely undescribed. Second, how early in development is the ANS engaged, and what is its early acuity? At present nothing is known of numerical approximation in children younger than 6 months old. Third, what are the individual differences in the acuity of this system across the lifespan? Although previous research suggests that, on average, adults can discriminate arrays differing by a 7:8 ratio, individual adults may vary widely in ANS acuity. Fourth, what are the individual differences in children's numerical approximation abilities? Variation in the precision of individual children's ANS representations may remain stable over development, or may fluctuate with age and experience. Fifth, what is the relationship between individual differences in the acuity of the ANS and performance on tests of symbolic math ability? Identifying the relationship between the ANS and math performance may be critical to the goals of identifying subtypes of math deficits and improving children's math proficiency. Sixth, what mechanism underlies developmental improvement in the ANS? While maturation may play a role, experience may also serve to hone ANS acuity. The current project aims to answer these questions by examining the numerical abilities of infants, children, and adults, and in doing so to characterize the development of a foundational mechanism for representing number. Ultimately, the proposed studies will contribute to the broader goal of understanding continuities and discontinuities in the development of quantitative knowledge. Given that by some estimates 3 to 7% of the general population (1 in 15) suffers from some form of numerical processing deficit (dyscalculia), this project may have important repercussions for studying impairments in numerical cognition. Patients suffering damage to the ANS due to disease or stroke, those with genetically mediated dyscalculia, and children with math- specific deficits will benefit from an understanding of the development and function of the Approximate Number System because of the importance of numerical reasoning to daily and professional life. PUBLIC HEALTH RELEVANCE: The proposed project aims to contribute to the larger goal of understanding numerical thinking by investigating approximate number representations in normally-developing infants, children, and adults. In documenting the development of numerical approximation, individual differences in numerical approximation, and the relationship between numerical approximation and mathematics performance, this project may have repercussions for understanding disorders of numerical processing and for strategies for improving math education.