Development and Function of Nonverbal Number Approximation

描述（由申请人提供）：行为学、神经心理学和脑成像研究指出了一个处理数字的专用系统，该系统在不同的发育阶段和不同的物种之间共享（Dehaene, 1998; Feigenson et al., 2004）。这个基本的近似数字系统（以下简称ANS）形成了场景中物体、声音或事件数量的模态表示。重要的是，它是不精确的，在这方面不同于精确的口头计数。这个系统为更复杂、独特的人类数学能力（包括符号计算）提供了基础。虽然这个数值近似系统的这些方面已经被很好地记录下来，但它们也提出了重要的问题。首先，在发展过程中，近似数字系统的敏锐度是如何变化的？有证据表明，婴儿的ANS表征不如成年人精确，但婴儿和成年之间ANS的定性变化几乎完全无法描述。第二，ANS的开发阶段有多早？它的早期敏锐度如何？目前还不知道6个月以下儿童的数值近似。第三，在整个生命周期中，这个系统的敏锐度有什么个体差异？尽管先前的研究表明，平均而言，成年人可以区分7比8的不同阵列，但个体的ANS敏锐度可能存在很大差异。第四，儿童数值近似能力的个体差异是什么？个别儿童的ANS表征的精确度变化可能在发展过程中保持稳定，也可能随着年龄和经验而波动。第五，ANS敏锐度的个体差异与符号数学能力测试的表现之间的关系是什么？确定ANS和数学成绩之间的关系对于确定数学缺陷的亚型和提高儿童的数学熟练程度的目标至关重要。第六，ANS发育改善的机制是什么？虽然成熟可能起作用，但经验也可能有助于磨练ANS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，并以此来描述表示数字的基本机制的发展特征。最终，提出的研究将有助于理解定量知识发展中的连续性和非连续性这一更广泛的目标。据估计，总人口中有3%到7%的人（15人中有1人）患有某种形式的数字处理缺陷（计算障碍），该项目可能对研究数字认知障碍有重要影响。由于疾病或中风导致ANS受损的患者、遗传介导的计算障碍患者以及有数学特异性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，因为数值推理对日常和职业生活的重要性。公共卫生相关性：拟建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征，为理解数字思维的更大目标做出贡献。通过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表现之间的关系，本项目可能会对理解数值处理障碍和改善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.