Intuitive Mathematical Operations in Infancy and Childhood

描述（由申请人提供）：这个项目的具体目的是确定婴儿和儿童在进行算术推理时具有什么样的认知能力，并具有更广泛的长期目标，即找出开发直觉数学技能的创造性方法。它强调“数感”，这是一种古老的进化能力，可以在没有阿拉伯数字等符号的情况下粗略估计场景中物体的数量。该项目探讨了在加法、减法、乘法和除法的数学运算推理的发展中连续性或不连续的领域。因此，这些研究有助于NIH追求生命系统行为知识的使命，以及NICHD数学和科学认知学习计划的使命，以鼓励对数学能力正常发展的基础研究。建议本科生研究助理参与该项目的各个方面，旨在鼓励早期对基础研究的兴趣，并促进对高级发展心理学方法的指导，尽管该学院是一个不授予研究生学位的机构。因此，这组离散的研究项目适合AREA计划，该计划面向那些为大量未来科学家提供本科学位的机构，但尚未得到NIH的大力支持。提出了三组主要的研究。在所有的实验中，参与者将通过动画视频来描述各种类型的非符号算术运算，他们对这些运算结果的理解将通过言语、手指或鼠标点击（儿童）或观看时间（婴儿）来决定。一组研究调查了婴儿和儿童是否能够确定两个视觉对象阵列之间的分裂关系，并将这个比例常数推广到一个新的对象阵列。第二组研究探讨了儿童是否表现出对反转原理的非学校理解，其中A x b / b必须等于A。最后，第三组研究探讨了运算动量的新现象，其中非符号加法和减法问题的结果分别被系统地高估或低估。操作动量还捕获了独特的空间-数值相互作用，加法问题增强了对空间右侧的关注，减法问题增强了对空间左侧的关注。研究建议着眼于这一现象的发展时间进程和这一现象的文化决定因素，例如从左到右阅读流畅性的增加。

DESCRIPTION (provided by applicant): The specific aim of this project is to determine what cognitive capacities infants and children possess when reasoning about arithmetic, with the broader long-term objective of pinpointing inventive ways to tap into intuitive mathematical skills. There is an emphasis on the "number sense", an evolutionarily-ancient ability to roughly estimate the number of objects in a scene without the benefit of symbols such as Arabic numerals. The project explores areas of continuity or discontinuity in the development of reasoning about the mathematical operations of addition, subtraction, multiplication, and division. Thus, these studies contribute to the NIH mission to pursue knowledge about the behavior of living systems, as well as the NICHD Mathematics and Science Cognition Learning program mission to encourage basic research on the normal development of mathematical proficiency. The proposed participation of undergraduate research assistants in every aspect of this project aims to encourage early interest in basic research, and to foster mentoring in advanced developmental psychology methods despite the college's status as a non-graduate degree granting institution. As such, this set of discrete research projects is suitable for the AREA program, which is geared towards institutions which provide undergraduate degrees for a significant number of future scientists, but have not been significantly supported by NIH. Three main sets of studies are proposed. In all experiments, the participants will be engaged via animated videos depicting various types of non-symbolic arithmetic operations, and their comprehension of the outcomes to these operations will be determined by speech, pointing, or mouse-clicking (children), or looking time (infants). One set of studies examines whether infants and children can determine a divisive relationship between two visual arrays of objects, and generalize this proportional constant to a new array of objects. A second set of studies probes whether children exhibit an unschooled understanding of the principle of inversion, in which a x b / b must necessarily equal a. Finally, a third set of studies explores the new phenomenon of operational momentum, in which outcomes to non-symbolic addition and subtraction problems are systematically over- or under-estimated, respectively. Operational momentum also captures a unique spatial-numerical interaction, with addition problems enhancing attention to the right side of space, and subtraction problems to the left side of space. Studies are proposed which look at the developmental time-course of this phenomenon and the cultural determinants of this phenomenon, such as increased left-to-right reading fluency. PUBLIC HEALTH RELEVANCE: The research proposed here is relevant to public health in two main ways. First, mapping the development of this unschooled 'intuitive math' leads to better methods for conveying difficult math topics, when children eventually enter into the educational system. Second, research on non-symbolic arithmetic provides an invaluable baseline from which one can detect and begin intervention on abnormal mathematical development and mathematical disabilities such as dyscalculia.