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Intuitive Mathematical Operations in Infancy and Childhood

婴儿期和儿童期的直观数学运算

基本信息

批准号：
7940030
负责人：
Koleen McCrink
金额：
$ 42.67万
依托单位：
BARNARD COLLEGE
依托单位国家：
美国
项目类别：
财政年份：
2010
资助国家：
美国
起止时间：
2010-04-26 至 2013-09-30
项目状态：
已结题

来源：
https://reporter.nih.gov/project-details/7940030
关键词：
Adult Area Attention Basic Science Behavior Characteristics Child Childhood Cognition Cognitive Complex Comprehension Development Education Ensure Exhibits Fostering Foundations Funding Future Generations Grant Human Individual Infant Institution Intervention Knowledge Language Left Link Logic Maps Mathematics Mentors Methods Mind Mission Mus National Institute of Child Health and Human Development Nature Organism Outcome Participant Performance Population Programmed Learning Psyche structure Public Health Reader Reading Research Research Personnel Research Project Grants Science Scientist Screening procedure Side Speech Stimulus System Testing Time United States National Institutes of Health Visual Work base college developmental psychology disability infancy interest mathematical ability mathematics disability operation programs public health relevance research study skills spatial relationship stem tool

项目摘要

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.

描述(由申请者提供)：这个项目的具体目标是确定婴儿和儿童在进行算术推理时的认知能力，更广泛的长期目标是确定利用直觉数学技能的创造性方法。强调“数感”，这是一种进化上古老的能力，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。该项目探索关于加法、减法、乘法和除法的数学运算的推理发展中的连续或不连续的领域。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使命，以鼓励对数学能力正常发展的基础研究。建议的本科生研究助理参与这个项目的每一个方面，旨在鼓励人们对基础研究的早期兴趣，并促进在高级发展心理学方法方面的指导，尽管学院是一个非研究生学位授予机构。因此，这组离散的研究项目适用于AREA计划，该计划面向为大量未来科学家提供本科学位但尚未得到NIH显著支持的机构。提出了三组主要的研究。在所有实验中，参与者将通过描述各种非符号算术运算的动画视频参与进来，他们对这些运算结果的理解将通过语音、指向或鼠标点击(儿童)或观看时间(婴儿)来确定。一组研究考察了婴儿和儿童是否能够确定两个物体视觉阵列之间的分裂关系，并将这个比例常数推广到一个新的物体阵列。第二组研究探索儿童是否表现出对反转原理的未受教育的理解，即a x b/b必须等于a。最后，第三组研究探索运算动量的新现象，在这种现象中，非符号加法和减法问题的结果分别被系统性地高估或低估。操作动量也捕捉到了一种独特的空间-数字交互作用，加法问题加强了对空间右侧的关注，减法问题增加了对空间左侧的关注。这项研究着眼于这一现象的发展过程和文化决定因素，如从左向右阅读流畅度的提高。公共卫生相关性：这里提出的研究在两个主要方面与公共卫生相关。首先，当孩子们最终进入教育系统时，绘制这种未受过教育的“直觉数学”的发展图，可以找到更好的方法来传达困难的数学主题。其次，对非符号算术的研究提供了一个宝贵的基线，人们可以从这个基线上发现并开始干预不正常的数学发展和数学残疾，如计算障碍。