Origins and Logic of Counting Algorithms

计数算法的起源和逻辑

基本信息

批准号：
9769990
负责人：
Jessica F Cantlon
金额：
$ 31.35万
依托单位：
CARNEGIE-MELLON UNIVERSITY
依托单位国家：
美国
项目类别：
财政年份：
2018
资助国家：
美国
起止时间：
2018-09-01 至 2021-02-28
项目状态：
已结题

来源：
https://reporter.nih.gov/project-details/9769990
关键词：
Address Affect Age Algorithms Animals Architecture Basic Science Behavioral Child Child Development Cognition Cognitive Computational algorithm Computer Analysis Computer Simulation Computing Methodologies Conditioned Reflex Data Data Analyses Development Diagnosis Disease Early treatment Elements Foundations Human Human Development Impaired cognition Impairment Intervention Knowledge Learning Learning Disorders Logic Mathematics Mental disorders Methods Modeling Monkeys Neurology Outcome Primates Process Quality of life Quantitative Reasoning Rehabilitation therapy Research Resolution Series Structure Support System System Techniques Testing Time Work cognitive capacity cognitive process cognitive system computational basis developmental disease developmental psychology early childhood experimental study frontier human data innovation insight interdisciplinary approach mathematical ability mathematics disability nonhuman primate novel operation programs psychologic public health relevance skills theories

项目摘要

DESCRIPTION (provided by applicant): Cognitive impairments in mathematics, which affect a substantial percentage of children, could be addressed earlier in development if we had an empirically-grounded theory of the fundamental algorithms that children need to become numerate. For instance, an understanding of the cognitive system supporting early numeracy could be used to focus interventions specifically to each child's representational or process-level problems. Previous research from our group and others suggests that some of the cognitive mechanisms underlying human verbal counting are derived from developmentally and evolutionarily more primitive processes. However, a formal theory of the logical principles that relate human counting to these earlier capacities is currently lacking. By using computational modeling and behavioral analyses in human children and non-human primates, we will assess the logical principles that serve as cognitive precursors to human counting. Our behavioral experiments will provide a new empirical basis for accounts of human counting acquisition and our computational approach will formalize the logical principles underlying this capacity. We ground our formal theories in behavioral data using a novel Bayesian data analysis method that permits us to statistically evaluate a wide range of alternative hypotheses. The proposed experimental aims are innovative in that they test a new frontier of unexplored relations between children's counting and evolutionarily primitive logical reasoning. The approach is innovative in the field of child development in its application of state-of-the-art computational methods to data from human children and non-human animals. The proposed research thus stands to break substantial new ground in the methods that are used to study child development. Insights about the logical architecture underlying counting acquisition will have broad implications for our understanding of learning and development, and will provide a a new empirical basis to describe the neurology behind learning impairments in children.

描述（由申请人提供）：如果我们对儿童需要学会计算的基本算法有一个基于经验的理论，那么影响很大一部分儿童的数学认知障碍可以在早期得到解决。支持早期算术的认知系统可用于将干预措施专门针对每个孩子的表征或过程水平我们小组和其他人之前的研究表明，人类言语计数背后的一些认知机制源自发展和进化上更原始的过程，然而，目前缺乏将人类计数与这些早期能力联系起来的逻辑原理的正式理论。通过对人类儿童和非人类灵长类动物使用计算模型和行为分析，我们将评估作为人类计数认知先驱的逻辑原理，我们的行为实验将为人类计数获取和我们的计算方法提供新的经验基础。将形式化这种能力背后的逻辑原则。我们使用新颖的贝叶斯数据分析方法来研究行为数据的形式理论，该方法使我们能够具体评估各种替代假设。所提出的实验目标具有创新性，因为它们测试了儿童计数与进化原始逻辑推理之间未经探索的关系的新领域。该方法在儿童发展领域具有创新性，它将最先进的计算方法应用于数据。因此，拟议的研究将在用于研究儿童发展的方法方面开辟实质性新天地，对计数习得背后的逻辑架构的见解将对我们对学习和发展的理解产生广泛的影响。并将为描述儿童学习障碍背后的神经学提供新的经验基础。