Origins and Logic of Counting Algorithms

 描述（由申请人提供）：数学认知障碍，影响了相当大比例的儿童，可以在发展的早期得到解决，如果我们有一个基本算法的理论基础，儿童需要成为计算。例如，对支持早期算术能力的认知系统的理解可以用于将干预措施专门针对每个儿童的表征或过程水平 问题我们小组和其他人之前的研究表明，人类语言计数的一些认知机制来自于发展和进化上更原始的过程。然而，一个正式的理论的逻辑原则，人类计数这些早期的能力目前缺乏。通过在人类儿童和非人类灵长类动物中使用计算建模和行为分析，我们将评估作为人类计数认知先驱的逻辑原则。我们的行为实验将提供一个新的经验基础的帐户人类计数收购和我们的计算方法将正式的逻辑原则，这种能力。我们地面我们的正式理论的行为数据使用一种新的贝叶斯数据分析方法，使我们能够统计评估范围广泛的替代假设。建议的实验目标是创新的，因为他们测试一个新的前沿未开发的儿童的计数和进化原始的逻辑推理之间的关系。该方法在儿童发展领域的创新在于将最先进的计算方法应用于数据 从人类儿童和非人类动物身上。因此，拟议中的研究将在用于研究儿童发展的方法中开辟实质性的新天地。深入了解计数习得背后的逻辑结构将对我们理解学习和发展产生广泛的影响，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。

 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.