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，如果我们对儿童需要成为数学家所需的基本算法有一个以经验为基础的理论，那么认知障碍在儿童发展的早期就可以得到解决。例如，对支持早期计算的认知系统的理解可以用来专门针对每个儿童的表征或过程水平进行干预 有问题。我们小组和其他人之前的研究表明，人类言语计数的一些认知机制来自于发育和进化上更原始的过程。然而，目前还缺乏将人类计数与这些早期能力联系起来的逻辑原则的正式理论。通过在人类儿童和非人类灵长类动物中使用计算模型和行为分析，我们将评估作为人类计数认知前驱的逻辑原则。我们的行为实验将为人类计数习得的描述提供一个新的经验基础，我们的计算方法将正式确定这种能力背后的逻辑原理。我们使用一种新的贝叶斯数据分析方法将我们的正式理论建立在行为数据上，这种方法允许我们对广泛的替代假设进行统计评估。提出的实验目标是创新的，因为他们测试了儿童计数和进化原始逻辑推理之间未被探索的关系的新前沿。这一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 来自人类儿童和非人类动物。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的新天地。对计数习得背后的逻辑结构的洞察将对我们理解学习和发展具有广泛的意义，并将为描述儿童学习障碍背后的神经学提供一个新的经验基础。

 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.