Empirical Research - Collaborative Research - A Bayesian Approach to Number Reasoning

这个项目的最终目标是提供一个关于数字认知的认知和神经基础的新模型，并利用这些知识来指导新的训练方法的发展，从而提高儿童的数学能力。该项目是罗切斯特大学、约翰·霍普金斯大学和冷泉港实验室的研究人员合作完成的。最近的研究表明，在正规的数学教育中，数字判断的敏锐性是成功的预测，类似的认知过程可以通过特定类型的一般领域经验来训练。其核心思想是，神经元的放电对概率分布进行编码，从而同时表示来自该分布的最可能样本和估计的方差(即，置信度)。这个项目将开发和测试一个正式的贝叶斯模型，该模型具有自然地解释一些元认知因素的独特特征，这是获得专业知识的关键但未得到检验的因素。这种贝叶斯方法的主要优点是它能够自然地描述：1)学习者的信心如何与他们的数字知识的精确度有关；2)学习者如何结合关于数字的多个来源的信息；3)直觉偏好(也称为先验信念)如何预测学习者的错误；以及4)概率推理的改进如何有助于提高数感的精确度。

The ultimate goal of this project is to provide a novel model of the cognitive and neural basis of numerical cognition, and to use this knowledge to guide the development of new training methods that could improve mathematical abilities in children. The project is a collaboration among investigators at the University of Rochester, Johns Hopkins University, and Cold Spring Harbor Laboratories. Recent research suggests that acuity of numerosity judgments is predictive of success in formal mathematics education, and that similar cognitive processes can be trained by specific kinds of domain-general experience. The core idea is that the firing of neurons encodes a probability distribution, thereby representing simultaneously the most probable sample from the distribution and the variance (i.e., confidence) of the estimate. This project will develop and test a formal Bayesian model that has the unique feature of naturally accounting for a number of metacognitive factors, a critical but undertested factor in the acquisition of expertise. The primary advantages of this Bayesian approach are its ability to provide a natural description of: 1) how the confidence of a learner relates to the precision of their number knowledge; 2) how a learner can combine information from multiple sources of information about number; 3) how intuitive preferences (also known as prior belief) predict learners' errors; and 4) how improvements in probabilistic inference may benefit the precision of the number sense.