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

该项目的最终目标是提供一种新的数字认知的认知和神经基础模型，并利用这些知识来指导开发新的训练方法，以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之间的合作。最近的研究表明，数字判断的敏锐度是正规数学教育成功的预测，并且类似的认知过程可以通过特定类型的领域一般经验来训练。核心思想是神经元的激发编码概率分布，从而同时表示来自分布和方差的最可能的样本（即，的估计）。该项目将开发和测试一个正式的贝叶斯模型，该模型具有自然解释一些元认知因素的独特功能，这是获得专业知识的关键但未经测试的因素。这种贝叶斯方法的主要优点是它能够提供以下自然描述：1）学习者的信心如何与他们的数字知识的精度相关; 2）学习者如何联合收割机从关于数字的多个信息源中组合信息; 3）直观偏好如何与数字相关。（也称为先验信念）预测学习者的错误;以及4）概率推理的改进如何有益于数感的精确性。

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.