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关于数字认知的认知和神经基础的模型，并利用这些知识来指导开发新的训练方法，从而提高儿童的数学能力。该项目由罗切斯特大学、约翰霍普金斯大学和冷泉港实验室的研究人员合作完成。最近的研究表明，数字判断的敏锐性预示着正规数学教育的成功，类似的认知过程可以通过特定种类的领域一般经验来训练。其核心思想是，神经元的放电编码一个概率分布，从而同时表示分布中最可能的样本和估计的方差（即置信度）。该项目将开发和测试一个正式的贝叶斯模型，该模型具有自然地考虑许多元认知因素的独特特征，元认知因素是获得专业知识的关键因素，但尚未得到充分测试。这种贝叶斯方法的主要优点是它能够提供一个自然的描述：1)学习者的信心如何与他们的数字知识的准确性相关；2)学习者如何结合来自多个数字信息来源的信息；3)直觉偏好（也称为先验信念）如何预测学习者的错误；4)概率推理的改进如何有利于数字感觉的精度。

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.