基于复合记忆-遗忘模型框架的连续教学策略优化控制

The optimal control strategy in continuous teaching based on the compound memory-forgetting model frame

通过对教学现象进行数学建模和分析,定量地研究教学策略对知识传播系统的影响并优化控制教学管理目标。深入考察学习者认知学习时大脑中知识存量的变化规律,将学习者大脑分为短时记忆室和长时记忆室两个仓室,提出连续教学中的复合记忆-遗忘模型框架;并根据两个仓室内知识扩散的不同方式,进一步构建双边连续扩散、单边脉冲扩散和双边脉冲扩散三种不同的知识扩散模型;针对不同的记忆模型,应用种群动力学基本理论和数学分析法,通过控制教学力度E或教学周期Th这两种教学策略,优化知识存量或学习成效这两个教学管理目标;最后通过实例予以说明和验证。

The influence of teaching strategies on knowledge dissemination systems are investiga- ted and teaching management objective is optimized through mathematical modeling and analysis of teaching phenomena. Specifically, learners＇ brains are divided into two rooms： the short-term and long-term memory rooms teaching is proposed. Further, and the compound memory-forgetting model frame in continuous three knowledge diffusion models are built： bilateral continuous diffusion model, unilateral impulsive diffusion model, and bilateral impulsive diffusion model according to the different forms of diffusion between two rooms. Based on the theory of population dynamics and mathematical analysis methods, we then explore the optimal teaching strategy like the teaching effort E or the teaching cycle Th, which can maximize the teaching management objectives such as stock knowledge or learning effectiveness. Finally, several examples are provided for further explanation and verification.