自然科学版
陕西师范大学学报(自然科学版)
数学与计算机科学
基于复合记忆-遗忘模型框架的连续教学策略优化控制
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刘丹青1,2,3, 李雅芝4, 吴振强1,3, 郭强5, 刘建国6*
(1 现代教学技术教育部重点实验室, 陕西 西安 710119; 2 青海师范大学 计算机学院, 青海 西宁 810008;3 陕西师范大学 计算机科学学院, 陕西 西安 710119; 4 黔南民族师范学院 数学与统计学院, 贵州 都匀 558000;5 上海理工大学 复杂系统科学研究中心, 上海 200093;6 上海财经大学 科研实验中心, 上海 200433)
刘建国,男,教授,博士生导师,主要从事网络科学、个性化推荐及知识管理研究。E-mail: Liujg004@ustc.edu.cn
摘要:
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。
关键词:
复合记忆-遗忘模型框架; 知识扩散模型; 连续教学; 教学策略; 优化控制
收稿日期:
2018-04-04
中图分类号:
O232
文献标识码:
A
文章编号:
1672-4291(2018)04-0012-09
基金项目:
中央高校基本科研业务费专项资金(20150108,261001236);国家自然科学基金(71371125,61374177)
Doi:
The optimal control strategy in continuous teaching based on the compound memory-forgetting model frame
LIU Danqing1,2,3, LI Yazhi4, WU Zhenqiang1,3, GUO Qiang5, LIU Jianguo6*
(1 Key Laboratory of Modern Teaching Technology, Ministry of Education, Xi′an 710119, Shaanxi, China;2 School of Computer, Qinghai Normal University, Xining 810008, Qinghai, China;3 School of Computer Science, Shaanxi Normal University, Xi′an 710119, Shaanxi, China;4 School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun 558000, Guizhou, China;5 Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, China;6 Data Science and Cloud Service Research Center, Shanghai University of Finance and Economics, Shanghai 200433, China)
Abstract:
The influence of teaching strategies on knowledge dissemination systems are investigated 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 and the compound memory-forgetting model frame in continuous teaching is proposed. Further, 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.
KeyWords:
the compound memory-forgetting model frame; knowledge diffusion model; continuous teaching; teaching strategy; optimal control