自适应个性化巩固学习模型  

Adaptive Personalized Consolidated Learning Model

作　　者：王功勋 李进金 WANG Gongxun;LI Jinjin(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《山西大学学报(自然科学版)》2025年第1期1-19,共19页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12271191)。

摘　　要：“巩固学习推荐”是指向学生推荐需要复习巩固的学习内容的过程。本文研究了基于能力的知识空间理论的个性化巩固学习推荐问题,针对能力状态与知识状态之间缺乏一一对应关系的挑战,提出了一种有效的推荐方法。该方法首先通过学生的知识状态计算内掌握边缘,并据此推导出退步前后的知识状态,然后通过这些知识状态确定相应能力状态的顶或底,最终根据顶和底推荐需要巩固学习的技能集,以防止学生因遗忘等因素导致知识退步。本文提出了两个刻画定理:一是用技能函数刻画能力状态的顶或底,二是用问题函数刻画知识状态的内掌握边缘。利用这些定理,可在不建立知识结构的前提下直接获取能力状态的顶或底及知识状态的内掌握边缘。最后本文分别给出了根据定义和刻画定理获取内掌握边缘的算法,并通过对比实践说明后者耗时平均减少了77%,内存占用平均降低了67%。"Consolidated Learning Recommendations"refers to the process of recommending learning content that students need to review and consolidate.This paper investigates the issue of personalized consolidated learning recommendations based on competence-based knowledge space theory,and proposes an effective recommendation method to address the challenge of the lack of oneto-one correspondence between competence states and knowledge states.The method firstly calculates the inner master fringe based on the student's knowledge state.It uses this to deduce the knowledge states before and after potential regression.Based on these knowledge states,it identifies the tops or bottoms of the corresponding competence states.Finally,according to these tops or bottoms,it recommends the skill set that needs to be consolidated.This approach helps prevent knowledge regression due to factors like forgetting.This paper presents two characterization theorems:the first uses a skill function to characterize the tops or bottoms of competence states,and the second uses a problem function to characterize the inner master fringe of knowledge states.By applying these theorems,the tops or bottoms of competence states and the inner master fringe of knowledge states can be directly obtained without constructing a knowledge structure.Finally,this paper presents algorithms to obtain the inner master fringe based on definitions and characterization theorems,and demonstrates through comparative practice that the latter reduces time consumption by an average of 77%and memory usage by an average of 67%.

关 键 词：知识状态 能力状态 内掌握边缘 技能函数 问题函数 个性化学习 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]