基于表现水平与能力水平协同依赖视角的自适应个性化学习指导模型  

Adaptive personalized learning guidance model based on the perspective of synergistic dependence between performance level and ability level

作　　者：王功勋 李进金 Wang Gongxun;Li Jinjin(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,363000,China;School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou,362000,China)

机构地区：[1]闽南师范大学数学与统计学院,漳州363000 [2]泉州师范学院数学与计算机科学学院,泉州362000

出　　处：《南京大学学报(自然科学版)》2024年第6期1009-1027,共19页Journal of Nanjing University(Natural Science)

基　　金：国家自然科学基金(12271191,11871259);福建省自然科学基金(2023J01122,2023J01125,2023J05175,2022J01306,2022J05169)

摘　　要：基于能力的知识空间理论为教育评估及学习指导提供了科学且有效的理论框架.在该理论中,教育评估的目的在于通过学生的答卷情况(知识状态),了解他们在特定领域的能力水平(能力状态),并根据评估结果为学生提供个性化的学习指导.然而,能力状态与知识状态之间缺乏一一对应关系,仅依据知识状态只能确定一类能力状态,而无法精准判断学生的能力状态.因此,提出了一种基于同一类能力的顶或底直接计算知识状态掌握边缘,再进行个性化学习指导的一般方法,即第一步获取学生当前知识状态的掌握边缘;第二步根据掌握边缘选择目标知识状态;第三步获取当前和目标知识状态对应的能力状态的顶或底;第四步根据顶或底推送即将要学习的技能集,使其达到目标知识状态.此外,给出两种刻画定理,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掌握边缘.在不建立知识结构的前提下,获取能力状态的顶或底和知识状态的掌握边缘,可以提高获取效率.最后,分别给出了根据定义和刻画定理获取掌握边缘的算法,并通过对比实验证明后者耗时更短、占用内存更小.The competence‐based knowledge space theory provides a scientific and effective theoretical framework for educational assessment and learning guidance.In this theory,the purpose of educational assessment is to understand students'competence levels(competence state)in specific domains based on their answers(knowledge state),and provide personalized learning guidance based on the assessment results.However,there is no one‐to‐one correspondence between competence state and knowledge state.Solely relying on knowledge state only determines a category of competence state,without accurately judging the students'competence state.Therefore,this paper proposes a general method for the direct calculation of the master fringe of the knowledge state and personalized learning guidance based on the ceiling or floor of the same category of competence.The first step is to obtain the master fringe of the current knowledge state,the second step is to choose the target knowledge state based on the master fringe,the third step is to attain the ceiling or floor of the competence state corresponding to the current knowledge state and the target knowledge state,and the fourth step is to push the skill set to be learned soon based on the ceiling or floor,to achieve the target knowledge state.This paper also provides two characterization theorems,using the skill function to describe the ceiling or floor of the competence state,and using the problem function to describe the master fringe of the knowledge state.Obtaining the ceiling or floor of the competence state,and the master fringe of the knowledge state without establishing the knowledge structure improves acquisition efficiency.Finally,this paper presents algorithms to obtain the master fringe based on definitions and characterization theorems,and comparative practice demonstrates that the latter has shorter time consumption and smaller memory usage.

关 键 词：知识状态 能力状态 掌握边缘 技能函数 问题函数 个性化学习 

分 类 号：G434[文化科学—教育学]