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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 63-76.doi: 10.6040/j.issn.1671-9352.4.2022.5723

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面向属性概念在自适应技能测评中的实践应用

何秋红1,3(),李进金2,4,*(),周银凤2,吴靖5   

  1. 1. 闽南师范大学计算机学院，福建 漳州 363000
    2. 闽南师范大学数学与统计学院，福建 漳州 363000
    3. 闽南师范大学数据科学与智能应用福建省高校重点实验室，福建 漳州 363000
    4. 闽南师范大学福建省粒计算及其应用重点实验室，福建 漳州 363000
    5. 闽南师范大学附属中学(漳州市第二中学)，福建 漳州 363000
  • 收稿日期:2022-03-31 出版日期:2023-12-20 发布日期:2023-12-19
  • 通讯作者: 李进金 E-mail:hqh1129@mnnu.edu.cn;jinjinlimnu@126.com
  • 作者简介:何秋红(1977—)，女，副教授，研究方向为知识空间理论和形式概念分析等. E-mail: hqh1129@mnnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11871259);国家自然科学基金资助项目(12271191);福建省自然科学基金资助项目(2019J01748);福建省自然科学基金资助项目(2020J02043);福建省自然科学基金资助项目(2020J01812);福建省自然科学基金资助项目(2022J01306);福建省自然科学基金资助项目(2022J05169);福建省2022本科高校教育教学研究项目(一般项目)(FBJG20220091)

Practical application of property-oriented concepts in adaptive assessment of skills

Qiuhong HE1,3(),Jinjin LI2,4,*(),Yinfeng ZHOU2,Jing WU5   

  1. 1. School of Computer Science, Minnan Normal University, Zhangzhou 363000, Fujian, China
    2. School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, Fujian, China
    3. Fujian Provincial University Key Laboratory of Data Science and Intelligent Application, Minnan Normal University, Zhangzhou 363000, Fujian, China
    4. Fujian Key Laboratory of Granular Computing and Application, Minnan Normal University, Zhangzhou 363000, Fujian, China
    5. Affiliated High School of Minnan Normal University(Zhangzhou No.2 Middle School), Zhangzhou 363000, Fujian, China
  • Received:2022-03-31 Online:2023-12-20 Published:2023-12-19
  • Contact: Jinjin LI E-mail:hqh1129@mnnu.edu.cn;jinjinlimnu@126.com

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摘要：

将技能多映射与面向属性概念相结合可获得概念(X, B)，由此得到构建知识结构与技能结构的方法应用于自适应技能测评。首先，由专家教师给出问题集Q和技能集S及其技能多映射(Q, S; μ)；其次，从概念(X, B)外延和内涵分别获得知识结构和技能结构；再次，由知识结构进行考生样本的自适应知识测评，并统计样本的知识状态比例；然后，优化知识空间理论“二分法”的等比例选题规则为样本比例选题规则，获得针对不同地域和年龄段考生更快速的测评效果；最后，画出技能集学习路径图。

关键词: 知识结构, 技能结构, 学习路径, 技能背景, 面向属性概念

Abstract:

Certain concepts (X, B) can be obtained via the combination of skill multimaps with property-oriented concepts, which leads to a method for constructing knowledge and skill structures that can be applied to the adaptive assessment of skills. The processis as follows. First, expert teachers provide the question set Q, skill set S, and their corresponding skill multimaps (Q, S; μ). Next, the knowledge and skill structures are obtained from the extension and the intention of (X, B). Thereafter the knowledge structure is used to conduct the adaptive assessment of the sample, and the proportion of their knowledge states is calculated. Subsequently, the equal proportion selection rule of knowledge space theory "binary responses" is optimized to the sample proportion selection rule, facilitate faster assessment effects for examinees in different regions and age groups. Finally, the figure of learning paths for skill sets is drawn.

Key words: knowledge structure, skill structure, learning path, skill context, property-oriented concept

中图分类号: 

  • TP182

图1

FCA在KST中的实践应用流程图"

表1

B4×5第一行的技能背景"

(Q, S) a b c d e f
1 1 0 0 0 0 0
2 1 1 1 0 0 0
3 0 0 0 1 1 0
4 1 1 0 0 0 1
5 1 1 1 0 0 1

表2

技能相关问题个数"

技能 问题集 问题个数
a {1, 2, 4, 5} 4
b {2, 4, 5} 3
c {2, 5} 2
d {3, 4, 5} 3
e {3, 5} 2
f {4, 5} 2

图2

技能推测关系哈斯图"

表3

4个合取技能背景的概念格"

背景1概念 背景2概念 背景3概念 背景4概念
(?, ?) (?, ?) (?, ?) (?, ?)
(1, a) (1, a) (1, a) (1, a)
(3, de) (3, de) (3, de) (3, de)
(12, abc) (12, abc) (12, abc) (12, abc)
(13, ade) (13, ade) (13, ade) (13, ade)
(14, abf) (14, abf) (14, adf) (14, adf)
(123, abcde) (123, abcde) (123, abcde) (123, abcde)
(1245, abcf) (124, abcf) (125, abcf)
(1245, abcdf) (124, abcdf)
(135, adef) (134, adef) (1345, adef)
(134, abdef) (1345, abdef)
(Q, S) (Q, S) (Q, S) (Q, S)

图3

背景1的面向属性概念格"

图4

等比例二元决策树"

表4

样本测评过程步骤"

知识状态 步骤数 选择问题及考生样本反馈序列
? 3 (3, 0), (2, 0), (1, 0)
{1} 4 (3, 0), (2, 0), (1, 1), (4, 0)
{3} 3 (3, 1), (2, 0), (1, 0)
{1, 2} 3 (3, 0), (2, 1), (4, 0)
{1, 3} 4 (3, 1), (2, 0), (1, 1), (4, 0)
{1, 4} 4 (3, 0), (2, 0), (1, 1), (4, 1)
{1, 2, 3} 3 (3, 1), (2, 1), (4, 0)
{1, 2, 4, 5} 3 (3, 0), (2, 1), (4, 1)
{1, 3, 4, 5} 4 (3, 1), (2, 0), (1, 1), (4, 1)
{1, 2, 3, 4, 5} 3 (3, 1), (2, 1), (4, 1)

表5

样本知识状态分布比例"

知识状态 卷数 比例
? 1 0.005
{1} 3 0.014
{3} 6 0.028
{1, 2} 0 0
{1, 3} 2 0.009
{1, 4} 5 0.023
{1, 2, 3} 5 0.023
{1, 2, 4, 5} 2 0.009
{1, 3, 4, 5} 81 0.375
{1, 2, 3, 4, 5} 111 0.514
共10 216 1

图5

考生知识状态比例二元决策树"

表6

考生测评过程步骤"

知识状态 步骤数 选择问题及新考生反馈序列
? 5 (2, 0), (5, 0), (3, 0), (4, 0), (1, 0)
{1} 5 (2, 0), (5, 0), (3, 0), (4, 0), (1, 1)
{3} 4 (2, 0), (5, 0), (3, 1), (1, 0)
{1, 2} 4 (2, 1), (4, 0), (1, 1), (3, 0)
{1, 3} 4 (2, 0), (5, 0), (3, 1), (1, 1)
{1, 4} 4 (2, 0), (5, 0), (3, 0), (4, 1)
{1, 2, 3} 4 (2, 1), (4, 0), (1, 1), (3, 1)
{1, 2, 4, 5} 3 (2, 1), (4, 1), (3, 0)
{1, 3, 4, 5} 2 (2, 0), (5, 1)
{1, 2, 3, 4, 5} 3 (2, 1), (4, 1), (3, 1)

图6

技能集S学习路径"

表7

技能集S学习路径分解"

路径 技能集S学习路径
1 $\varnothing \stackrel{a}{\longrightarrow}\{1\} \stackrel{b c}{\longrightarrow}\{1, 2\} \stackrel{f}{\longrightarrow}\{1, 2, 4, 5\} \stackrel{d e / e}{\longrightarrow} \boldsymbol{Q}$
2 $\varnothing \stackrel{a}{\longrightarrow}\{1\} \stackrel{b c}{\longrightarrow}\{1, 2\} \stackrel{d e}{\longrightarrow}\{1, 2, 3\} \stackrel{f}{\longrightarrow} \boldsymbol{Q}$
3 $\varnothing \stackrel{a}{\longrightarrow}\{1\} \stackrel{b f / d f}{\longrightarrow}\{1, 4\} \stackrel{b c / c}{\longrightarrow}\{1, 2, 4, 5\} \stackrel{d e / e}{\longrightarrow} \boldsymbol{Q}$
4 $\varnothing \stackrel{a}{\longrightarrow}\{1\} \stackrel{b f / d f}{\longrightarrow}\{1, 4\} \stackrel{d e / e}{\longrightarrow}\{1, 3, 4, 5\} \stackrel{b c / c}{\longrightarrow} \boldsymbol{Q}$
5 $\varnothing \stackrel{a}{\longrightarrow}\{1\} \stackrel{d e}{\longrightarrow}\{1, 3\} \stackrel{b c}{\longrightarrow}\{1, 2, 3\} \stackrel{f}{\longrightarrow} \boldsymbol{Q}$
6 $\varnothing \stackrel{a}{\longrightarrow}\{1\} \stackrel{d e}{\longrightarrow}\{1, 3\} \stackrel{f}{\longrightarrow}\{1, 3, 4, 5\} \stackrel{b c / c}{\longrightarrow} \boldsymbol{Q}$
7 $\varnothing \stackrel{d e}{\longrightarrow}\{3\} \stackrel{a}{\longrightarrow}\{1, 3\} \stackrel{b c}{\longrightarrow}\{1, 2, 3\} \stackrel{f}{\longrightarrow} \boldsymbol{Q}$
8 $\varnothing \stackrel{d e}{\longrightarrow}\{3\} \stackrel{a}{\longrightarrow}\{1, 3\} \stackrel{f}{\longrightarrow}\{1, 3, 4, 5\} \stackrel{b c / c}{\longrightarrow} \boldsymbol{Q}$

表 

常见符号表"

符号 名称 说明
Q 非空有限问题集 所有问题的集合
q 问题 一个问题q∈Q
K 知识状态 解答正确的问题集
Kq K含q知识状态集族 K含q的知识状态构成的集族
$\mathscr{K}$ 知识状态集族 Q的子集构成的集族且至少包含?和Q
U 对象集 形式背景三元组之一
A 属性集 形式背景三元组之二
I 二元关系I?U×A 形式背景三元组之三
x* x所具有的属性集合 x*={a|a∈A, (x, a)∈Ι}
a* 具有属性a的对象集合 a*={x|x∈U, (x, a)∈Ι}
X◇ X中对象所具有的属性集合 X◇={a∈A|a*∩X≠?}
B□ 只具有B中属性的对象集合 B□={x∈U|x*?B}
S 非空有限技能集 所有技能的集合
s 技能 一个技能s∈S
C 技能子集 正确解答K相关的最小技能子集
T 技能背景中的技能子集 技能子集T?S
$\mathscr{T}$ 技能状态集族 S的子集T构成的集族
τ 技能映射(技能单映射) 从Q到2S\{?}的映射
μ 技能多映射 从Q到(22S\{?})\{?}的映射
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