JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (12): 63-76.doi: 10.6040/j.issn.1671-9352.4.2022.5723

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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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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

CLC Number: 

  • TP182

Fig.1

Flow chart of the practical application of FCA in KST"

Table 1

Skill context for the first row of B4×5"

(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

Table 2

Number of skill-related questions"

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

Fig.2

Hasse diagram of skills surmise relation"

Table 3

Concept lattice of four conjunctive skill context"

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)

Fig.3

Property-oriented concept lattice for context 1"

Fig.4

Equally scaled binary decision tree"

Table 4

Assessment process steps of the sample"

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)

Table 5

Proportion of sample knowledge state distribution"

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

Fig.5

Student knowledge state proportional binary decision tree"

Table 6

Steps assessment process of the student"

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)

Fig.6

Learning paths for skill set S"

Table 7

Breakdown of Learning paths for skill set S"

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 $\varnothing \stackrel{d e}{\longrightarrow}\{3\} \stackrel{a}{\longrightarrow}\{1, 3\} \stackrel{f}{\longrightarrow}\{1, 3, 4, 5\} \stackrel{b c / c}{\longrightarrow} \boldsymbol{Q}$

"

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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[7] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[8] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[9] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[10] DONG Wei-wei. A new method of DEA efficiency ranking for decision making units with independent subsystems[J]. J4, 2013, 48(1): 89 -92 .
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