形式背景下的技能约简与评估

doi:10.3778/j.issn.1673-9418.2008024

计算机科学与探索 ›› 2022, Vol. 16 ›› Issue (3): 692-702.DOI: 10.3778/j.issn.1673-9418.2008024

形式背景下的技能约简与评估

周银凤, 李进金⁺()

闽南师范大学数学与统计学院,福建漳州 363000

收稿日期:2020-08-10 修回日期:2021-01-07 出版日期:2022-03-01 发布日期:2021-01-28
通讯作者: + E-mail: jinjinlimnu@126.com
作者简介:周银凤（1995—）,女,广东揭阳人,硕士研究生,主要研究方向为知识空间理论。
李进金（1960—）,男,福建泉州人,教授,博士生导师,CCF会员,主要研究方向为拓扑学、粗糙集、概念格等。
基金资助:
国家自然科学基金(11871259);国家自然科学基金(11701258);国家自然科学基金(61379021)

Skill Reduction and Assessment in Formal Context

ZHOU Yinfeng, LI Jinjin⁺()

School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, China

Received:2020-08-10 Revised:2021-01-07 Online:2022-03-01 Published:2021-01-28
About author:ZHOU Yinfeng, born in 1995, M.S. candidate. Her research interest is knowledge space theory.
LI Jinjin, born in 1960, professor, Ph.D. supervisor, member of CCF. His research interests include topology, rough set, concept lattices, etc.
Supported by:
National Natural Science Foundation of China(11871259);National Natural Science Foundation of China(11701258);National Natural Science Foundation of China(61379021)

摘要/Abstract

摘要：

知识空间理论（KST）为构建知识评价体系提供了有效的途径。形式概念分析（FCA）是知识发现的有力工具。知识空间理论与形式概念分析间存在密不可分的联系。知识空间理论被运用于评估学习者的知识和指导未来的学习。目前,如何构建准确的知识结构是知识空间理论的重点研究问题。基于技能与问题间的关系,对知识空间理论与形式概念分析间的联系进行研究。首先,提出技能背景的概念,建立技能映射与技能背景间一一对应的关系,得到技能映射与技能背景互相转换的方法。其次,基于技能背景,讨论知识结构的构建问题,得到由技能背景的概念格来构建知识结构的方法。随后,基于技能背景,介绍寻找知识基的方法和保持知识基不变的技能约简方法,以及通过知识基构建技能背景的方法。最后,在已知学习者知识状态的情形下,通过判断学习者对技能的掌握情况来对其进行技能评估,并通过选择学习能够促使知识状态发生改变的技能来讨论学习路径选择等问题。

关键词: 知识空间理论（KST）, 形式概念分析（FCA）, 技能背景, 知识基, 技能约简, 技能评估

Abstract:

Knowledge space theory (KST) provides an effective way to construct knowledge evaluation system. Formal concept analysis (FCA) is a powerful tool for knowledge discovery. The knowledge space theory is closely related to the formal concept analysis. Knowledge space theory is applied to assessing learners’ knowledge and guiding future learning. At present, how to construct accurate knowledge structure is the key research problem of knowledge space theory. Based on the relationship between skills and items, this paper studies the relationship between knowledge space theory and formal concept analysis. Firstly, the concept of skill context is proposed, the one-to-one correspondence relationship between skill map and skill context is established, and the method of mutual conversion between skill map and skill context is obtained. Secondly, based on the skill context, the problem of knowledge structure construction is discussed, and the method of knowledge structure construction based on the concept lattice of skill context is obtained. Then, based on the skill context, the method of finding the knowledge base, the skill reduction method of keeping the knowledge base unchanged, and the method of building the skill context through the knowledge base are introduced. Finally, in the case of known knowledge state of learners, skills are assessed by judging the skills that learners must master, and learning path selection is discussed by selecting skills that can promote the change of knowledge state.

Key words: knowledge space theory (KST), formal concept analysis (FCA), skill context, knowledge base, skill reduction, skill assessment

中图分类号:

TP182

周银凤, 李进金. 形式背景下的技能约简与评估[J]. 计算机科学与探索, 2022, 16(3): 692-702.

ZHOU Yinfeng, LI Jinjin. Skill Reduction and Assessment in Formal Context[J]. Journal of Frontiers of Computer Science and Technology, 2022, 16(3): 692-702.

图/表 13

表1 技能背景 ( S 1 , Q 1 , I 1 )

Table 1 Skill context ( S 1 , Q 1 , I 1 )

S₁	a	b	c	d	e
s	1	0	1	1	1
t	0	1	0	0	1
u	0	0	1	0	0
v	1	0	1	1	1

图1 概念格 L ( S 1 , Q 1 , I 1 )

Fig.1 Concept lattice L ( S 1 , Q 1 , I 1 )

表2 技能背景 ( S 2 , Q 2 , I 2 )

Table 2 Skill context ( S 2 , Q 2 , I 2 )

$S 2$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 2$					$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$
$s 6$		$×$	$×$

表2 技能背景 ( S 2 , Q 2 , I 2 )

Table 2 Skill context ( S 2 , Q 2 , I 2 )

$S 2$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 2$					$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$
$s 6$		$×$	$×$

表3 技能背景 ( X , Q 2 , I X )

Table 3 Skill context ( X , Q 2 , I X )

$X$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$

表3 技能背景 ( X , Q 2 , I X )

Table 3 Skill context ( X , Q 2 , I X )

$X$	1	2	3	4	5
$s 1$		$↙$	$×$	$↙$	$×$
$s 3$	$×$	$↙$	$↙$	$×$	$×$
$s 4$	$↙$	$×$	$×$	$×$	$×$
$s 5$	$×$	$×$	$×$	$↙$	$↙$

表4 技能背景 ( T , Q 1 , I T )

Table 4 Skill context ( T , Q 1 , I T )

$T$	a	b	c	d	e
s	$×$	$↙$	$×$	$×$	$×$
t	$↙$	$×$	$↙$	$↙$	$×$
u	$↙$		$×$	$↙$	$↙$

表4 技能背景 ( T , Q 1 , I T )

Table 4 Skill context ( T , Q 1 , I T )

$T$	a	b	c	d	e
s	$×$	$↙$	$×$	$×$	$×$
t	$↙$	$×$	$↙$	$↙$	$×$
u	$↙$		$×$	$↙$	$↙$

表5 技能背景 ( S , Q , I )

Table 5 Skill context ( S , Q , I )

$S$	1	2	3	4
x	0	1	0	1
y	1	0	1	0
z	1	1	0	0

表5 技能背景 ( S , Q , I )

Table 5 Skill context ( S , Q , I )

$S$	1	2	3	4
x	0	1	0	1
y	1	0	1	0
z	1	1	0	0

表6 K 1中知识状态的技能掌握情况

Table 6 Skill mastery of knowledge state in K 1

知识状态	需掌握的核心技能
$∅$	$∅$
$b$	$∅$
${a, c, d}$	$t$
${a, b, d, e}$	$u$
${a, b, c, d}$	$t$
$Q 1$	${t, u}$

表6 K 1中知识状态的技能掌握情况

Table 6 Skill mastery of knowledge state in K 1

知识状态	需掌握的核心技能
$∅$	$∅$
$b$	$∅$
${a, c, d}$	$t$
${a, b, d, e}$	$u$
${a, b, c, d}$	$t$
$Q 1$	${t, u}$

图2 K 1的学习路径

Fig.2 Learning path in K 1

图3 概念格 L ( S 2 , Q 2 , I 2 )

Fig.3 Concept lattice L ( S 2 , Q 2 , I 2 )

表7 K 2中知识状态的技能掌握情况

Table 7 Skill mastery of knowledge state in K 2

知识状态	需掌握的核心技能
$∅$	$∅$
${1}$	${s 4}$
${2,3}$	${s 3}$
${4,5}$	${s 5}$
${1,2, 3}$	${s 3, s 4}$
${1,2, 4}$	${s 1}$
${1,4, 5}$	${s 4, s 5}$
${1,2, 3,4}$	${s 1, s 3}$
${1,2, 4,5}$	${s 1, s 5}$
${2,3, 4,5}$	${s 3, s 5}$
$Q 2$	${s 1, s 3, s 5}$

表7 K 2中知识状态的技能掌握情况

Table 7 Skill mastery of knowledge state in K 2

知识状态	需掌握的核心技能
$∅$	$∅$
${1}$	${s 4}$
${2,3}$	${s 3}$
${4,5}$	${s 5}$
${1,2, 3}$	${s 3, s 4}$
${1,2, 4}$	${s 1}$
${1,4, 5}$	${s 4, s 5}$
${1,2, 3,4}$	${s 1, s 3}$
${1,2, 4,5}$	${s 1, s 5}$
${2,3, 4,5}$	${s 3, s 5}$
$Q 2$	${s 1, s 3, s 5}$

图4 K 2的学习路径

Fig.4 Learning path in K 2

表8 L 1中知识状态的技能掌握情况

Table 8 Skill mastery of knowledge state in L 1

知识状态	必掌握技能
$∅$	$∅$
${c}$	${t}$
${e}$	${u}$
${b, e}$	${s, u, v}$
${a, c, d, e}$	${t, u}$
$Q 1$	$S 1$

表8 L 1中知识状态的技能掌握情况

Table 8 Skill mastery of knowledge state in L 1

知识状态	必掌握技能
$∅$	$∅$
${c}$	${t}$
${e}$	${u}$
${b, e}$	${s, u, v}$
${a, c, d, e}$	${t, u}$
$Q 1$	$S 1$

图5 L 1的学习路径

Fig.5 Learning path in L 1

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形式背景下的技能约简与评估

Skill Reduction and Assessment in Formal Context

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