知识点网络下的知识评估和学习路径选择

doi:10.13232/j.cnki.jnju.2023.04.010

南京大学学报(自然科学版) ›› 2023, Vol. 59 ›› Issue (4): 629–643.doi: 10.13232/j.cnki.jnju.2023.04.010

知识点网络下的知识评估和学习路径选择

王大利¹^,², 许晴媛¹^,²(), 李进金³^,⁴, 朱泳帆¹^,²

^1.闽南师范大学计算机学院，漳州，363000
^2.数据科学与智能应用福建省高校重点实验室，闽南师范大学，漳州，363000
^3.闽南师范大学数学与统计学院，漳州，363000
^4.福建省粒计算及其应用重点实验室，闽南师范大学，漳州，363000

收稿日期:2023-06-13 出版日期:2023-07-31 发布日期:2023-08-18
通讯作者: 许晴媛 E-mail:xqyyuan871@163.com
基金资助:
国家自然科学基金(62076221);福建省自然科学基金(2022J01912)

Knowledge assessment and learning paths selection under knowledge⁃point network

Dali Wang¹^,², Qingyuan Xu¹^,²(), Jinjin Li³^,⁴, Yongfan Zhu¹^,²

^1.School of Computer Science，Minnan Normal University，Zhangzhou，363000，China
^2.Fujian Provincial University Key Laboratory of Data Science and Intelligent Application，Minnan Normal University，Zhangzhou，363000，China
^3.School of Mathematics Sciences and Statistics，Minnan Normal University，Zhangzhou, 363000，China
^4.Fujian Provincial Key Laboratory of Granular Computing and Its Application，Minnan Normal University，Zhangzhou，363000，China

Received:2023-06-13 Online:2023-07-31 Published:2023-08-18
Contact: Qingyuan Xu E-mail:xqyyuan871@163.com

摘要/Abstract

摘要：

学习者在认知过程中可能掌握了某些知识点，但自身的知识状态并未改变，因此，为了提高学习效率并对学习者进行知识评估，在知识点网络下运用形式概念分析方法讨论如何对学习者进行知识评估和学习路径选择问题.首先，给出了知识点网络的构造方法、有效知识点组合的概念及知识点网络下题库的构造方法；其次，通过知识点网络诱导知识点背景，在已知学习者知识状态的情况下对学习者掌握的知识点进行评估，并给出知识点网络下的学习路径图及其算法；最后，通过实验验证了提出的算法的有效性和可行性.研究发现，由知识点网络诱导的知识点背景确定的知识点结构满足良级性.

关键词: 知识点网络, 有效知识点组合, 知识点背景, 知识评估, 学习路径

Abstract:

In the cognitive process，learners may master some knowledge points，but their own knowledge state does not change. Therefore，in order to improve the learning efficiency and assessment of the learners' knowledge，this paper discusses how to assess the learners' knowledge and select learning paths for learners by using formal concept analysis method under the knowledge?point network. Firstly，the construction method of knowledge?point network，the concept of valid knowledge?point combination and the construction method of question bank under the knowledge?point network are given. Secondly，the knowledge?point context is induced by the knowledge?point network. Furthermore，in circumstances known learners' knowledge state，the knowledge point mastered by learners are assessed and the learning paths diagram and its algorithm under the knowledge?point network are given. Finally，the effectiveness and feasibilities of the proposed algorithm are verified by experiments. This research finds that the knowledge?point structure determined by the knowledge?point context induced by the knowledge?point network satisfies the well?graded.

Key words: knowledge?point network, valid knowledge?point combination, knowledge?point context, knowledge assessment, learning paths

中图分类号:

TP182

王大利, 许晴媛, 李进金, 朱泳帆. 知识点网络下的知识评估和学习路径选择[J]. 南京大学学报(自然科学版), 2023, 59(4): 629–643.

Dali Wang, Qingyuan Xu, Jinjin Li, Yongfan Zhu. Knowledge assessment and learning paths selection under knowledge⁃point network[J]. Journal of Nanjing University(Natural Sciences), 2023, 59(4): 629–643.

图/表 17

图1

图2

表1

图3

表2

知识点网络T1的知识评估表"

知识状态	知识点组合
$∅$	$∅$
1	a
1,2	$a, b$
1,3	$a, c$
1,3,5	$a, c, e$
1,2,4	$a, b, d$
1,2,3,6	$a, b, c$
1,2,3,5,6,7	$a, b, c, e$
1,2,3,4,6,8	$a, b, c, d$
Q₁	D₁

表2

表3

图4

表4

图5

表5

“一元一次不等式”的相关知识点"

知识点	知识点描述
a	不等式的概念
b	不等式性质1：如果 $a > b$ ，那么 $a + c > b + c$ ，或者 $a - c > b - c$
c	不等式性质2：如果 $a > b, c > 0$ ，那么 $a c > b c$ ，或者 $a / c > b / c$
d	不等式性质3：如果 $a > b, c < 0$ ，那么 $a c < b c$ ，或者 $a / c < b / c$
e	解“一元一次不等式”

表5

图6

表6

表7

知识点背景(D2,Q2,I2)下的知识评估"

知识状态	知识点组合
$∅$	$∅$
1	a
1,4	$a, c$
1,2	$a, b$
1,4,9	$a, c, e$
1,4,5	$a, c, d$
1，2，3，4	$a, b, c$
1，2，3，4，9，10	$a, b, c, e$
1，4，5，8，9	$a, c, d, e$
1,2,3,4,5,6	$a, b, c, d$
Q₂	D₂

表7

图7

表8

表9

知识点背景(D3,Q3,I3)下的知识评估"

知识状态	知识点组合
$∅$	$∅$
1	a
1,2	$a, b$
1,3	$a, c$
1,4	$a, d$
1,2,3,5	$a, b, c$
1,2,4,6	$a, b, d$
1,3,4,7	$a, c, d$
1,2,3,4,5,6,7,8	$a, b, c, d$
Q₃	D₃

表9

图8

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知识点	知识点描述
a	圆的概念
b	圆的位置判断
c	圆的面积
d	扇形的表面积
e	圆锥的表面积

知识点网络下的知识评估和学习路径选择

Knowledge assessment and learning paths selection under knowledge⁃point network

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D₁/Q₁	1	2	3	4	5	6	7	8	9
a	1	1	1	1	1	1	1	1	1
b	0	1	0	1	0	1	1	1	1
c	0	0	1	0	1	1	1	1	1
d	0	0	0	1	0	0	0	1	1
e	0	0	0	0	1	0	1	0	1

D₁/Q₁	1	2	3	4	5	6	7	8	9
a	1	1	1	1	1	1	1	1	1
b	0	1	0	1	0	1	1	1	1
c	0	0	1	0	1	1	1	1	1
d	0	0	0	1	0	0	0	1	1
e	0	0	0	0	1	0	1	0	1

D₂/Q₂	1	2	3	4	5	6	7	8	9	10
a	1	1	1	1	1	1	1	1	1	1
b	0	1	1	0	0	1	1	0	0	1
c	0	0	1	1	1	1	1	1	1	1
d	0	0	0	0	1	1	1	1	0	0
e	0	0	0	0	0	0	1	1	1	1

D₃/Q₃	1	2	3	4	5	6	7	8	9
a	1	1	1	1	1	1	1	1	1
b	0	1	0	0	1	1	0	1	1
c	0	0	1	0	1	0	1	1	1
d	0	0	0	1	0	1	1	1	1
e	0	0	0	0	0	0	0	0	1