Elsevier

Computers & Education

Volume 49, Issue 3, November 2007, Pages 691-707
Computers & Education

A new approach for constructing the concept map

https://doi.org/10.1016/j.compedu.2005.11.020Get rights and content

Abstract

In recent years, e-learning system has become more and more popular and many adaptive learning environments have been proposed to offer learners customized courses in accordance with their aptitudes and learning results. For achieving the adaptive learning, a predefined concept map of a course is often used to provide adaptive learning guidance for learners. However, it is difficult and time consuming to create the concept map of a course. Thus, how to automatically create a concept map of a course becomes an interesting issue. In this paper, we propose a Two-Phase Concept Map Construction (TP-CMC) approach to automatically construct the concept map by learners’ historical testing records. Phase 1 is used to preprocess the testing records; i.e., transform the numeric grade data, refine the testing records, and mine the association rules from input data. Phase 2 is used to transform the mined association rules into prerequisite relationships among learning concepts for creating the concept map. Therefore, in Phase 1, we apply Fuzzy Set Theory to transform the numeric testing records of learners into symbolic data, apply Education Theory to further refine it, and apply Data Mining approach to find its grade fuzzy association rules. Then, in Phase 2, based upon our observation in real learning situation, we use multiple rule types to further analyze the mined rules and then propose a heuristic algorithm to automatically construct the concept map. Finally, the Redundancy and Circularity of the concept map constructed are also discussed. Moreover, we also develop a prototype system of TP-CMC and then use the real testing records of students in junior high school to evaluate the results. The experimental results show that our proposed approach is workable.

Introduction

With vigorous development of the Internet, e-learning system has become more and more popular. Therefore, in the last 5 years, many adaptive learning and testing systems have been proposed to offer learners customized courses in accordance with their aptitudes and learning results (Appleby et al., 1997, Carchiolo et al., 2002, Chang et al., 1998, Frosini et al., 1998, Gamboa, 2001, Hsu et al., 1998, Hwang, 2003, Hwang et al., 2003, Triantafllou et al., 2003, Tsai et al., 2001). For achieving the adaptive learning, a predefined concept map of a course, which provides teachers for further analyzing and refining the teaching strategies, is often used to generate adaptive learning guidance. However, it is difficult and time consuming to create the concept map of a course. Thus, how to automatically create a correct concept map of a course becomes an interesting issue.

Therefore, in this paper, we propose a Two-Phase Concept Map Construction (TP-CMC) algorithm to automatically construct a concept map of a course by historical testing records. In the first phase, we apply Fuzzy Set Theory to transform the numeric testing records of learners into symbolic, apply Education Theory (Item Analysis for Norm-Referencing) to further refine it, and apply Data Mining approach to find its grade fuzzy association rules. The mined grade fuzzy association rules include four rule types, L–L, L–H, H–L, and H–H, which denote the casual relations between learning concepts of quizzes. For example, if a rule type is Q1 · L  Q2 · L which means that learners get low grade on quiz Q1 implies that they may also get low grade on quiz Q2. We call this rule type is L–L type. The previous articles use single rule type, e.g. L–L type, to analyze the testing data, which may decrease the quality of concept map (Hsu et al., 1998, Hwang et al., 2003, Tsai et al., 2001). Therefore, in the second phase, based upon our observation in real learning situation, we use multiple rule types to further analyze the mined rules and then propose a heuristic algorithm to automatically construct the concept map according to analysis results, which can be used to develop adaptive learning system and refine the learning strategies of learners.

The main contributions of this paper are:

  • (1)

    Apply Fuzzy Set Theory to transform the numeric testing records of learners into symbolic data, Education Theory (Item Analysis for Norm-Referencing) to further refine it, and Data Mining approach to find its grade fuzzy association rules.

  • (2)

    Analyze the mined association rules to generate related prerequisite relationships among concept sets of test item based on our observation in real learning situation.

  • (3)

    Propose a heuristic algorithm to automatically construct the concept map of a course.

Section snippets

Related work

Novak (1998) proposed Concept Map to organize or represent the knowledge as a network consisting of nodes (points/vertices) as concepts and links (arcs/edges) as the relations among concepts. Thus, a wide variety of different forms of concept maps have been proposed and applied in various domains (Bruillard and Baron, 2000, Gaines and Shaw, 1995, Gordon, 2000). In the adaptive learning environment, the Concept Map can be used to demonstrate how the learning status of a concept can possibly be

Two-phase concept map construction (TP-CMC)

In TP-CMC, the Test item-Concept Mapping Table records the related learning concepts of each test item. As shown in Table 2, five quizzes contain these related learning concepts A, B, C, D and E, where “1” indicates the quiz contains this concept, and “0” indicates not. Moreover, a concept set of quiz i is denoted as CSQi, e.g., CSQ5 = {B, D, E}. The main idea of our approach is to extract the prerequisite relationships among concepts of test items and construct the concept map. Based upon

Grade fuzzification

As described in Section 3.1, we apply fuzzy concept to transform numeric grade data into symbolic, called Grade Fuzzification. Three membership functions of each quiz’s grade are shown in Fig. 2. In the fuzzification result, “Low”, “Mid” and “High” denote “Low Grade”, “Middle Grade” and “High Grade” respectively. Qi · L, Qi · M, and Qi · H denote the value of LOW fuzzy function, MIDDLE fuzzy function, and HIGH fuzzy function for the quiz i, respectively. By given membership functions, the

Concept map constructor

Before constructing the concept map, we can get the prerequisite relationship among concepts of quiz from analyzing four association rule types, L–L, L–H, H–L, and H–H, based upon our observation obtained by interviewing the educational experts, in real learning situation. Therefore, we can conclude the Heuristic 1: given two quizzes Q1 and Q2, if concepts of Q1 are the prerequisite of concepts of Q2, Learner gets low grade on Q1 implies that s/he may also get low grade on Q2 or Learner gets

Evaluating the redundancy and circularity of concept map

In this paper, creating a concept map without Redundancy and Circularity is our concern. As shown in Fig. 10, we create three concept maps by using different approaches and evaluate their difference in terms of Redundancy and Circularity. Thus, we use three processing steps including anomaly diagnosis, the prerequisite relationship based upon analyzing L–L or L–L, L–H, H–L, H–H rule types, and cycle detection to create different concept maps. As shown in Fig. 10, the prerequisite relationship

The experiment of TP-CMC in physics course

In this section, we describe our experiment results of the Two-Phase Concept Map Construction (TP-CMC) approach.

Conclusion

The concept map is often used to provide teachers for further analyzing and refining the teaching strategies and to generate adaptive learning guidance in adaptive learning environment. However, creating the concept map of a course is difficult and time consuming. Therefore, in this paper, we propose a Two-Phase Concept Map Construction (TP-CMC) approach to automatically construct a concept map of a course by learners’ historical testing records. Phase 1 is used to preprocess the testing

Acknowledgement

This research was partially supported by National Science Council of Republic of China under the number of NSC94-2524-S009-001, NSC94-2524-S009-002, and NSC 93-2524-S-009-004-EC3.

References (16)

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