Automatically constructing concept maps based on fuzzy rules for adapting learning systems
Introduction
In recent years, some researchers focused on the research topics of adaptive learning systems (Appleby et al., 1997, Bai and Chen, 2006a, Bai and Chen, 2006b, Bai and Chen, 2007a, Bai and Chen, 2007b, Carchiolo et al., 2002, Gamboa, 2001, Hwang, 2003, Hsu et al., 1998, Hwang et al., 2003, Novak, 1998, Popham, 1999, Rasmani and Shen, 2006, Tsai et al., 2001). Appleby et al. (1997) presented a method for dealing with knowledge-based diagnostic tests of basic mathematical skills. Bai and Chen (2006a) presented a method for automatically constructing grade membership functions for students’ evaluation for fuzzy grading systems. Bai and Chen (2006b) presented a method for students’ learning achievement using fuzzy membership functions. Bai and Chen (2007a) presented a method for evaluating students’ learning achievement using fuzzy membership functions and fuzzy rules. Carchiolo et al. (2002) presented a method for dealing with adaptive formative paths in a web-based learning environment. Gamboa (2001) presented a method for designing intelligent tutoring systems. Hwang (2003) presented a method for applying the conceptual map model for developing intelligent tutoring systems. Hwang et al. (2003) presented a computer-assisted approach for diagnosing students’ learning problems in science courses. Hsu et al. (1998) presented a concept inheritance method for learning diagnosis of a network-based testing and evaluation system. Novak (1998) presented a method for using concept maps as facilitative tools in schools and corporations. Popham (1999) pointed out what teachers need to know for classroom assessment. Rasmani and Shen (2006) presented a method for using a data-driven fuzzy rule induction approach for evaluation of student academic performance. Tsai et al. (2001) presented a method for a two-phase fuzzy mining and learning algorithm for an adaptive learning environment. Sue, Weng, Su, and Tseng (2004) presented a two-phase concept map construction (TP-CMC) algorithm to automatically construct a concept map of a course by students’ historical testing records. They find the fuzzy association rules by students’ historical testing records, then construct a concept map based on the fuzzy association rules and the question-concept mapping table. However, the influence weights between questions on the constructed concept map shown in Sue et al. (2004) are too high. Moreover, because the two-phase concept construction algorithm presented in Sue et al. (2004) uses fuzzy data mining techniques to obtain fuzzy association rules for constructing concept maps, it is not efficient enough.
In this paper, we present a new method to automatically construct concept maps based on fuzzy rules and students’ testing records for adaptive learning systems. It constructs concept maps by using fuzzy reasoning techniques based on fuzzy rules. The proposed method can overcome the drawbacks of Sue et al. (2004). It provides a useful way to construct concept maps in adaptive learning systems.
The rest of this paper is organized as follows: In Section 2, we briefly review Su et al’s method from Sue et al. (2004). In Section 3, we present a new method to automatically construct concept maps based on fuzzy rules for adaptive learning systems. In Section 4, we use an example to illustrate the process of automatically constructing concept maps based on fuzzy rules. The conclusions are discussed in Section 5.
Section snippets
Preliminaries
Sue et al. (2004) presented a two-phase concept map construction (TP-CMC) algorithm to automatically construct a concept map of a course by learners’ historical testing records. In the following, we briefly review Su et al. method as follows:
(A) Phase 1: This phase consists of 3 steps, shown as follows:
Step 1: Fuzzify learners’ historical testing records into fuzzy sets based on the fuzzy sets (Zadeh, 1965) shown in Fig. 1.
Step 2: Sort the total scores of the students in a descending order
A new method for automatically constructing concept maps for adaptive learning systems
In this section, we present a new method for automatically constructing concept maps for adaptive learning systems. Let Si denote the ith student, where 1 ⩽ i ⩽ m. Assume that there are n questions Q1, Q2, …, and Qn in the students’ answerscripts, then we can get a grade matrix G, shown as follows:where gij denotes the grade of the ith student Si with respect to the jth question Qj, gij ∈ [0, markj], markj denotes the mark allotted to the jth question Qj
An example
Assume that there are five questions Q1, Q2, Q3, Q4, Q5 and five concepts A, B, C, D, E. Assume that there are ten students S1,S2, ⋯, S10 to answer these questions. Assume that the grade matrix G and the question-concepts matrix QC are shown as follows:
[Step 1] Based on Eq. (1), we can get
Conclusions
To automatically construct concept maps based on students’ testing records is an important research topic for adapting learning systems. In this paper, we have presented a new method based on fuzzy rules and students’ testing records to automatically construct concept maps for adaptive learning. The proposed method constructs concept maps by using fuzzy reasoning techniques based on fuzzy rules. It can overcome the drawback of the method presented in Sue et al. (2004). The proposed method
Acknowledgement
This work was supported in part by the National Science Council, Republic of China, under Grant NSC 95-2213-E-011-116-MY2.
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