A new approach for constructing the concept map
Shian-Shyong Tseng
a,b,*, Pei-Chi Sue
a,1, Jun-Ming Su
a,2,
Jui-Feng Weng
a,1, Wen-Nung Tsai
a,3aDepartment of Computer Science, National Chiao Tung University, 1001 Ta Hsueh Rd., Hsinchu, Taiwan 300, Taiwan b
Department of Information Science and Applications, Asia University No. 500, Liufeng Rd., Wufeng Shiang, Taichung, Taiwan 413, Taiwan
Received 24 August 2005; received in revised form 31 October 2005; accepted 7 November 2005
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 asso-ciation rules. Then, in Phase 2, based upon our observation in real learning situation, we use multiple rule
0360-1315/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compedu.2005.11.020
*Corresponding author. Tel.: +886 3 5712121 56662; fax: +886 3 5721490.
E-mail addresses: sstseng@cis.nctu.edu.tw (S.-S. Tseng), gis91510@cis.nctu.edu.tw (P.-C. Sue), jmsu@csie.nctu.
edu.tw (J.-M. Su),roy@cis.nctu.edu.tw(J.-F. Weng),tsaiwn@csie.nctu.edu.tw(W.-N. Tsai).
1 Tel.: +886 3 5712121 56658; fax: +886 3 5721490. 2
Tel.: +886 3 5712121 56658; fax: +886 3 5724176.
3 Tel.: +886 3 5712121 31882; fax: +886 3 5724176.
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 dis-cussed. 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.
2005 Elsevier Ltd. All rights reserved.
Keywords: Adaptive learning environments; Concept map; Data mining; Testing records
1. Introduction
With vigorous development of the Internet, e-learning system has become more and more pop-ular. Therefore, in the last 5 years, many adaptive learning and testing systems have been pro-posed to offer learners customized courses in accordance with their aptitudes and learning results (Appleby, Samuels, & Jones, 1997; Carchiolo, Longheu, & Malgeri, 2002; Chang, Liu, & Chen, 1998; Frosini, Lazzerini, & Marcelloni, 1998; Gamboa, 2001; Hsu, Tu, & Hwang, 1998; Hwang, 2003; Hwang, Hsiao, & Tseng, 2003; Triantafllou, Pomportsis, & Demetriadis, 2003; Tsai, Tseng, & Lin, 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 fur-ther 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 Q1ÆL! Q2ÆL 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 con-cept 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 fur-ther 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. 2. 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 con-cepts. Thus, a wide variety of different forms of concept maps have been proposed and applied in various domains (Bruillard & Baron, 2000; Gaines & 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 influenced by learning status of other concepts and give learners adaptive learning guidance.
Thus,Appleby et al. (1997)proposed an approach to create the potential links among skills in math domain . The direction of a link is determined by a combination of educational judgment, the relative difficulty of skills, and the relative values of cross-frequencies. Moreover, a harder skill should not be linked forwards to an easier skill. As shown inTable 1, fABrepresents the amount of learners with wrong answers of skill A and right answers of skill B. If fAB > fAB, a skill A could be linked to a harder skill B, but backward link is not permitted.
Hsu et al. (1998)also proposed a conceptual map-based notation, called Concept Effect Rela-tionships (CER), to model the learning effect relaRela-tionships among concepts. In brief, for two con-cepts, Ciand Cj, if Ciis the prerequisite for efficiently learning the more complex and higher level
concept Cj, then a CER Ci! Cjexists. A single concept may have multiple prerequisite concepts,
and can also be a prerequisite concept of multiple concepts. Thus, based upon CER, the learning guidance of necessary concepts to enhance their learning performance can be derived by analyzing the test results of students. Later, based upon statistical prediction and approach of Hsu et al. (1998), a CER Builder was proposed byHwang et al. (2003). Firstly, CER Builder finds the test item that most students failed to answer correctly and then collects the other test items failed to answer by the same students. Thus, CER Builder can use the information to determine the rela-tionships among the test items. Though the CER Builder is easy to understand, only using single rule type is not enough to analyze the prerequisite relationship among concepts of test items, which may decrease the quality of concept map.
Tsai et al. (2001) proposed a Two-Phase Fuzzy Mining and Learning Algorithm. In the first phase, Look Ahead Fuzzy Mining Association Rule Algorithm (LFMAlg) was proposed to find the embedded association rules from the historical learning records of students. In the second phase, the AQR algorithm was applied to find the misconcept map indicating the missing con-cepts during students learning. The obtained misconcept map as recommendation can be fed
Table 1
Relative skills frequency
A is right A is wrong
B is right fAB fAB
back to teachers for remedy learning of students. However, because the creating misconcept map, which is not a complete concept map of a course, only represents the missing learning con-cepts, its usefulness and flexibility are decreased. In addition, their approaches generate many noisy rules and only use single rule type to analyze the prerequisite relationship among learning concepts.
3. 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 assumptions, for each record of learners, each test item has a grade.
As shown inFig. 1, our Concept Map Construction includes two phases: Grade Fuzzy Associ-ation Rule Mining Process Phase and Concept Map Constructing Process Phase. The first phase applies fuzzy theory, education theory, and data mining approach to find four fuzzy grade asso-ciation rule types, L–L, L–H, H–H, H–L, among test items. The second phase further analyzes the mined rules based upon our observation in real learning situation. Even based upon our assump-tions, constructing a correct concept map is still a hard issue. Accordingly, we propose a heuristic algorithm which can help construct the concept map.
3.1. Grade fuzzy association rule mining process
In (Tsai et al., 2001), the Look Ahead Fuzzy Association Rule Miming Algorithm (LFMAlg) has been used to find the associated relationship information embedded in the testing records of learners. In this phase, we propose an anomaly diagnosis process to improve LFMAlg and reduce the input data before the mining process.
3.1.1. Grade fuzzification
Firstly, because the numeric testing data are hard to analyze by association rule mining approach, we apply Fuzzy Set Theory to transform these into symbolic. Thus, after the fuzzifica-tion, the grade on each test item will be labeled as high (H), middle (M), and low (L) degree, which can be used as an objective judgment of learner’s performance.
Table 2
Test item–concept mapping table
A B C D E Q1 0 0 0 1 0 Q2 1 0 1 0 0 Q3 1 0 0 0 0 Q4 0 1 1 0 0 Q5 0 1 0 1 1
3.1.2. Anomaly diagnosis
Based upon Item Analysis for Norm-Referencing of Educational Theory (Popham, 1999), the discrimination of item can tell us how good a test item is, i.e., item with high degree of discrim-ination denotes that the item is well designed. If the discrimdiscrim-ination of the test item is too low (most students get high score or low score), this item as redundant data will have no contribution to construct the concept map. For decreasing the redundancy of test data, we propose a fuzzy item analysis, called Anomaly Diagnosis, to refine the test data.
3.1.3. Fuzzy data mining
Then, we can apply LFMAlg (Tsai et al., 2001) to find the grade fuzzy association rules of test items from the historical testing data. In this paper, we analyze the prerequisite relation-ships among learning concepts of quizzes according to 4 association rule types, L–L, L–H, H–L, H–H, generated from Large 2 Itemset. QiÆL notation denotes that the ith question (Q)
was tagged with low (L) degree, e.g., Q2ÆL! Q3ÆL means that learners get low grade on
Q2 implies that they may also get low grade on Q3.
3.2. Concept map constructing process 3.2.1. Concept map constructor
Firstly, the result of analyzing four association rule types, L–L, L–H, H–H, and H–L, are used to construct the prerequisite relationships between concept sets, which are used to define the edge between nodes of concept set and provide teachers with information for further refining the test sheet, of learning concepts of test items. Then, based on the prerequisite relationships of concept set and the Test item-Concept Mapping Table, we propose a Concept Map Constructing (CMC) Algorithm to find the corresponding learning concepts of concept set to construct the concept map according to the join principles of concept-pair.
4. Grade fuzzy association rule mining process 4.1. Grade fuzzification
As described in Section3.1, we apply fuzzy concept to transform numeric grade data into sym-bolic, 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. QiÆL, QiÆ M, and QiÆH denote the value of LOW fuzzy
function, MIDDLE fuzzy function, and HIGH fuzzy function for the quiz i, respectively. By given membership functions, the fuzzification of testing records is described in Example 1.
Example 1. In Fig. 3, assume there are 10 testing records with 5 quizzes of learners and the highest grade on each quiz is 20.
4.2. Anomaly diagnosis
For refining the input testing data, we propose the anomaly diagnosis, called Fuzzy Item Anal-ysis for Norm-Referencing (FIA-NR) by applying Item AnalAnal-ysis for Norm-Referencing of Edu-cational Theory, shown inFig. 4. A test item will be deleted if it has low discrimination.
Fig. 2. The given membership functions of each quiz’s grade.
Example 2. Table 3shows the fuzzified testing grades of learners on Q4sorted in the descending
order of each learner’s total score in the test sheet. For example, inFig. 3, because the result of fuzzification of learner ID 4 is (0.3, 0.5, 0.0), her/his Grade Level can be tagged with M by the Max(L, M, H) function.
Then, by applying FIA-NR algorithm, we can get the Difficulty and Discrimination of every quiz. For example, the P4H and P4L of Q4 are P4H ¼NR4H
4H¼ HþLþL 3 ¼ 1þ0þ0 3 ¼ 1 3 and P4L ¼ 0 3¼ 0,
respectively. Therefore, its Difficulty P4 and Discrimination D4 are P4 ¼ 1 P4HþP2 4L¼ 1 1=3þ0
2 ¼
5
6¼ 0:83 and 0.33 respectively. Thus, learners’ grade on Q4 will be deleted because its
Discrimination is too low to use during the mining process and the construction of the concept map. Accordingly, the test sheet can be redesigned. All evaluated results are shown inTable 4.
Fig. 4. Fuzzy item analysis for norm-referencing (FIA-NR).
Table 3
Sorted fuzzified testing grade on Q4
Group High Middle Low
Learner ID 1 2 3 4 6 5 7 8 9 10
Total (100) 77 54 53 48 44 36 35 28 26 21
Grade level = Max(L, M, H) H L L M L L L L L L
Table 4
Difficulty and discrimination degree of each quiz
Q1 Q2 Q3 Q4 Q5
Difficulty (0 to 1) 0.25 0.42 0.42 0.83 0.75
4.3. Fuzzy data mining
After filtering out these useless quizzes, we can apply Look Ahead Fuzzy Association Rule Mining Algorithm (Tsai et al., 2001) as shown inFig. 5to find the fuzzy association rules of test items. In LFMAlg Algorithm, the support value of every itemset x in candidate C‘can be evaluated by
the support(x) function, where x = {A, B}˝ C‘1, A\ B = /. Then, the support(x) = support
ðA [ BÞ ¼Pn1 MinðA; BÞ, where n is the number of learners. For example, inFig. 3, support(Q1ÆL,
Q3ÆH) = Min(1.0, 0.7) + Min(1.0, 0.7) = 1.4.
Fig. 5. Look ahead Fuzzy Association Rule Mining Algorithm (LFMAlg).
Example 3. For the data shown in Examples 1 and 2, Fig. 6 shows the process of finding the association rules with large 2 itemset by LFMAlg algorithm.
Thus,Table 5shows the grade fuzzy association rules with minimum confidence 0.8 generated from large 2 itemset into L–L, L–H, H–H, and H–L types. The Confi(Confidence) is used to
indi-cate the important degree of ith mined association rule. For example, the Confidence (Conf1) of
rule Q2ÆL! Q3ÆL can be obtained as follows.
Q2 L ! Q3 L : Confidence ¼
supportðQ2 L [ Q3 LÞ
supportðQ2 LÞ ¼ 0:95
5. Concept map constructing process 5.1. 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. There-fore, we can conclude the Heuristic 1: given two quizzes Q1and Q2, if concepts of Q1are the
pre-requisite of concepts of Q2, Learner gets low grade on Q1implies that s/he may also get low grade
on Q2 or Learner gets high grade on Q2 implies that her/his grade on Q1 is high. As shown in
Table 6, for each rule type, we use Heuristic 1 to get its prerequisite relationships among concept
Table 5
The mining results (Confi> 0.8)
Rule types Mined rules Confi
L–L Q2 Æ L! Q3 Æ L 0.95 Q3 Æ L! Q2 Æ L 1.00 Q2 Æ L! Q5 Æ L 0.86 Q3 Æ L! Q5 Æ L 0.90 L–H Q1 Æ L! Q5 Æ H 0.90 Q5 Æ L! Q1 Æ H 0.82 H–H Q2 Æ H! Q3 Æ H 0.91 H–L Q5 Æ H! Q1 Æ L 1.00 Table 6
Prerequisite relationship of association rule
Rule Wi Prerequisite relationship
QiÆL! QjÆL 1.0 CSQi! pre. CSQj QiÆL! QjÆH 0.8 CSQj! pre. CSQi QiÆH! QjÆH 1.0 CSQj! pre. CSQi QiÆH! QjÆL 0.8 CSQi! pre. CSQj
sets of quizzes with parameterized possibility weight, which are used to construct the concept map. The definition of the symbols used in Table 6is described as follows.
Symbol definition:
CSQi indicate concept set of quiz i
Wi indicate the possibility of the possible scenario of the rule
In this paper, association rules generated from Large 2 Itemset are firstly used to analyze the prerequisite relationships between learning concepts of quizzes. Therefore, by looking up Table 6, we can obtain the prerequisite relationships of concept set of quizzes with the possibility weight (Wi) for each mined rule inTable 5. The possibility Wiis a heuristic parameter of CMC algorithm
because it can be modified according to different domains and learners’ background. Moreover, the related explanations of the analysis inTable 6are shown inTable 7.Table 8shows the result of transforming association rules inTable 5by analyzing the prerequisite relationships inTable 6. For example, in Fig. 7, the mined rules, Q1 Æ L! Q2 Æ H and Q1 Æ H ! Q2 Æ L, can be trans-formed into corresponding prerequisite relationship of concept set, resulting in a confused relation as a cycle between concept sets, called circularity. That is to say, concepts of Q1and concepts of
Q2are prerequisite of each other, which is a conflict in our analysis. Therefore, during creating the
concept map, we have to detect whether a cycle exists or not, e.g., CSQ1! CSQ2! CSQ1.
Because each concept set may contain one or more learning concepts, we further define a prin-ciple of joining two concept sets and then generate corresponding concept-pair, (Ci, Cj), that is, if
CSQ1¼ f[n1aig and CSQ2¼ f[m1bjg, the set of concept-pair is CSQ1 JOIN CSQ2¼ f[k1ðai; bjÞg, Table 7
The explanations of rule types
Rule Description of learning scenario
L! L If the association rule QiÆL! QjÆL is mined, it means that the CSQiis the prerequisite of CSQj,
represented as CSQi! pre.
CSQj. That is why getting low grade on Qimight imply getting low grade on Qj.
H! H If the association rule QiÆH! QjÆH is mined, it means that the CSQiis the prerequisite of CSQj.
L! H If the association rule QiÆL! QjÆH is mined, it means that the CSQjis the prerequisite of CSQibecause
CSQimay be not learned well resulting from CSQj.
H! L If the association rule QiÆH! QjÆL is mined, it means that the CSQiis the prerequisite of CSQj.
Table 8
Result by analyzing the prerequisite relationships inTable 6
Rule type Association rules of quiz Prerequisite relationship of concept set Confi Wi
L–L Q2 Æ L! Q3 Æ L CSQ2! pre. CSQ3 0.95 1.0 Q3 Æ L! Q2 Æ L CSQ3! pre. CSQ2 1.00 1.0 Q2 Æ L! Q5 Æ L CSQ2! pre. CSQ5 0.86 1.0 Q3 Æ L! Q5 Æ L CSQ3! pre. CSQ5 0.90 1.0 L–H Q1 Æ L! Q5 Æ H CSQ5! pre. CSQ1 0.90 0.8 Q5 Æ L! Q1 Æ H CSQ1! pre. CSQ5 0.82 0.8 H–H Q2 Æ H! Q3 Æ H CSQ2! pre. CSQ3 0.91 1.0 H–L Q5 Æ H! Q1 Æ L CSQ5! pre. CSQ1 1.00 0.8
where ai6¼ bj and k 5 n· m. For example, if CSQ1= {a1, a2} and CSQ2= {b1, b2}, CSQ1 JOIN
CSQ2= {(a1, b1), (a1, b2), (a2, b1)}, where a2= b2is deleted. The related definition used in creating
the concept map is given as follows: Concept Map CM = (V, E), where V = {Cij the node is unique for each i}
E ¼ fC!iCjj i 6¼ jg
The node, Ci, denotes the learning concept and the edge, C!iCj, which connects Ci and Cj,
denotes that Ciis the prerequisite of Cj. The C!iCjhas an Influence Weight, IWk, denotes the degree
Fig. 8. Concept Map Constructing (CMC) Algorithm. Fig. 7. The transforming of association rules.
of relationship between learning concepts. The formulation of IWk is ((k 1) · IWk1+ Wk·
Confk)/k, 1 6 k 6 n, where n is the amount of C!iCj.
The proposed Concept Map Constructing (CMC) algorithm is shown inFig. 8.
For the CMC algorithm shown in Fig. 8, the main purpose of Cycle Detection Process is to detect the unreasonable prerequisite relationship as a cycle among concept sets. It should be noted that the prerequisite relationship in the concept set map also fulfills the indicator f12 > f12inTable
9, which is an extension ofAppleby et al. (1997)after cycle detection. The indicator denotes that if concepts of Q1 are prerequisite of concepts of Q2, it is reasonable that f12 > f12, where
f12¼ CountðQ1 H \ Q2 LÞ and f12¼ CountðQ1 L \ Q2 HÞ. In addition, the Influence Weight,
IWk, denotes the degree how the learning status of concept Ci influences Cj. Therefore, the
num-ber of C!iCjwill enhance the value of Influence Weight. In the formulation of influence weight, the
Widenotes the possibility of the learning scenario of the association rule in our analysis. Thus, the
educational experts can assign different value of Wi to the algorithm according to different
domains and learner’s backgrounds.
For the association rules given inTable 8, the process of CMC algorithm is shown inFig. 9. In
Fig. 9b, the edges drawn as dash line have the lowest confidences in cycles will be deleted in Cycle
Table 9
Relative quizzes frequency
(Q1) Higher (Q1) Lower
(Q2) Higher f12 f12
(Q2) Lower f12 f12
Detection Process. Moreover,Table 10shows the example of computing the Influence Weight of Concept-Pair (B, E) inFig. 9f. Because the Concept-Pair (B, E) has two edges between CSQ5and
CSQ1, we have to compute the Influence Weight twice.
6. Evaluating the redundancy and circularity of concept map
In this paper, creating a concept map without Redundancy and Circularity is our concern. As shown inFig. 10, we create three concept maps by using different approaches and evaluate their
Table 10
The result of computing the influence weight of concept-pair (B, D) inFig. 9f
Rule Prerequisite relationship Confi Wi IWi
Q1ÆL! Q5ÆH CSQ5! CSQ1 0.90 0.8 W1· Conf1= 0.9 * 0.80@0.72 Q5ÆH! Q1ÆL CSQ5! CSQ1 1.00 0.8 ð21ÞIW1þW2Conf2 n ¼ ð1Þ0:72þð0:8Þ1:00 2 ffi 0:76
Fig. 10. The (a) and (b) created based upon analyzing L–L rule type only. The (c) and (d) are created based upon Anomaly Diagnosis and analyzing L–L rule type only. The (e) and (f) created by our approach.
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 pre-requisite relationship between concept sets in Fig. 10a is created based upon analyzing L–L rule type only, andFig. 10c is created based upon analyzing L–L rule type and anomaly diagnosis we proposed. Then, the concept maps asFig. 10b and d are transformed according to the Test Item– Concept Mapping Table. Fig. 10e and f are created by our proposed approach.
Based upon these results of different approaches, the characteristics of approach are concluded as follows.
Non-redundancy: the anomaly diagnosis can filter many useless test items with low discrimina-tion for refining the input data. For example, inFig. 10a, the Q4with low discrimination results
in generating many co-prerequisite links as a cycle in Fig. 10b.
Non-circularity: the cycle detection process can delete these cycles, e.g., the cycle between A and C inFig. 10d, to make the concept map un-ambiguous. Moreover, analyzing association rule with L–L, L–H, H–L, and H–H types can refine the concept map, e.g., the edges ED!and BD! connect the node D only in Fig. 10f.
7. The experiment of TP-CMC in physics course
In this section, we describe our experiment results of the Two-Phase Concept Map Construc-tion (TP-CMC) approach.
7.1. Experimental results
The participants of experiment are the 104 students of junior high school in Taiwan and the domain of examination is the Physics course. The related statistics of testing results and related concepts of testing paper are shown in Tables 11 and12.
The prototype system of TP-CMC is developed based on PHP4 web language, MySQL data-base, and JGraph web graphic tool (JGraph, 2004). As shown inFig. 11a–c, the concept maps with Discrimination 0.0 and 0.3, and 0.5 are created by TP-CMC approach respectively. As mentioned in Section4.2, Anomaly Diagnosis process in TP-CMC can refine the test data for decreasing its redundancy. As we see, the concept maps with low discrimination criteria inFig. 11a and b shows
Table 11
The related statistics of testing results in physics course
Subject Information
Educational degree Junior high school
The number of students 104
Average score of exam 61.06
Standard deviation of scores 18.2
The number of test items 50
that the prerequisite relationships between learning concepts are very disordered and confused. However, with increasing the value of discrimination, the test data can be refined such that the clarity of concept map can be heightened, shown in Fig. 11c. Moreover, the created concept
Table 12
Concepts list of testing paper in physics course
Concept ID Learning concept
1 Tools and theories for timing
2 Unit of time
3 Isochronism of pendulum
4 Change of position
5 Movements
6 Speed and direction of motion
7 Average and instant speed
8 X–t diagram
9 Change of speed and direction
10 Acceleration
11 Uniform acceleration
12 Free fall
13 V–t diagram
14 The resultant of forces
15 Balance of forces
16 Torque
17 Balance of rotation
Fig. 11. The concept maps (a)–(c) with Discrimination 0.0, 0.3, and 0.5 are created by TP-CMC approach respectively (support = 50, confidence = 0.85).
map can provide the embedded learning information of students during learning Physics. For example, the relationship of concept-pair (6, 9) inFig. 11c represents that if students do not learn concept 6 (Speed and direction of motion) well, their learning performance of concept 9 (Change of speed and direction) are most likely bad. Therefore, teachers can modify their teaching strategies to enhance students’ learning performance of concept 6 for getting high performance of concept 9.
8. Conclusion
The concept map is often used to provide teachers for further analyzing and refining the teach-ing strategies and to generate adaptive learnteach-ing guidance in adaptive learnteach-ing environment. How-ever, 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 automati-cally construct a concept map of a course by learners’ historical testing records. Phase 1 is used to preprocess the testing records and Phase 2 is used to transform the mined association rules into prerequisite relationships between learning concepts for creating concept map. Thus, in Phase 1, we 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 Min-ing approach to find its grade fuzzy association rules. In Phase 2, based upon our observation in real learning situation, we use multiple rule types to further analyze the mined association rules and then propose a heuristic algorithm to automatically construct the concept map without Redundancy and Circularity according to analysis results. Thus, the created concept map which can be used to develop adaptive learning system and refine the learning strategies of learners. 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. In the near future, we will analyze the effect of rules with large-3 itemset for improving the concept map, enhance the TP-CMC system with scalability and flexibil-ity for providing the web service, and do some experiments based upon real learning testing records, too.
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.
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