概念圖建構方法之研究

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(1)國立交通大學資訊科學系碩士論文. 概念圖建構方法之研究 A New Approach for Constructing the Concept Map. 研究生：蘇培綺指導教授：曾憲雄博士. 中華民國九十三年六月.

(2) 概念圖建構方法之研究 A New Approach for Constructing the Concept Map. 研究生：蘇培綺. Student：Pei-Chi Sue. 指導教授：曾憲雄. Advisor：Shian-Shyong Tseng. 國立交通大學資訊科學研究所碩士論文. A Thesis Submitted to Institute of Computer and Information Science College of Electrical Engineering and Computer Science National Chiao Tung University in partial Fulfillment of the Requirements for the Degree of Master in Computer and Information Science June 2004 Hsinchu, Taiwan, Republic of China. 中華民國九十三年六月.

(3) 概念圖建構之研究. 研究生: 蘇培綺. 指導教授: 曾憲雄博士. 國立交通大學資訊科學系. 摘要. 隨著網路學習(e-Learning)的蓬勃與發展，如何在「適性化」理念下發展出智慧型網路學習系統，並依照不同學習能力與背景的學習者來提供適性化的學習路徑已是當今網路學習不可忽視的重要課題。為了更容易達到適性化教學的目的，大部分的網路學習系統會將學生的學習成績加以分析，並依據事先建構好的「課程概念圖」來調整適合學生的學習路徑。然而，雖然概念圖在適性化的網路學習相關策略設計上非常有用，可是，每當學習一新課程，教育設計者或是相關領域專家就必須進行一段冗長、費時且艱鉅的知識擷取過程才能將此概念圖建立起來。. 為了解決這個問題，本文研究提出了「二階段概念圖建構法」，希望達到自動化建立概念圖的目的。在第一階段裡，結合了泛析理論、教育理論、資料探勘等相關技術，藉此找出學生成績間的相關法則 ;在第二階段裡，深入分析成績相關法則所代表的意義，並判斷試題所包含概念之間的先備關係及其可能的相對應的情境解釋。最後，根據之前所做的相關分析，量身訂作了一個「概念圖建構演算法」，藉由此演算法來自動建構出課程概念圖，以利教師或專家進一步分析及應用。. i.

(4) A New Approach for Constructing the Concept Map. Student: Pei-Chi Sue. Advisor: Dr. Shian-Shyong Tseng. Department of Computer and Information Science National Chiao Tung University. Abstract. In recent years, e-learning system has become 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 thesis, 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.. ii.

(5) Therefore, in Phase 1, we apply Fuzzy Set Theory to transform the numeric testing records of learners into symbolic form, 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 feasible.. iii.

(6) 誌謝. 能夠順利完成這篇論文，首先要感謝的是我的指導教授，曾憲雄博士。曾老師兩年來不論是專業上的知識或是領導處事的技巧，都讓我獲益良多。尤其是在二年級時不斷的給予我鼓勵及耐心的指導，讓我可以在畢業前將論文投至國際會議上發表，深表感激。同時也非常感謝我的論文口試委員，孫春在教授，楊錦潭教授及黃國禎教授，他們給予了我許多寶貴的建議。. 接下來要感謝實驗室各位學長，尤其是蘇俊銘學長和翁瑞鋒學長。他們給予我這個題目最初的靈感及想法，並且接受我隨時隨地的詢問及討論，在論文的的修改上給予了我很大的協助，而在課業與待人處世上，也讓我受益匪淺，在此深表感激。另外，也非常感謝同窗伙伴們互相幫助鼓勵的情誼，以及學弟妹們在友情上的支持，讓忙碌的碩士班兩年生涯，能夠愉快而充實的度過。. 最重要的，還要感謝我的家人長久以來對我的支持與照顧，在我成長及求學的過程中陪伴我一路走來，是鼓勵我努力向前的最大力量。. 最後要感謝的是現在正在閱讀我的論文的您。希望這篇論文能對您有所幫助。有任何問題或建議也都歡迎與我討論，感激不盡。. iv.

(7) Table of Contents. 摘要.............................................................................................................................................................................i Abstract......................................................................................................................................................................ii 誌謝...........................................................................................................................................................................iv Table of Contents......................................................................................................................................................v List of Figures..........................................................................................................................................................vii List of Tables ..........................................................................................................................................................viii Chapter 1. Introduction.............................................................................................................................................1 Chapter 2. Related Work..........................................................................................................................................4 2.1 Concept Map .....................................................................................................................................................................4 2.2 Uses of Concept Map in Education................................................................................................................................6 2.3 Construction of Concept Map.........................................................................................................................................6. Chapter 3. Two Phase Concept Map Construction (TP-CMC) .......................................................................10 3.1 Grade Fuzzy Association Rule Mining Process .........................................................................................................11 3.2 Concept Map Constructing Process ............................................................................................................................ 13. Chapter 4. Grade Fuzzy Association Rule Mining Process ..............................................................................15 4.1 Grade Fuzzification........................................................................................................................................................ 15 4.2 Anomaly Diagnosis ....................................................................................................................................................... 16 4.3 Fuzzy Data Mining........................................................................................................................................................ 19. Chapter 5. Concept Map Constructing Process..................................................................................................22 5.1 Association Rules Analyzer.......................................................................................................................................... 22 5.2 Concept Map Constructor............................................................................................................................................. 28. Chapter 6. Evaluating the Redundancy and Circularity of Concept Map.......................................................33 Chapter 7. The Implementation of TP-CMC......................................................................................................35 7.1 Construction of Related Database..............................................................................................................35 7.2 Construction of Concept Maps ..................................................................................................................37 Chapter 8. The Experiment of TP-CMC .............................................................................................................40. v.

(8) 8.1 Experimental Results in Physics Course..................................................................................................................... 40. Chapter 9. Conclusion and Future Work..............................................................................................................44 Reference.................................................................................................................................................................46. vi.

(9) List of Figures. Figure 1. An example of concept map ...................................................................................................................5 Figure 2. The Flowchart of Two Phase Concept Map Construction (TP-CMC)...........................................11 Figure 3. The Given Membership Functions of Each Quiz’s Grade ...............................................................15 Figure 4. The Fuzzification of Learners’ Testing Records.................................................................................16 Figure 5. Fuzzy Item Analysis for Norm-Referencing (FIA-NR)....................................................................17 Figure 6. Look ahead Fuzzy Association Rule Mining Algorithm (LFMAlg)..............................................20 Figure 7. Mining Process of LFMAlg algorithm................................................................................................21 Figure 8. The Transforming of Association Rules..............................................................................................28 Figure 9. Concept Map Constructing (CMC) Algorithm..................................................................................30 Figure 10. The Process of Concept Map Constructing Algorithm...................................................................31 Figure 11. The (a) and (b) created based up analyzing L-L rule type only. The (c) and (d) are created based upon Anomaly Diagnosis and analyzing of L-L rule type. The (e) and (f) created by our approach (only large 2 itemset)..............................................................................................................................................33 Figure 12. The process of constructing Test Item-Concept Mapping Database and Historical Testing Records Database ...................................................................................................................................................36 Figure 13. The process of constructing the concept map...................................................................................37 Figure 14. The concept maps (a) and (b) are created with Scenario 1 and 2 of Heuristic 1 by TP-CMC approach respectively. (Discrimination 0.5, Support=50, Confidence=0.85).................................................39 Figure 15. Association Rules Generated from Large 3 itemset (Discrimination 0.5, Support=50, Confidence=0.85)...................................................................................................................................................39 Figure 16. The concept maps (a), (b), and (c) with Discrimination 0.0, 0.3, and 0.5 are created by TP-CMC approach respectively. (Support=50, Confidence=0.85)..................................................................42 Figure 17. The comparison of percentage of rules found and concepts involved ..........................................43. vii.

(10) List of Tables. Table 1. Relative Skills Frequency .........................................................................................................................8 Table 2. Test Item–Concept Mapping Table........................................................................................................10 Table 3. Sorted Fuzzified Testing Grade on Q4 ...................................................................................................17 Table 4. Difficulty and Discrimination Degree of Each Quiz...........................................................................18 Table 5. The Mining Results (Confi > 0.8)..........................................................................................................21 Table 6. Prerequisite Relationship of Association Rule......................................................................................24 Table 7. The Explanations of Rule Type..............................................................................................................24 Table 8. Result by Analyzing the Prerequisite Relationships in Table 6..........................................................25 Table 9. Prerequisite Relationships of Association Rule....................................................................................26 Table 10. Association Rules generated from Large n (>= 3) Itemset (Confidence > 0.8).............................27 Table 11. The Computing of the Influence Weight for Concept-Pair (B, D) in Figure 10.f..........................32 Table 12. The Related Statistics of Testing Results in Physics Course.............................................................40 Table 13. Concepts List of Testing Paper in Physics Course.............................................................................41. viii.

(11) Chapter 1. Introduction. With the vigorous development of computer and WWW technology, computer and web based learning environments are becoming mainstream area of research and development. There are three main paradigms in computer based tutoring systems [15]: Computer Assisted Instruction (CAI) systems, hypermedia systems, and Intelligent Tutoring Systems (ITS).. Computer Assisted Instruction (CAI) systems are usually based on a fixed presentation of didactic material and do not support adaptive tutoring for each individual student. The learning path through the learning material is linear and predefined in the design stage.. Hypermedia systems provide user-driven exploration of the teaching material, where the user has full control over the learning process. However, this is also their drawback, because Hypermedia systems lack expert guidance in the instructional sequence and therefore it is difficult for users to find information and get an overview of the material. Finally, the users may lose focuses on their educational goals.. Intelligent tutoring systems (ITS) are system-driven learning systems, which were developed to adapt the learning speed and level of material for each individual student. The definition of an ITS is based on some kind of knowledge. This "knowledge" includes: (1) domain knowledge containing objects, relations among them, explanations, examples and exercises, (2) teachers’ knowledge as a strategy for the. 1.

(12) process of learning and teaching and (3) students’ knowledge as a model which is dynamically generated as a result of overlaying it with teachers’ knowledge.. In. recent. years,. many. intelligent. adaptive. learning. and. testing. systems. [3][6][7][9][10][12][14][19][20][23] have been proposed to offer learners customized courses in accordance with their aptitudes and learning results. For achieving the adaptive learning, in many learning environments [3][6][9][10][14][23], a predefined concept map of a course, as domain knowledge in ITS, which provides teachers for further analyzing and refining the teaching strategies, is often used to generate adaptive learning guidance for learners.. Though concept map as a navigation tool in adaptive learning system is widespread, 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 thesis, we propose a Two-Phase Concept Map Construction (TP-CMC) algorithm to automatically construct a concept map of a course by 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 form input data, and Phase 2 is used to transform the mined association rules into prerequisite relationships between learning concepts for creating concept map. Therefore, in. 2.

(13) the first phase, we apply Fuzzy Set Theory to transform the numeric testing records of learners into symbolic form, 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 [12][23]. 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 thesis are to: (1) Apply Fuzzy Set Theory to transform the numeric testing records of learners into symbolic form, 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.. 3.

(14) Chapter 2. Related Work. 2.1 Concept Map. Concept map, developed by Novak [16] in 1984, is a technique for organizing or representing knowledge as networks. Networks consist of nodes (points/vertices) and links (arcs/edges). Nodes represent concepts and links represent the relations among concepts. Links can be non-, uni- or bi-directional. According to Jonassen et al. [7], concept maps are “representations of concepts and their interrelationships that are intended to represent the knowledge structures that humans store in their minds”.. Concept map has been widely applied in the evaluation of students’ learning in the school system, policy studies, and the philosophy of science to provide a visual representation of knowledge structures. In many disciplines various forms of concept map are already used as formal knowledge representation systems, for example: semantic networks in artificial intelligence, bond graphs in mechanical and electrical engineering, CPM and PERT charts in operations research, Petri nets in communications, and category graphs in mathematics.. An example of a concept map is shown in Figure 1. In this example, each node is a learning concept, and each uni-directional link denotes relationship “prerequisite of “.. 4.

(15) Figure 1. An example of concept map. Concept maps are very useful in that they can be considered from different points of views and a wide variety of different forms of concept map have been defined and applied in various domains and can be done for several purposes [4][10][20]. The functions of concept map are shown as follows.. (1) Knowledge representation (to design a complex structure, etc.) (2) Knowledge acquisition/communication (to communicate complex ideas, etc.) (3) Meaningful learning for education (to help brain storming in mapping process, etc.) (4) Navigation tools in adaptive learning system (to find learning paths by assessment and diagnosis for understanding of learning concept). 5.

(16) 2.2 Uses of Concept Maps as Navigational Tools in Education. As described in Section 2.1, the concept map has many potential roles in education on hypermedia learning. They can be used to help designers in designing hypermedia or, as navigational tools, for helping learners to find an appropriate learning path. After the test results of students were analyzed based on concept maps, the students were given guidance on concepts needing improvement to enhance their learning performance. To model the learning effect relationships among concepts, a conceptual map-based notation, Concept Effect Relationships (CER), is proposed by Hsu [14]. Consider two concepts, Ci and Cj, if Ci is prerequisite to the more complex and higher level concept Cj, then a concept effect relationship Ci Æ Cj exists. A single concept may have multiple prerequisite concepts and can also be a prerequisite concept of multiple concepts. In the computer-assisted instructional environment [3][4][6][9][10][14][23], for achieving the adaptability of learning, the predefined CER-like concept map of the course is often 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 to improve their learning performances.. 2.3 Construction of Concept Map. Since the use of concept map as education tools in the hypermedia is widespread, the eliciting of concept maps from domain expert or experienced teachers becomes very important. However, the job for. 6.

(17) constructing the concept maps is still hard and very time consuming.. Therefore, due to the usefulness of the concept map, many approaches are proposed to construct the concept map. The construction of concept maps can be generally classified into manual [2], semi-automatic [21] and nearly automatic [13][17] three categories. In semi-automatic or nearly automatic construction of concept maps, the technique of extracting predicates from a text file or dialog using syntactic and discourse knowledge is often used. Moreover, the browsing behavior and testing records of learners can even be analyzed to construct the concept map.. The following approaches proposed to construct prerequisite relationships among learning concepts of the concept maps are built by analyzing the testing records of students.. Appleby, et al. [3] 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 in Table 1, f. AB. represents the amount of learners with wrong. answers of skill A and right answers of skill B. If f AB >> f AB , a skill A could be linked to a harder skill B, but backward link is not permitted. 7.

(18) Table 1. Relative Skills Frequency A is right A is wrong B is right. f. AB. f. AB. B is wrong. f. AB. f. AB. Later, based upon statistical prediction and approach of Hsu, et al. [14], a CER Builder was proposed by Hwang [12]. Firstly, CER Builder finds the test item that most students failed to answer correctly and then collects the other test items which were failed to answer by the same students. Thus, CER Builder can use the information to determine the relationships among the test items. Though the CER Builder is easy to understand, only using single rule type is not enough to analyze the prerequisite relationships among concepts of test items, which may decrease the quality of concept map.. Tsai, et al. [23] 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 is applied to find the misconcept map indicating the missing concepts during students learning. The obtained misconcept map as recommendation can be fed 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 concepts, 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.. 8.

(19) Thus, in this thesis, we propose a Two Phase Concept Map Construction (TP-CMC) to construct the complete concept map with influence weights among learning concepts of a course. For improving [23], we apply anomaly diagnosis process to reduce the noise rules and then we take multiple rule types into account to further analyze the mined rules for refining the quality of concept map. Therefore, according to the analysis results, we propose an algorithm to automatically construct the concept map of a course.. 9.

(20) Chapter 3. Two Phase Concept Map Construction (TP-CMC). As mentioned above, the concept map of a course is quite useful. However, the construction is time consuming. Therefore, in this thesis, we propose an approach to automatically construct the concept map as a directional graph with influence weights among learning concepts of a course.. 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.. 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. As shown in Figure 2, our Concept Map Construction includes two phases: Grade Fuzzy Association Rule Mining Process Phase and Concept Map Constructing Process Phase. The first. 10.

(21) phase applies fuzzy theory, education theory, and data mining approach to find four fuzzy grade association 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 assumptions, constructing a correct concept map is still a hard issue. Accordingly, we propose a heuristic algorithm which can help construct the concept map.. Historical Testing Records Database. Test Item-Concept Mapping Database Mined Association Rules L-L Rule Type. Grade Fuzzification. Anomaly Diagnosis. Fuzzy Data Mining. L-H Rule Type H-L Rule Type. Concept Map Association Rule Analyzer. Concept Map Constructor. A. E C. D B. H-H Rule Type Phase 1: Grade Association Rule Mining Process. Dicussion. Phase 2: Concept Map Constructing Process. Educational Experts. Figure 2. The Flowchart of Two Phase Concept Map Construction (TP-CMC). 3.1 Grade Fuzzy Association Rule Mining Process. In [23], the Look Ahead Fuzzy Association Rule Miming Algorithm (LFMAlg) can be used to find the associated relationship information embedded in the testing records of learners. In the first phase, we propose an anomaly diagnosis process, a preprocessing, to improve LFMAlg and reduce the input data before the mining process.. 11.

(22) In the following, three steps of Phase 1 shown in Figure 2 will be briefly described.. (1) Grade Fuzzification Firstly, we apply Fuzzy Set Theory to transform these numeric testing data into symbolic form. Thus, after the fuzzification, 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. Then, the association mining approach can be used to find the association rule among these testing items.. (2) Anomaly Diagnosis Based upon Item Analysis for Norm-Referencing of Educational Theory [1][17], the discrimination of item can tell us how good a test item is, i.e., item with high degree of discrimination denotes that the item is well designed. If the discrimination 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 using difficulty and discrimination of test item, called Anomaly Diagnosis, to refine the test data.. (3) Fuzzy Data Mining Then, we apply LFMAlg [23] to find the grade fuzzy association rules of quizzes from the historical testing data. In this thesis, we analyze the prerequisite relationships among learning concepts of. 12.

(23) quizzes according to 4 association rule types, L-L, L-H, H-L, H-H. We use Qi.L notation to denote that the ith question (Q) was tagged with low (L) degree, e.g., Q2.L→Q3.L means that learners get low grade on Q2 implies that they may also get low grade on Q3.. 3.2 Concept Map Constructing Process. In the second phase, based upon the heuristic of our observation in real learning situation, we further analyze the mined rules. According to the analysis result, we propose a heuristic algorithm to construct the concept map of a course.. In the following, the process of Phase 2 shown in Figure 2 will be briefly described.. (1) Association Rule Analyzer Firstly, we analyze the four association rule types, L-L, L-H, H-H, and H-L, to generate related prerequisite relationships among concept sets of test item based on our observation in real learning situation. The result of analysis is used to define the edge between nodes of concept set and provide teachers with the possible learning scenario of students for further refining the test sheet.. 13.

(24) (2) Concept Map Constructor Then, based on the prerequisite relationships of concept sets described above 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 mapping.. 14.

(25) Chapter 4. Grade Fuzzy Association Rule Mining Process. 4.1 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 Figure 3. In the fuzzification result, “Low”, “Mid” and “High” denotes “Low Grade”, “Middle Grade” and “High Grade” respectively. Qi.L denotes the value of LOW fuzzy function, Qi.M denotes the value of MIDDLE fuzzy function i, and Qi.H denotes the value of HIGH fuzzy function for the quiz i. By given membership functions, the fuzzification of testing records is described in Example 1.. Degree 1. LOW. MIDDLE. HIGH. 0.7. 0 10%. 20%. 40%. 60%. 70%. Figure 3. The Given Membership Functions of Each Quiz’s Grade Example 1: In Figure 4, assume there are 10 testing records with 5 quizzes of learners and the highest grade on each quiz is 20.. 15.

(26) Fuzzification. Figure 4. The Fuzzification of Learners’ Testing Records. 4.2 Anomaly Diagnosis. For refining the input testing data, we propose the anomaly diagnosis, called Fuzzy Item Analysis for Norm-Referencing (FIA-NR) by applying Item Analysis for Norm-Referencing of Educational Theory, shown in Figure 5. By the anomaly diagnosis process, a test item will be deleted if it has low discrimination.. 16.

(27) Algorithm: Fuzzy Item Analysis for Norm-Referencing (FIA-NR) Symbol Definition: RiH /RiL: The sum of the fuzzy grades ( H=1, M = 0.5, L=0 ) on test item i of each student in the high(H)/Low(L) group. NiH /NiL:The number of learners in high/low group. PiH & PiL:The ratios of RiH to NiH and of RiL to NiL , respectively. Input : Fuzzified testing records of learners Output : The Difficulty index (Pi ) and the Discrimination index (Di) of each test item Step1: Sort Scores in descending order and divide it into High, Middle, and Low groups, each has 1/3 learners. Step2: Let. P iH. Step3: Compute. =. R i H and P iL N iH. Pi = 1 −. =. R iL . N iL. PiH + PiL and D = P − P , for i=1,…, k. i iH iL 2. Step 4: Delete the test items with low Discrimination (<0.5). Figure 5. Fuzzy Item Analysis for Norm-Referencing (FIA-NR) Example 2: Table 3 shows the fuzzified testing grades of learners on Q4 sorted in the descending order of each learner's total score in the test sheet. For example, in Figure 4, 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.. 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. 17.

(28) 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. P. 4H. =. R N. 4H. =. 4H. Therefore, its Difficulty P4 and Discrimination D4 are. H + L + L 1+ 0 + 0 1 = = 3 3 3. P. 4. = 1−. P. 4H. + 2. P. 4L. = 1−. and. P. 1/ 3 + 0 5 = = 0.83 2 6. 4L. =. 0 = 0 3. .. 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 in Table 4.. 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. Discrimination (-1 to 1 ). 0.5 0.83 0.83 0.33 0.5. 18.

(29) 4.3 Fuzzy Data Mining. After filtering out these useless quizzes, we can apply Look Ahead Fuzzy Association Rule Mining Algorithm [23] as shown in Figure 6 to 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. n , A∩B= φ . Then, the support(x) = support(A∪B) = ∑1 Min(A, B),. where n is the number of learners. For example, in Figure 4, support(Q1.L, Q3.H) = Min(1.0, 0.7) + Min(1.0, 0.7) = 1.4.. 19.

(30) Algorithm: LFMAlg Algorithm Symbol Definition:. α : The minimum support threshold in the C : The. -Candidate itemset.. L : The. -large itemset. -large itemset.. λ: The minimum confidence threshold. Input: The test records of learners after Fuzzification and Anomaly Diagnosis. The minimum support threshold α 1 and λ. Output : The fuzzy association rules of test records of learners.. Step1: Repeatedly execute this step until C = NULL. 1.1: Generate and insert the 1.2: α. = max(. α. −1. 2. , α −1 −. -itemset into C α. −1. ( − 1) × c. 1.3: L = { x | support(x) ≥ α ,. ) , where. for. >1 and c is constant.. x∈C. }. 1.4: = +1 Step2: Generate the association rules according to the given λ in L . Figure 6. Look ahead Fuzzy Association Rule Mining Algorithm (LFMAlg) ). Example 3: For the data shown in Examples 1 and 2, Figure 7 shows the process of finding the association rules by LFMAlg algorithm.. 20.

(31) Figure 7. Mining Process of LFMAlg algorithm. Thus, Table 5 shows 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 indicate the important degree of ith mined association rule. For example, the Confidence (Conf1) of rule Q2.L→Q3.L can be obtained as follows. Q 2 . L → Q 3 .L : Confidence =. suuport (Q 2 . L ∩ Q 3. L) suuport (Q 2 . L). Table 5. The Mining Results (Confi > 0.8) Large 2 Itemset Rule Types. Mined Rules. Confi. Q2.LÆQ3.L. 0.95. Q3.LÆQ2.L. 1.00. Q2.LÆQ5.L. 0.86. Q3.LÆQ5.L. 0.90. Q1.LÆQ5.H. 0.90. Q5.LÆQ1.H. 0.82. H-H. Q2.HÆQ3.H. 0.91. H-L. Q5.HÆQ1.L. 1.00. L-L. L-H. 21. = 0.95.

(32) Chapter 5. Concept Map Constructing Process. In Phase 2, the rules mined in Phase 1 will be analyzed based upon the heuristics of our observation in real learning situation. Accordingly, we propose a heuristic algorithm to automatically construct the concept map of a course. The Concept Map Constructing Process shown in Figure 2 is described as follows.. 5.1 Association Rules Analyzer. (1) Analysis of association rules generated from Large 2 Itemset. 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 as follows.. Heuristic 1 : Given two quizzes Q1 and Q2, if concepts of Q1 are prerequisite of concepts of Q2, we summarize the possible learning scenarios of students as follows.. 22.

(33) z Illustrations of rule Q1.LÆQ2.L Scenario 1) Learners get low grade on Q1 implies that they must get low grade on Q2. Scenario 2) Learners get low grade on Q2 implies that their grade on Q1 might be bad. z Illustrations of rule Q1.HÆQ2.H Scenario 3) Learners get high grade on Q1 implies that they may also get high grade on Q2 Scenario 4) Learners get high grade on Q2 implies that they must get high grade on Q1. z llustrations of rule ( Q1.HÆQ2.L or Q2.LÆQ1.H) Scenario 5) Learners get higher grade on Q1 (an easier quiz) but get lower grade on Q2 (a harder quiz).. As shown in Table 6, for convenience to explain the following process in this thesis, we adopt Scenario 1, 4, and 5 of Heuristic 1 to get prerequisite relationships among concept sets of quizzes with parameterized possibility weight for each rule type, which are used to construct the concept map. The definition of the symbols used in Table 6 is described as follows.. Symbol Definition:. CSQi : indicate concept set of quiz i Wi : indicate the possibility of the possible scenario of the rule. 23.

(34) Table 6. Prerequisite Relationship of Association Rule Rule. Wi Prerequisite Relationship. Qi.LÆQj.L. 1.0. CS Qi ⎯ ⎯→ CS Qj. Qi.LÆQj.H. 0.8. CS Qj ⎯ ⎯ → CS Qi. Qi.HÆQj.H. 1.0. CS Qj ⎯ ⎯ → CS Qi. Qi.HÆQj.L. 0.8. CS Qi ⎯⎯→ CS Qj. pre.. pre .. pre .. pre.. In this thesis, 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 in Table 5. The possibility Wi is 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 in Table 6 are shown in Table 7. Table 8 shows the result of transforming association rules in Table 5 by analyzing the prerequisite relationships in Table 6.. Table 7. The Explanations of Rule Type Rule Qi.LÆQj.L Qi.HÆQj.H Qi.LÆQj.H. Description of Learning Scenario CSQi is the prerequisite of CSQj. That is, learners get low grade on Qi implies that they must get low grade on Qj. CSQj is the prerequisite of CSQi. That is, learners get high grade on Qj implies that they must get high grade on Qi CSQj is the prerequisite of CSQi That means learners get higher grade on Qj (an easier or simpler quiz) but get lower grade on Qi (a harder or more complex quiz).. CSQi is the prerequisite of CSQj That means learners get higher grade Qi.HÆQj.L on Qi (an easier or simpler quiz) but get lower grade on Qj (a harder or more complex quiz).. 24.

(35) Table 8 shows the result of transforming association rules in Table 5 by analyzing the prerequisite relationships in Table 6.. Table 8. Result by Analyzing the Prerequisite Relationships in Table 6 Rule Type Association rules of quiz Prerequisite relationship of Concept Set Conf i Wi Q2.LÆQ3.L. CS Q 2 ⎯ ⎯→ CS Q 3 pre.. 0.95. 1.0. Q3.LÆQ2.L. pre.. CS Q 3 ⎯ ⎯→ CS Q 2. 1.00. 1.0. Q2.LÆQ5.L. CS Q 2 ⎯ ⎯→ CS Q 5. 0.86. 1.0. Q3.LÆQ5.L. CS. pre. Q 3 ⎯ ⎯→ CS Q 5. 0.90. 1.0. Q1.LÆQ5.H. pre.. CS Q 5 ⎯ ⎯→ CS Q1. 0.90. 0.8. Q5.LÆQ1.H. pre.. CS Q1 ⎯ ⎯→ CS Q 5. 0.82. 0.8. H-H. Q2.HÆQ3.H. pre.. CS Q 2 ⎯ ⎯→ CS Q 3. 0.91. 1.0. H-L. Q5.HÆQ1.L. CS Q 5 ⎯ ⎯→ CS Q1. 1.00. 0.8. L-L. L-H. pre.. pre.. 25.

(36) (2) Analysis of association rules generated from Large n (>= 3) Itemset. In addition to Large 2 itemset, Large 3 itemset may also help refining learning strategies. The possible scenario is as follows. z. pre. pre. We may find CSQ1 ⎯⎯→ ⎯ CSQ2 and CSQ2 ⎯⎯→ ⎯ CSQ3 generated from large 2 itemset, but. we are not sure if concepts of Q1 and Q2 must be learned together to ensure concepts of Q3 well pre. learned. However, we can clarify the uncertainty if we find CSQ1 ∩ CSQ 2 ⎯⎯→ ⎯ CSQ3 generated. from large 3 itemset.. The scenarios of the larger n ( >3 ) itemset are the same as that described above. Therefore, in this section, we extend Heuristic 1 and only adopt the L-L, H-H rule types to help analyzing the prerequisite relationships between learning concept sets for further analyzing and refining the teaching strategies. For not losing focus on the analysis of Large n itemsets, now we only adopt rules with prerequisite pre. relationship of N:1 (CS Qi ∩ CS Qj ∩ ... ∩ CS Qk ⎯⎯→ CS Qh ) format after applying Heuristic 1. As. shown in Table 9, Scenario 1 and Scenario 4 of Heuristic 1 are adopted here as an example.. Table 9. Prerequisite Relationships of Association Rule Association Rules. WRi. Qi.L∩ Qj.L ∩ … ∩ Qk.L Æ Qh.L. 1.0. Qh.H Æ Qi.H∩ Qj.H∩ … ∩ Qk.H. 1.0. Prerequisite relationship. CS Qi ∩ CS Qj ∩ ... ∩ CS Qk ⎯⎯→ CS Qh pre. CS Qi ∩ CS Qj ∩ ... ∩ CS Qk ⎯⎯→ CS Qh pre.. 26.

(37) The mining results of Large n (>= 3) itemsets are shown in Table 10. From the table, we can see concept sets of Q2, Q3, and Q5 seem to be prerequisite of each other. However, from Table 2, the Test Item–Concept Mapping Table, we know that learning concepts of Q2 and Q3 almost overlap. Thus, we may think rule (Q2.L∩ Q3.L Æ Q5.L) is more meaningful than the others although the confidence of rule (Q2.L∩ Q3.L Æ Q5.L) is smaller than others. With the prerequisite relationship CSQ2 ∩ CSQ3 Æ CSQ5 of the rule, the learning strategies may be adapted to learn concepts of Q2 and Q3 together to ensure concepts of Q5 well learned.. Table 10. Association Rules generated from Large n (>= 3) Itemset (Confidence > 0.8) Rule(Ri). L-L. Prerequisite relationship of Concept Set of Quiz. Conf (Ri). Q2.L ∩ Q3.L Æ Q5.L. CSQ2 ∩ CSQ3 Æ CSQ5. 0.9. Q3.L ∩ Q5.L Æ Q2.L. CSQ3 ∩ CSQ5 Æ CSQ2. 1. Q2.L ∩ Q5.L Æ Q3.L. CSQ2 ∩ CSQ5 Æ CSQ3. 1. 27.

(38) 5.2 Concept Map Constructor. Based on the analysis of association rules generated from Large 2 itemset in Section 5.1, we propose a heuristic algorithm to automatically construct the concept map of a course. This algorithm has the function to detect the unreasonable prerequisite relationships of concept sets. According to our literature survey, there is no prior research similar to ours with respect to the capability of detection. For example, in Figure 8, the mined rules, Q1.LÆQ2.H and Q1.HÆQ2.L, can be transformed into corresponding prerequisite relationship of concept set resulting in a confused relation as a cycle between concept set, called circularity. That is to say, concepts of Q1 are prerequisite of concepts of Q2 and concepts of Q2 are prerequisite of concepts of Q1, 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., CSQ1ÆCSQ2ÆCSQ1.. Association Rules Q2.H. Q1.LÆQ2.H Transforming. Q1.HÆQ2.L. (Conf1,W1) =(0.8,1.0). Corresponding. Merging Q2.L CSQ2. (0.91,0.8). Cycle appeared. Q1.L. Q1.H. CSQ2. CSQ1. Prerequisite Relationship of Concept Set. CSQ1. Figure 8. The Transforming of Association Rules. Because each concept set may contain one or more learning concepts, we further define a principle of joining two concept sets and then generate corresponding concept-pair, (Ci, Cj), that is, if CSQ1={∪ 1n ai }. 28.

(39) and CSQ2 = {∪ 1m b j } , the set of concept-pair is CSQ1 JOIN CSQ2 ={∪ 1k (ai , b j )} , where ai ≠ bj and S. For example, if CSQ1 = {a1, a2} and CSQ2 = {b1, b2}, CSQ1 JOIN CSQ2 = {(a1, b1),(a1, b2),(a2, b1)}, where a2 = b2 is deleted. The related definition used in creating the concept map is given as follows.. Concept Map CM = (V, E), where z. V = {Ci| the node is unique for each i}. z. E = { CiC j | i ≠ j }∪{ Si C j | for each concept set S }. Ci denotes the learning concept as a node. CiC j denotes the edge connecting Ci and Cj, where Ci is the prerequisite of Cj. The CiC j has an Influence Weight, IW(CiÆ Cj), which denotes the degree of relationship between learning concepts Ci and Cj. The formulation of IWk is = (k −1 ) × IWk-1 + Wk × Confk , k. 1≦k≦n, where n is the amount of CiC j .. The proposed Concept Map Constructing (CMC) algorithm is shown in Figure 9.. 29.

(40) Algorithm : Concept Map Constructing (CMC) Algorithm Input : Association rules of quiz with its grade level Output : Concept Map Step 1 : CM = {Null}; Step 2 : For each association rule 2.1: Insert CSQi for Qi.L or Qi.H and CSQj for Qj.L or Qj.H. 2.2: Create a new prerequisite edge with confidence and weight of rule to connect the CSQi and CSQj according to Table 6. Step 3 : In CM, repeatedly execute this step until no cycle is found. 3.1 Do Cycle Detection Process. 3.2 If a cycle is found Then Remove the edge with the lowest confidence. Step 4 : Delete all independent nodes without connected edges. Step 5 : For each node CSQi in CM { Insert node’s corresponding learning concepts according to Test item–Concept Table } Step 6 : For each edge CSQiCSQj in CM, perform the following substeps. Step 6.1: Use JOIN principle to join two connected concept sets for generating the concept-pair, (Ci, Cj) which replaces the original concept sets. Step 6.2: Re-compute the Influence Weight IWk of the kth concept-pair (Ci,Cj) according to weight (Wk) and confidence (Confk) of CSQiCSQj . Step 4: Output the CM. Figure 9. Concept Map Constructing (CMC) Algorithm. In CMC algorithm, the main purpose of Cycle Detection Process is to detect the unreasonable prerequisite relationship as a cycle among concept sets. Thus, the CMC algorithm can generate reasonable prerequisite relationships among concept sets of quizzes. Moreover, the Influence Weight, IW, denotes the degree how the learning status of concept Ci or concept set Si influences Cj. Therefore,. 30.

(41) the number of CiC j will enhance the value of Influence Weight. In the formulation of influence weight, the WRi denotes the possibility of the learning scenario of the association rule in our analysis. Thus, the educational experts can assign different value of WRi to the algorithm according to different domains and learner’s backgrounds.. For the association rules given in Table 8, the process of CMC algorithm is shown in Figure 10. In Figure 10.b, the edges, CSQ1CSQ5 and CSQ2CSQ3 , which have lowest confidences in a cycle, will be deleted by Cycle Detection Process. Moreover, Table 11 shows the example of computing the Influence Weight of Concept-Pair (B, D) in Figure 10.f. Because the Concept-Pair (B, D) has two edges between CSQ5 and CSQ1, we have to compute the Influence Weight twice.. Delete this edge with lowest confidence (0.82,0.8). (0.82,0.8) (0.86,1.0) (0.95,1.0) CSQ1. CSQ2. (0.86,1.0). (0.9,1.0). CSQ5. CSQ1. CSQ2. CSQ3. ×. (1.0,1.0). (0.91,1.0). (0.91,1.0). (0.9,0.80. (0.9,0.8). CSQ1. (1.0,0.8). (1.0,0.8). CSQ2. (1.0,1.0). CSQ3. CSQ5. (0.9,1.0). CSQ5. (0.9,1.0). (0.9,0.8). (a). The CSM After Step 2. CSQ3. (1.0,1.0). (0.9,1.0). (0.9,0.8) (1.0,0.8) (d). Insert Process After Step 5. (1.0,0.8). (c). The Final CSM. (b). Cycle Detection Process (0.86,1.0). CSQ1 = { D } CSQ2 = { A, C } (0.86,1.0) CSQ3 = { A } CSQ5= { B, D, E } CSQ2. (0.86,1.0). (0.95,1.0). CSQ3 (1.0,1.0). CSQ1. × ×. D CSQ5. A, C. (1.0,1.0). A. (0.9,1.0). (0.9,0.8). ×. delete. Influence Weight (IW) 0.88. B, D, E (B,D) (D,D) (E,D). CSQ1 JOINCSQ5 (e). JOIN Process After Step 6.1. 0.88 A 1.0 C. 0.86. E. 0.76. 0.86. B. 0.76. D. 0.88. Figure 10. The Process of Concept Map Constructing Algorithm. 31. 0.86. (f). The Final Concept Map (CM).

(42) Table 11. The Computing of the Influence Weight for Concept-Pair (B, D) in Figure 10.f Association rules. Q1.LÆQ5.H. Prerequisite relationship of Concept Set. CSQ5ÆCSQ1. Confi. Wi. IWi. 0.90. 0.8. W1 × Conf1 = 0.9 * 0.80 ≅ 0.72 + W 2 × Conf 2 = n (1) × 0.72 + ( 0 . 8 ) × 1 . 00 ≅ 0 . 76 2. ( 2 − 1 ) × IW. Q5.HÆQ1.L. CSQ5ÆCSQ1. 1.00. 32. 0.8. 1.

(43) Chapter 6. Evaluating the Redundancy and Circularity of Concept Map. In this thesis, creating a concept map without Redundancy and Circularity is our concern. Therefore, we create four concept maps 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 Figure 11, the prerequisite relationship between concept sets in Figure 11.a is created based upon analyzing L-L rule type only, and the Figure 11.c is created based upon analyzing L-L rule type and anomaly diagnosis we proposed. Then, the concept maps as Figure 11.b and Figure 11.d are transformed according to the Test Item–Concept Mapping Table. The Figure 11.e and Figure 11.f are created by our proposed approach.. CSQ1 CSQ2. CSQ3. CSQ5. CSQ4. CSQ1. (a). Concept Set Map. CSQ3. .82 A. C. 1.0. .82 .94. .88. .88. .88 E. E. .86 .93. .95 D. .82 B. .86. (b). Concept Map. .82. A. C. 1.0. CSQ5. (e). Concept Set Map. .88 .82. .95. CSQ3. CSQ5. (c). Concept Set Map. .88 .88. CSQ2. .86 .86. D. A. 1.0. B. .88. .88. .86. (d). Concept Map. .86. E. .76. .86. B. .76. C. D. .86. (f). Concept Map. Figure 11. The (a) and (b) created based up analyzing L-L rule type only. The (c) and (d) are created based upon Anomaly Diagnosis and analyzing of L-L rule type. The (e) and (f) created by our approach (only large 2 itemset).. 33.

(44) Based upon these results using different approaches, we can conclude that the concept map we proposed has the following characteristics.. z. Non-Redundancy : The anomaly diagnosis can filter many useless test records with low discrimination for refining the input data. For example, in Figure 11.a, the Q4 with low discrimination results in generating many co-prerequisite links as a cycle in Figure 11.b.. z. Non-Circularity : The cycle detection process can delete these cycles, e.g., the cycle between A and C in 10.d, to make the concept map un-ambiguous.. Moreover, analyzing association rule with L-L, L-H, H-L, and H-H types generated from Large 2 itemset can refine the concept map, e.g., the edges ED and BD connect the node D only in Figure 11.f.. 34.

(45) Chapter 7. The Implementation of TP-CMC. In this chapter, we describe our implementation of the Two Phase Concept Map Construction. The TP-CMC is realized in Java (jdk1.4.2), JGraph (graphic tool for Java), PHP web language and MySQL DBMS.. 7.1 Construction of Related Database. The Two Phase Concept Map Constructor provides a friendly graphical user interface to help educational experts or domain experts to construct the Historical Testing Records Database and Test Item-Concept Mapping Database. As shown in Figure 12, you can construct Test Item-Concept Mapping Database of a new course in Figure 12.a, Figure 12.b, and Figure 12.c and construct Historical Testing Records Database of students in Figure 12.d.. For constructing Test Item-Concept Mapping Database of a new course, the course name, number of quizzes and learning concepts of the testing paper must be input first in Figure 12.a and then in Figure 12.b, input the learning concepts contained in the testing paper and the highest grade on each quiz of the testing paper. After the two steps described above, domain experts or teachers can choose the learning concepts of each quiz on the web directly in the Test Item-Concept Mapping choosing table shown in. 35.

(46) Figure 12.c.. For constructing Historical Testing Records Database of students, the file recording students’ grades on each quiz which domain experts and teachers upload must observe the grade format in Figure 12.d.. a. b. c. d. Figure 12. The process of constructing Test Item-Concept Mapping Database and Historical Testing Records Database. 36.

(47) 7.2 Construction of Concept Maps. As shown in Figure 13.a, the Two Phase Concept Map Constructor provides friendly user interface to help educational experts or domain experts adjusting the parameters to construct the course concept maps. Moreover, in the presentation of the constructed concept map, as Figure 13.b and Figure 13.c shows, each node is draggable in our constructor for a better view without obscurity.. b. a. c. Figure 13. The process of constructing the concept map. 37.

(48) The Large n itemset value represents the layer frequent itemsets found. The discrimination value represents the lowest acceptable degree of the discrimination of the test item. The Support, Confidence values represent the mining thresholds in LFMAlg. Cause of the design of LFMAlg, the Support value is not between 0 ~ 1. From the experiment, we find that better concept maps can be constructed when the Support value is set half of the number of the students participating in the testing. The Confidence value is between 0 ~ 1, representing the lowest acceptable connection level for two quizzes the grade level students get based upon the conditional probability.. The Prerequisite Direction of Rule Q1.LÆQ2.L or Q1.HÆQ2.H values decide which scenario of Heuristic 1 chosen. Take Prerequisite Direction of Rule Q1.LÆQ2.L as an example, Figure 14.a represents the adoption of prerequisite direction Q1ÆQ2 and Figure 14.b represents the adoption of prerequisite direction Q2ÆQ1. As shown in Figure 14, learning concept (Speed and direction of motion) in Figure 14.a is more complex than other concepts, however, in Figure 14.b learning concept (Speed and direction of motion) is prerequisite of most learning concepts. Though Scenario 1 is more intuitive than Scenario 2, the concept map constructed in Figure 14.b is more reliable than concept map in Figure 14.a. Therefore, in our approach, the Prerequisite Direction of Rule is configurable according to different domains and learner’s backgrounds. Finally, the Weight of L-L, L-H, H-H and H-L value is between 0 ~ 1, representing how reliable the rule type domain experts or experienced teachers think is.. 38.

(49) b. aa. Figure 14. The concept maps (a) and (b) are created with Scenario 1 and 2 of Heuristic 1 by TP-CMC approach respectively. (Discrimination 0.5, Support=50, Confidence=0.85). Moreover, after click on button “Computer Aided Pedagogical Strategies”, as shown in Figure 15, rules generated from Large 3 Itemset can provide the information for refining pedagogical strategies. For example, prerequisite relationship Q8 ∩ Q38Æ Q5found may provide information for teachers that sound learning of concepts of Q8 and Q38 may make learning concepts of Q5 better.. Figure 15. Association Rules Generated from Large 3 itemset (Discrimination 0.5, Support=50, Confidence=0.85). 39.

(50) Chapter 8. The Experiment of TP-CMC. In this chapter, we describe our experiment results of the Two-Phase Concept Map Construction (TP-CMC) approach.. 8.1 Experimental Results in Physics Course. The participants of the experiment are the 104 students of junior high school in Taiwan and the domain of the examination is the Physics course. The related statistics of testing results and related concepts of testing paper are shown in Table 12 and Table 13.. Table 12. 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. The Number of Concepts. 17. 40.

(51) Table 13. 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. As shown in Figure 16.a, Figure 16.b, and Figure 16.c, the concept maps with Discrimination 0.0 and 0.3, and 0.5 are created by TP-CMC approach respectively. As mentioned in Section 4.2, 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 in Figure 16.a and Figure 16.b show that the prerequisite relationships between learning concepts are very disorderly 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 Figure 16.c.. 41.

(52) Figure 16. The concept maps (a), (b), and (c) with Discrimination 0.0, 0.3, and 0.5 are created by TP-CMC approach respectively. (Support=50, Confidence=0.85). The comparison of percentage of rules found and concepts involved are shown in Figure 17, the anomaly diagnosis function in the first phase indeed reduces many ambiguous and useless relationships among learning concepts. From the figure, we know the lower the discrimination is, the larger the variation of the number of rules found is. However, the percentage of concepts involved doesn’t change so obviously.. 42.

(53) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10%. Percentage of rules found Percentage of concepts involved. 0% 0. 0.1. 0.2. 0.3. 0.4. 0.5. Discrimination. Figure 17. The comparison of percentage of rules found and concepts involved. Besides, the rationality of the concept map constructed has been also discussed with educational experts. The prerequisite relationships among the learning concepts are compatible with teachers’ teaching strategies. Moreover, the created concept map can provide the embedded learning information of students during learning Physics. For example, the relationship of concept-pair (6, 9) in Figure 16.c represents that if students don’t 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.. 43.

(54) Chapter 9. Conclusion and Future Work 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 thesis, 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 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 Mining 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 feasible.. 44.

(55) In the near future, we may further analyze the rules with Large 2 itemset from combinational view and will analyze the effect of rules with large-3 itemset for improving the concept map, enhance the TP-CMC system with scalability and flexibility for providing the web service, and do more experiments based upon real learning testing records, too.. 45.

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