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

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.

aa bb

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,

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

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.

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.

0%

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.

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.

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.

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