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.

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

W_i : indicate the possibility of the possible scenario of the rule

Table 6. Prerequisite Relationship of Association Rule Rule Wi Prerequisite Relationship Qi.LÆQj.L 1.0 CSQi⎯⎯→^pre. CSQj

Qi.LÆQj.H 0.8 CS^{Qj⎯⎯→pre⎯.} CS^Qi Qi.HÆQj.H 1.0 ^{CSQj⎯⎯→pre⎯. CSQi} Qi.HÆQj.L 0.8 ^{CSQi⎯⎯→pre. CSQj}

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 Description of Learning Scenario

Qi.LÆQj.L CSQi is the prerequisite of CSQj. That is, learners get low grade on Qi

implies that they must get low grade on Qj.

Q_i.HÆQ_j.H CSQj is the prerequisite of CSQi. That is, learners get high grade on Qj

implies that they must get high grade on Qi

Q_i.LÆQ_j.H 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).

Q_i.HÆQ_j.L

CSQi is the prerequisite of CSQj That means learners get higher grade on Qi (an easier or simpler quiz) but get lower grade on Qj (a harder or more complex quiz).

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 ^{CSQ2⎯pre.⎯→CSQ3} 0.95 1.0 Q³.LÆQ².L ^{CSQ3⎯pre.⎯→CSQ2} 1.00 1.0 Q2.LÆQ5.L CSQ2⎯^pre.⎯→CSQ5 0.86 1.0 L-L

Q³.LÆQ⁵.L CS^{Q3⎯pre.⎯→}CS^Q5 0.90 1.0 Q¹.LÆQ⁵.H CS^{Q5⎯⎯→pre.} CS^Q1 0.90 0.8

L-H Q⁵.LÆQ¹.H ^{CSQ1⎯pre.⎯→CSQ5} 0.82 0.8

H-H Q2.HÆQ3.H CSQ2⎯^pre.⎯→CSQ3 0.91 1.0

H-L Q⁵.HÆQ¹.L CS^Q5⎯⎯→^pre. CS^Q1 1.00 0.8

(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 We may find and 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 learned. However, we can clarify the uncertainty if we find generated from large 3 itemset.

CS

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

relationship of N:1 (_{CS CS CS CS}

Qh Qk

Qj

Qi∩ ∩...∩ ⎯⎯→^pre. ) 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 Prerequisite relationship

Qi.L∩Qj.L∩…∩Qk.L Æ Qh.L 1.0 CSQi∩CSQj∩...∩CSQk⎯⎯→^pre. CSQh

Qh.H Æ Qi.H∩Qj.H∩…∩Qk.H 1.0 CSQi∩CSQj∩...∩CSQk ⎯⎯→^pre. CSQh

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) 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}

L-L

Q2.L∩Q5.L Æ Q3.L CSQ2 ∩CSQ5 Æ CSQ3 1