Chapter 4 Research Results and Discussion
4.1 Results and Discussion of Experimental Test 1:Concept Diagnosis of English
Concept Diagnosis of English Grammar
During the teaching process, it is important to let the learners understand the foundation of the subject (Anderson and Krathwohl, 2001; Ferreira, 2011;
Wang et al, 2011a). The knowledge of subject matter content, and cognitive structure need to be established (Chen and Lin, 2011; Sheu and Lin, 1994).
Since English grammar is the foundation of English reading and writing, understanding the English grammatical structure not only soothes the English reading abilities, but also let people express their meanings clearly (Taillefer, 1996; Yamashita, 2002). In the Taiwanese classroom, most students try to memorize the grammatical rules; however, they fail to apply those rules in the real context (Bao and Sun, 2010; Petrovitz , 1997). Therefore, how to help students master the knowledge of English grammar becomes an essential task to English teachers.
The participants are thirty-seven daytime freshman students and thirty-seven extension freshman students in central Taiwan, and all of them are not English
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majors. Their English level is defined as “Basic level” which can be equivalent to TOEIC score 350.
The unified English grammar exam of the English proficiency test was used to examine the students’ performances (please see Appendix 1). The Cronbach’s alpha reliability coefficient (Cronbach, 1951) for the test of daytime and extension students are 0.829and0.765,respectively. This grammar section in the proficiency test consists of ten questions, and it measures four English verb concepts. Among the test items, items 1 and 9 test the same concept of simple past tense; items 3 and 4 test the same concepts of present tense and be verbs; items 5 and 6 test the same concept of present tense, simple past tense and be verbs. The concept attributes and the concept-attribute matrix of the test are shown in Table 4.1 and Table 4.2, respectively.
Table 4.1 The concept attributes of basic English verb test (Cited from Wang et al., 2011a, p89)
Concept Content
C1 Present tense C2 Simple past tense
C3 Be verbs
C4 Present continues and present tense
Table 4.2 The concept-attribute matrix of basic English verb test Verb
Content
Concepts
C1 C2 C3 C4
C1: Present Tense 0 1 1 0
C2: Simple past tense 0 0 0 1
C3: Be verbs 0 0 0 1
C4: Present continues
and present tense 0 0 0 0
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By using ISM and based on the information in Table 4.2, the concept structure of English grammar verb test is shown in Fig. 4.1.
C4: Present continues and present tense
C1: Present Tense
C2: Simple past tense C3: Be verbs
Fig. 4.1 The concept structure of English grammar verb test (Cited from Wang et al., 2011a, p90)
As shown in Fig. 4.1, the hierarchical structure of the verb tenses are displayed from easy to difficult, that is, teachers think students have to understand the present tense and then come simple past tense and be verbs, and finally they can reach the knowledge of present continues and present tense.
Besides, while looking deeply into the concepts in each item, the item-attribute matrix of the test is summarized in Table 4.3. Then method of GSM is applied to show the hierarchical structure of test items in Fig. 4.2.
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Table 4.3 The item-attribute matrix of the test (Cited from Wang et al., 2011a, p89)
Item Concepts
Fig. 4.2 The GSM structure of test items (Cited from Wang et al., 2011a, p90)
Based on Table 4.3 and Fig. 4.2, the following facts can be reached:
1. The items with more concepts are more difficult than items with only one concept;
2. The items with concepts 1, 2 and 3 are the basis of the item with concept 4.
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For comparing the performances of Takeya’s IRS algorithm, and the proposed GSM method, a grammar test with 10 items was administrated to thirty-seven daytime students and thirty-seven extension students in Taiwan.
The IRS of examines is shown in Fig. 4.3 while the GSM of examinees is shown in Fig. 4.4 hierarchically.
I8
Fig. 4.3 IRS of examinees generated by Takeya’s threshold 0.5
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Fig. 4.4 Concept hierarchy of daytime and extension students by using GSM
Besides, after students taking the test, the GSM of each class can be established by using Nagai’s equation, and Matlab 7 (Liang, 2011a~2011c ; Nagai et al, 2005; Yamaguchi, Li and Nagai, 2007) and the hierarchy of daytime and extension students are shown in Fig. 4.5 and Fig. 4.6, respectively (Wang et al, 2011a).
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Fig. 4.5 GSM of grammar (daytime) performances ) (Cited from Wang et al., 2011a, p94)
Fig. 4.6 GSM of grammar (extension) performances ) (Cited from Wang et al., 2011a, p94)
6
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Then based on the S-P charts of each class, the GSP Figures are formed in Fig. 4.7 and Fig. 4.8 (Wang et al, 2011a).
Fig. 4.7 GSP of daytime students (Cited from Wang et al., 2011a, p94)
Fig. 4.8 GSP of extension students (Cited from Wang et al., 2011a, p95)
According to Fig. 4.7 and Fig. 4.8, it is shown that the daytime students performed better on the test items than extension students. Besides, the ability
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of most students in both groups is below 0.5, which can be defined as the majorities are with poor English grammar ability.
Based on the raw data of the S-P charts, the correct rate and scoring rate are calculated (Sheu, Tzeng, Liang, Wang and Nagai, 2011). Then the worst score
)
(S and the worst correct rate (P) could be reached, and the figures of
distribution are shown in Fig. 4.9 and Fig. 4.10 (Wang et al, 2011a).
Fig. 4.9
Distribution of day-time students (Cited from Wang et al., 2011a, p95)Fig. 4.9 shows that the exam is too easy for the day-time students since the 78
. 0 )
(S which is larger than (P) 0.38 . The overall day-time students’
performances are also better than the averages of the test. However, in the following Fig. 4.10, the exam is a bit too difficult for the extension students due to the (P) 0.84 , which is larger than (S)0.76 . Also, there are more extension students who got low scores on this grammar exam.
0.38 0.78
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Fig. 4.10
Distribution of extension students (Cited from Wang et al., 2011a, p95)Finally, the level of students and the relevance of test items could be judged based on the
distribution figures (please see Fig. 4.9 and Fig. 4.10). The worst score (S) and the worst correct rate (P) could be reached.0.76 0.84
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