Microsoft Word - cet-01.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 46,2015 A publication of The Italian Association Of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Peiyu Ren, Yancang Li, Huiping Song Copyright © 2015, AIDIC ServiziS.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 Application of Fuzzy Synthetic Evaluation Model to the Assessment of Competency of Chinese Teachers Aiping W ang Weifang University of Science and Technology, Shandong, Shouguang, CHINA 779155469@qq.com Evaluation indicators of competency of Chinese teachers are determined by survey and looking up the references. The weights of each indicator are determined by analytic hierarchy process (AHP). The fuzzy synthetic evaluation model is established for competency assessment among Chinese teachers. 1. Introduction As more attention is given to foreign language teaching in China, the teaching of Chinese language is weakened. However, teaching of Chinese as the mother language is the basis of education, and the competency of Chinese teachers affects the development of China’s education on the whole. Chinese teachers should not only possess profound theoretical knowledge of the Chinese language, but also pay attention to the skills in oral communication and innovation of teaching method. In a word, Chinese teachers should undertake more social responsibilities and perform social roles more effectively. 2. Competency indicators and determination of weights of indicators The indicators of competency of Chinese teachers and their weights differ greatly. According to the features of Chinese language teaching, we propose the competency indicators as follows (Table 1). Table 1: System of competency indicators of Chinese teachers Primary indicator Secondary indicator Theoretical knowledge 1. Education theory; 2. Specialized knowledge of Chinese language; 3. Frontier knowledge of Chinese language; Teaching skills 4. Teaching competence; 5. Communication skills; 6. Learning ability; 7. Innovation ability; 8. Oral skills Teaching attitude 9. Enthusiasm in teaching; 10. Strictness in academic issues; 11. Integrity; 12. Respect for others Personality and motives 13. Confidence; 14. Sense of accomplishment; 15. Sense of social responsibility; 16. Commitment There are several methods to calculate the weights of competency indicators. Here we apply AHP to the calculation, which is divided into four steps. (1) Determining the hierarchy of evaluation indicators of competency of Chinese teachers (Figure. 1) Determining the hierarchy of evaluation indicators of competency of Chinese teachers (Figure. 1) DOI: 10.3303/CET1546070 Please cite this article as: Wang A.P., 2015, Application of fuzzy synthetic evaluation model to the assessment of competency of chinese teachers, Chemical Engineering Transactions, 46, 415-420 DOI:10.3303/CET1546070 415 Figure1: Hierarchy of evaluation indicators of competency of Chinese teachers (2) Establishing pairwise comparison matrix of evaluation indicators of each layer Suppose there are n indicators on one layer and pairwise comparison is carried out for n indicators. The pairwise comparison matrix is constructed based on the importance of the indicators relative to that of indicators in the upper layer. The matrix is denoted as ( ) ij n n A a   , where ij a indicates the importance of indicator i and indicator j relative to those in the upper layer. The importance is measured on a scale of 1-9 (Table 2). Here 0 ij a  and 1 ij ji a a  , A is positive reciprocal matrix. Table 2: Scale of 1-9 Value of ij a Importance of indicator i relative to that of indicator j 1 i A and j A have equal influence 3 i A has slightly stronger influence than j A 5 i A has stronger influence than j A 7 i A has much stronger influence than j A 9 i A has absolutely stronger influence than j A 2,4,6,8 The influence ratio of i A to j A lies between that of two adjacent layers 1 1 , , 2 9 The influence ratio of i A to j A is the reciprocal of ij a (3) Determining the relative weight vector of each competency indicator For the sake of convenience and practicality, the weights are obtained by geometric averaging in three steps: indicators of Chinese teachers Theoretical knowledge Education theory Specialized knowledge of Chinese language Frontier knowledge of Chinese language Teaching skills Teaching competence Communication skills Learning ability Innovation ability Oral skills Teaching attitude Enthusiasm in teaching Strictness in academic issues Integrity Respect for others Personality and motives Confidence Sense of accomplishment; Sense of social responsibility Commitment 416 a. The product i B of all elements in each row of pairwise comparison matrix A is calculated, i.e., 1 n i ij j B a    , 1, 2, ,i n . Thus vector 1 2 ( , , , ) T n B B B B ; b. The square root is calculated for each component of vector 1 2 ( , , , ) T n B B B B , i.e., n i i C B . Thus vector 1 2 ( , , , ) T n C C C C ; c. Vector 1 2 ( , , , ) T n C C C C is normalized, i.e., 1 i i n i i C W C    . Thus the weight of vector is 1 2 ( , , , ) T n W W W W , 1, 2, ,i n . (4) Consistency test The weights determined above are considerably affected by subjective factors. To confirm the validity, consistency test is carried out in three steps. a. Consistency index is calculated as max 1 n CI n     , where 1 max 1 1 n ij jn j i i a W n W       ; b. Random index RI is found by looking up the random consistency index table according to the value of n . Usually RI is given empirically. See Table 3. c. Consistency ratio is calculated as CI CR RI  . The pairwise comparison matrix is considered as passing the consistency index if 0.10CR  . Table 3: Random index n 1 2 3 4 5 6 7 8 RI 0 0 0.58 0.90 1.12 1.24 1.32 1.41 The weights of each competency indicator are calculated as follows. a. Weights of each competency indicators The pairwise comparison matrix is 11 1 2 2 2 1 2 3 11 1 2 2 1 1 1 1 2 3 2 A                 , vector 1 (1,12,1, ) 12 B  , vector 1 (1,1.861,1, 0.537)C  , and weight vector (0.227, 0.423, 0.227, 0.122)TW  . It is derived that max 1 (4.005 4.015 4.005 4.016) 4.010 4       and 4.010 4 0.003356 4 1 CI     . With 4n  , 0.90RI  by looking up the table. Thus the consistency test is passed. b. Weights of indicators of theoretical knowledge (here only the pairwise comparison matrix and the weights are given, but the process of calculation and consistency test is omitted) 1 11 5 3 5 1 3 13 1 3 A             , (0.11, 0.63, 0.26)TW  ; c. Weights of indicators of teaching skills 417 11 2 1 1 5 1 1 1 11 2 2 3 7 1 11 2 1 2 5 11 3 2 1 3 5 7 5 3 1 A                      ， (0.125, 0.062, 0.110, 0.174, 0.529) T W  ; d. Weights of indicators of teaching attitude 11 3 5 3 3 1 5 7 1 1 1 3 3 5 1 1 1 1 5 7 3 A                 ， (0.263, 0.564, 0.118, 0.055) T W  ; e. Weights of indicators of personality and motives 1 1 11 4 7 3 14 1 2 3 7 3 1 5 1 13 1 2 5 A                 ， (0.06, 0.23, 0.577, 0.133) T W  ． From the above process the weights of indicators of each layer are calculated, as shown in Table 4. Table 4: Weights of competency evaluation indicators Primary indicator Weight of primary indicator Secondary indicator Weight of secondary indicator Theoretical knowledge 0.227 Education theory 0.11 Specialized knowledge of Chinese language 0.63 Frontier knowledge of Chinese language 0.26 Teaching skills 0.423 Teaching competence 0.125 Communication skills 0.062 Learning ability 0.110 Innovation ability 0.174 Oral skills 0.529 Teaching attitude 0.227 Enthusiasm in teaching 0.263 Strictness in academic issues 0.564 Integrity 0.118 Respect for others 0.055 Personality and motives 0.122 Confidence 0.06 Sense of accomplishment 0.23 Sense of social responsibility 0.577 Commitment 0.133 3. Suggestions Fuzzy synthetic evaluation model is applied to the assessment of competency of Chinese teachers. For all secondary indicators a 5-category evaluation set is established. The weights of indicators and the fuzzy evaluation matrix are obtained by expert evaluation. The evaluation vector of competency of the Chinese teachers is solved, and the category to which the peak of the evaluation vector belongs indicates the level of 418 competency of the Chinese teacher (five-level evaluation system). For each secondary indicator the five-level evaluation set is determined, as shown in Table 5. Table 5: Evaluation set of competency indicators Secondary indicator Level 1 Level 2 Level 3 Level 4 Level 5 Education theory Very good Good Moderate Poor Very poor Specialized knowledge of Chinese language Very good Good Moderate Poor Very poor Frontier knowledge of Chinese language Very good Good Moderate Poor Very poor Teaching competence Very good Good Moderate Poor Very poor Communication skills Very good Good Moderate Poor Very poor Learning ability Very good Good Moderate Poor Very poor Innovation ability Very good Good Moderate Poor Very poor Oral skills Very good Good Moderate Poor Very poor Enthusiasm in teaching Very good Good Moderate Poor Very poor Strictness in academic issues Very good Good Moderate Poor Very poor Integrity Very good Good Moderate Poor Very poor Respect for others Very good Good Moderate Poor Very poor Confidence Very good Good Moderate Poor Very poor Sense of accomplishment Very good Good Moderate Poor Very poor Sense of social responsibility Very good Good Moderate Poor Very poor Commitment Very good Good Moderate Poor Very poor The expert panel consists of leaders, colleagues, students and other staff outside the school. The competency is evaluated using the evaluation set of secondary competency indicators. On this basis, the fuzzy evaluation matrix is established. The evaluation result of the i -th secondary indicator is 1 2 3 4 5 ( , , , , ) i i i i i r r r r r ( 1, 2, , )i m . Then the fuzzy evaluation matrix is 11 12 15 21 22 25 1 2 5m m m r r r r r r R r r r             ， where j ij n n r  ( 1, 2, , ; 1, 2, , 5)i m j  is the membership of the i -th secondary indicator to the j -th level. Thus the fuzzy evaluation matrices of 4 primary indicators are obtained as A R , B R , C R and D R , respectively. The comment vector is 1 2 3 4 11 12 13 14 15 3 3 3 3 3 21 22 23 24 25 1 2 3 4 5 1 1 1 1 131 32 33 34 35 41 42 43 44 45 ( , , , ) ( , , , , ) i i i i i A A A A A A A A i A i A i A i A i i i i i i r r r r r r r r r r V W R r r r r r r r r r r r r r r r                                   , 5 5 5 5 5 1 2 3 4 5 1 1 1 1 1 ( , , , , ) i i i i iB B B A i A i A i A i A i i i i i i V W R r r r r r                 ; 4 4 4 4 4 1 2 3 4 5 1 1 1 1 1 ( , , , , ) i i i i iC C C A i A i A i A i A i i i i i i V W R r r r r r                 ; 4 4 4 4 4 1 2 3 4 5 1 1 1 1 1 ( , , , , ) i i i i iD D D A i A i A i A i A i i i i i i V W R r r r r r                 . 419 Let ( , , , )T O A B C D R V V V V . Thus the evaluation vector of competency of the Chinese teacher is ( , , , )( , , , ) T A B C D A B C D V WR V V V V     . After normalization, the category to which the peak of the evaluation vector belongs indicates the level of competency of the Chinese teacher. 4. Application and analysis The fuzzy synthetic evaluation model established in this study can provide fast and reliable assessment of competency of Chinese teachers. Since the weights of the indicators are determined by AHP, the weights can be adjusted for different situations, preferably by questionnaire survey. This model may be criticized for the use of expert evaluation for determining the secondary indicators. We suggest that the weights of the scores given by different members of the expert panel should be also determined by AHP. 5. Summary To adapt to the needs of the society, Chinese teachers should undertake new social responsibilities and perform new social roles. Chinese teachers should advance with the times and constantly hone their learning ability and innovation ability, combining oral skills with professional knowledge. 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Shanghai Journal of Preventive Medicine, 6 (14):265-266. 420 http://dict.cn/big5/Application%20of%20comprehensive%20evaluation%20for%20the%20quality%20of%20the%20physical%20and%20chemical%20laboratory%20by%20fuzzy%20mathematics http://dict.cn/big5/Application%20of%20comprehensive%20evaluation%20for%20the%20quality%20of%20the%20physical%20and%20chemical%20laboratory%20by%20fuzzy%20mathematics