Competency Evaluation Model of English Teaching Position Based on Nonlinear Random Matrix

Nowadays, the economic globalization is advancing day by day. As the most widely used language for international communication, English is becoming more and more important. English education is the most important part of the whole English basic education, and English teachers play an important role in developing the cause of English basic education. Job competency assessment is a technical method to assess the sta’s working ability, which can comprehensively and objectively evaluate the English teaching position competency. Based on the in-depth study of the relevant theories of the job competency model, the nonlinear random matrix is applied to the job competency evaluation, and the components of English teachers’ job competency are deeply explored. e competency evaluation elements are constructed from three levels of knowledge ability, technical ability, and potential ability. Based on the established job competency evaluation model, this paper evaluates and analyzes the English teachers’ job competency.e results showed that the model had good structural validity, and the correlation between factors and the scale was 0.3∽0.8, with no signicant dierence in each factor, which provided strong support for the assessment of English teaching competence.


Introduction
Modern human resource management science plays an extremely critical role in social and economic development. Job competency refers to the ability of practitioners to complete their jobs. Only employees with job competency can do good jobs, while those without job competency cannot complete their jobs [1]. It can be seen that post competency is one of the key factors related to the employer's work e ciency, work process, and work completion. erefore, employers need to evaluate the job competency of employees, in order to master the situation of the employee's job competency, nd the problems of the employee's job competency in time, and formulate corresponding countermeasures to solve the problems of the job competency to ensure that every employee can have the job competency. e post competency evaluation can help the employer master the sta 's post competency, provide support for the employer's recruitment system, performance management, sta incentive and training, and then improve the sta 's work e ciency and promote the work process. English teaching has high requirements for English teachers, which require not only high knowledge and technical ability but also professional character and personal characteristics. e job competency of English teachers directly a ects the quality and e ect of English teaching and is related to the survival and development of training institutions [2]. Only by evaluating online English teachers' job competency and nding out the existing problems of English teachers' job competency, e ective promotion strategies can be put forward. At present, the job competency evaluation mainly adopts the method of establishing the job competency evaluation model to complete, but there is a lack of research on the English teachers' job competency evaluation, so it is necessary to establish the English teachers' job competency evaluation model and evaluation system. e job competency of English teachers helps the job competency of English teachers, provides support for performance management, staff motivation, and training, improves the quality of English teaching, and promotes the stable development of English teaching. However, at present, there is still a gap in the research on English teachers' job competency evaluation, which leads to the unclear problems of English teachers' job competency and the inability to put forward effective strategies to improve their job competency.

Related Work
Competency theory originated from Taylor's research, which is called "Management competency movement" in the industry. In the study of job competency, attention should be paid to the actual situation of practitioners' personal behavior and technical ability, instead of taking theoretical assumptions and assumptions as the basis of assessment, so as to realize the improvement of the overall operating efficiency of the employer. In order to clarify the job competency evaluation, the performance evaluation standard of the post practitioner should be able to evaluate the post practitioner; feedback on learning ability; the evaluation mechanism of post practitioners should be responsive and feasible. Clear operational mode of thinking on the position of the practitioner behavior. At home and abroad, a large number of post competency models have been studied and a series of post competency evaluation models have been constructed. Vaughn S and others to carry out the research on the construction of teachers' post competency model, this study puts forward teachers post competency includes education competency and collaboration competency two constituent elements, in the concrete of the construction of the teachers' competency model, need from the teachers' professional ability, teaching ability, learning ability, cooperation ability and discipline, and so on [3]. El Asame and Wakrim established a comprehensive evaluation model of knowledge competence of vocational and technical teachers by using expert interview method, and the constructed multidimensional knowledge competence evaluation model of vocational and technical teachers has validity and goodness of fit, indicating the validity of the established competency evaluation model [4]. e competency evaluation model is on the basis of iceberg model and onion model development, Akmandor et al. such as analytic hierarchy process is employed to establish the competency evaluation model of university teachers, including language ability and general ability, computer skills, management ability and professional talents from the five indexes, set up the competency model for evaluation of university teachers to practice. e competency model and its evaluation prove the possibility of using ANALYTIC hierarchy process as a potential tool for evaluating university employees [5]. For different industries and different types of posts, the construction and application of the competency evaluation model are studied. Sun and Bin proposed that competency evaluation should be related to job requirements, with knowledge, skills, ability, characteristics, or motivation related to the job\ and be able to effectively distinguish outstanding practitioners from mediocre practitioners and predict their performance [6]. Moradi et al. proposed that teachers' job competency is the sum of various characteristics formed according to the professional characteristics and job requirements of college teachers [7]. Gómez et al. put forward the teachers' competence is teachers under the background of core literacy should have the knowledge, ability to learn, practice experience, teaching mode, and personality characteristics of the current teachers' post competency is the core of quality education competency, including professional ability, professional knowledge, basic concept and professional ethics, etc., on the structure of both exist independently and interconnected [8].
Competency model connects organizational strategy and human resource strategy closely and becomes a very important tool and link linking strategy to execution. is model establishes the human resource management model, which is development oriented and aims at improving the ability and quality to achieve human resource management. It ensures that the human resource strategy effectively follows the organizational strategy. rough behavioral event interviews and questionnaire surveys, Hilty et al. preliminarily constructed the competency model of graduate tutor in colleges and universities and divided the competency model into 17 competency characteristics, which can be classified into three levels: personality traits, knowledge and skills, and management ability [9]. Diaz et al. constructed a competency model of university teachers by interviewing university teachers with behavioral events. e model includes five dimensions, including wisdom teaching concept and motivation, use and construction of intelligent environment, teaching organization, evaluation and feedback, and teaching improvement, 15 competency elements, and 31 competency indicators. e model has been verified, which proves that the constructed model has good robustness and can be used to effectively evaluate the competence of college teachers [10]. e research of Velasco-Martínez and Tójar-Hurtado shows that the competency model structure of college teachers includes four factors: personality charm, student orientation, teacher level, and scientific research ability [11]. eories and models are used for reference in the research on teacher post competency evaluation, but there are great differences in competency evaluation models for different teacher posts. erefore, the establishment of the corresponding post competency evaluation model needs to combine the characteristics of English and teachers. e research of applying nonlinear random matrix to English teacher's job competency evaluation is still in the blank stage. How to apply nonlinear random matrix to English teacher's job competency evaluation model has become the research focus.

Nonlinear Random Matrix.
With the development of science and technology, nonlinear matrix equation has played a very important role in various fields, and the solution of nonlinear matrix equation has become a hot topic in the research field. In this paper, the range of λ 1 and λ 2 in generalized transformation is given on the basis of the existing conclusions, and the values of λ 1 and λ 2 are selected.
Step size selection in this paper is 0.1. e transformation value was calculated to obtain the new observation matrix Y [12]. e matrix Y is shown in formula (1).
y � Calculate the correlation coefficient matrix: According to the transformation formula, the fuzzy relational matrix R is transformed nonlinear to avoid the problems in the later calculation. Let any two prominence degrees be λ 1 and λ 2 , respectively, λ 1 > λ 2 ≥ 1. If r ij does not perform nonlinear transformation, then RIj performs exponential operation with λ1. Because the value range of r ij is [0, 1] and λ 1 > λ 2 , (r ij ) λ1 ≤ (r ij ) λ2 , if and only if r ij � 0 or r ij � 1, the equal sign holds. Obviously, the prominence λ should be positively correlated with the corresponding fuzzy relation (r ij ) λ , which is contrary to the above description. erefore, the value range of r ij after nonlinear transformation is [1, e], and the fuzzy relation value (r ij ) λ is positively correlated with the prominence λ [13].
Construction refers to the index out of the path degree set. Λ � {λ 1 , λ 2 , ..., λ n }, let λ � Max{λ 1 , λ 2 ,..., λ n }, then the synthesis operator form of nonlinear fuzzy matrix is Where Calculate the comprehensive evaluation matrix. Combined with the above nonlinear fuzzy matrix synthesis operator, the comprehensive evaluation matrix B is calculated, and the grade with the largest value in the matrix B is selected as the final comprehensive evaluation grade.

Elements of Competency Assessment Model for English
Teaching Positions. In this paper, the iceberg model is applied to the teacher's job competency evaluation model, and combined with the actual teaching situation of English teachers, the evaluation indicators are selected and the job competency evaluation system is constructed. For English teachers, their English teaching methods are significantly different from other classroom teaching methods. English teachers need to have innovative spirit, seek innovation and change, and strengthen teaching research and innovation of teaching methods. English teaching can adopt a variety of modern teaching methods, especially information teaching methods, which require English teachers to have the ability to use modern teaching methods [14]. According to the iceberg model and the actual situation of English teachers, it is put forward that the elements of English teachers' job competency can be divided into three main levels, namely, knowledge level, technical level, and potential level. Knowledge competence usually includes English teachers' educational background, teaching knowledge, professional knowledge, and general knowledge. e level of technical competence usually includes English teachers' teaching ability, communication ability, teaching innovation ability, education and scientific research ability, modern educational means use ability, education inspiration ability, teaching summary ability, and so on. e level of latent competence covers the "below the iceberg," including social roles, self-concept, traits, and motivation. Social role reflects the role orientation of English teachers, mainly in two aspects: professional orientation and dedication and responsibility. Self-concept is mainly manifested in strong selfconfidence, physical and mental health, optimism, dedication, and so on. Characteristics are mainly reflected in honesty and integrity, seeking innovation and change, sense of responsibility, and so on. Motivation is mainly reflected in achievement motivation, interpersonal motivation, and so on [15]. According to the iceberg model and the actual situation of English teachers, this paper puts forward the components of English teachers' job competency, including four dimensions and 22 components. e components of English teachers' job competency are shown in Figure 1. e elements of model design are educational background, educational knowledge, and professional knowledge. e elements selected at the level of technical competence include education and scientific research ability, classroom teaching ability, teaching innovation ability, communication ability, ability to use modern educational means, and educational inspiration ability [16]. Based on the analysis of the constituent elements of English teachers' job competency, an indicator system for English teachers' job competency evaluation is integrated, as shown in Figure 2.

Job Competency Index of English Teachers Based on
Nonlinear Matrix. According to the developed evaluation index system and scoring standard, this study adopts the method of comparative judgment of proportional scale and the form of scoring, as shown in Table 1. e indexes at each level are compared in pairs and scored according to their importance [17]. is paper selects 10 experts with many years of experience in English teacher management in educational institutions and English teacher competency teaching research. ese 10 experts have a good understanding of the requirements of online English teacher competency and evaluation of training institutions and can provide relatively authoritative ratings. In the scoring process, wechat software or e-mail was used to send out the scoring form to the experts, who scored according to the importance. For the judgment matrix of each expert obtained, internal consistency test is carried out. Usually, the calculation method is as follows: rst, the sum of the computed rows is calculated, the average of the rows is obtained, then the feature vector of matrix B is normalized, and nally the consistency test is carried out. Consistency index CI is obtained by According to the randomness index RI and the CI/RI ratio, when CI/RI < 0.1, it can be considered that the consistency of the judgment matrix obtained by the evaluator's analysis meets the requirement. e above method was used to test the consistency of the judgment matrix of each expert. When CI/RI > 0.1 was found, it indicated that the judgment matrix of the expert did not meet the consistency requirements, and the expert was invited to re-score until it met the consistency requirements [18]. erefore, the CI/RI of the judgment matrix obtained by the expert score in this paper is all less than 0.1, which has passed the consistency test and can calculate the e ective weight without modi cation.
rough expert questionnaire data consistency of the judgment matrix, choosing the way of judgment matrix, and the weighted geometric mean, for all levels of each index weight is calculated, namely the rst according to the data of each expert judgment matrix, the average of all the elements of judgment matrix is obtained and the weight of evaluation indexes at all levels of English teacher post competency force is obtained.

Evaluation Process of English Teaching Position Competency Model Based on Random
Matrix. Fuzzy comprehensive evaluation re ects the basic characteristics of decomposition, judgment, and synthesis of people's decision-making thinking. Because it e ectively combines qualitative analysis with quantitative analysis, people's subjective judgment experience can be expressed and processed in the form of quantity, avoiding decision-makers' logical mistakes in complex structure and too many plans. Due to the fuzziness of this method, this method is mainly applied to the decision problems with roughly determined evaluation schemes, that is, when the expert opinions in the evaluation matrix are accurate and consistent, otherwise this method will have a great impact on the evaluation results. e comprehensive evaluation judgment matrix method based on judgment matrix method combines the whitening process and standardization process of qualitative indicators, thus simplifying the evaluation steps [19]. e evaluation result is onedimensional vector, which is convenient to draw the evaluation conclusion and easy to operate. In the processing of the index with the judgment matrix method, several eigenvalues may be obtained when the eigenvalues of the judgment matrix are obtained. erefore, the problem of how to obtain eigenvectors after determining the eigenvalues and nding the basic solution of the corresponding eigenvectors needs to be further studied. is paper adopts fuzzy comprehensive evaluation and judgment matrix evaluation,  which uses fuzzy evaluation method to evaluate the competency dimensions of the post quality model, so as to get the quantitative evaluation results of the indicators and the evaluation results of the whole post competency model [19]. When ranking the job competency, the judgment matrix method can be used to calculate the ranking results quickly and easily under the premise of ensuring scienti c and objective, which provides quantitative support for personnel selection, post promotion, and reserve talent selection and training. e overall process based on the post competency assessment model is shown in Figure 3. Competency is the judgment matrix of each indicator in the post competency indicator group and its characteristic value.
e feature vector of each indicator is used as a column vector to form a matrix. By applying the judgment matrix method to fuzzy comprehensive evaluation, the evaluation results of one-dimensional vector can be obtained, and the competency ranking of employees can be intuitively obtained.

Verification of Competency Assessment Model for English Teachers
Random sampling method was used to select in-service senior high school English teachers from 4 cities. is part rst summarizes the competency characteristics obtained from the preliminary veri cation and forms a preliminary test project on the competency characteristics of senior high

e Impact Degree of the Competency Factors of the
Position. e management department of an applicationoriented university evaluated the annual performance of full-time teachers in the department and determined the outstanding personnel in the annual performance appraisal. e orientation and training target of the college is professional and technical application-oriented talents with solid theoretical foundation and practical ability. e post competency of English teachers is evaluated by the secondary index. e relationship among various factors of post competency in the performance system was clari ed. e university organized ve experts to analyze the in uence relationship among factors and integrated expert judgment information with mean method to obtain the in uence matrix factors, as shown in Figure 4.
According to the comprehensive prospect value in the gure, the annual excellent index is the annual appraisal excellent personnel. In the process of performance evaluation, the linkage between individual goals of teachers and organizational goals of colleges and universities is realized, and then the realization of organizational goals of colleges and universities is promoted. e post competency model varies with organizational goals and positions, rather than establishing a set of post competency model can be done once and for all. erefore, it is necessary to combine the di erent positioning of colleges and universities and the di erent requirements of teachers' positions to study the competency models of teachers' positions in speci c situations and distinguish the competency di erences between teachers with average performance and excellent performance. In the study of post competency model, key elements can be found through the mutual in uence of indicators, which can effectively guide teachers to focus on developing key abilities and realize the e cient use of resources. Set up the performance standard of university teachers' post scienti cally, introduce the post competency index into the performance evaluation system, and guide teachers to produce high performance behavior from the driving factors.

Competency Trait Level Validity Test.
In the whole process of logic validity test from preliminary forming to preliminary testing and then to questionnaire modi cation, psychology postgraduate students of our school participated in many discussions and were supervised and guided by tutors. To some extent, this test can re ect the competence of real high school English teachers and has good content validity. Criterion validity veri es the relationship between test scores and external independent criteria, a measure of whether the questionnaire's predictions can be con rmed. In this study, the excellent performance group was selected as the index of having won the honors of teaching expert at all levels, special-grade teacher, excellent teacher, model teacher, etc. In the formal test, a total of 35 subjects were selected from the excellent performance group. e average of the total score obtained by each factor in this test was tested, and the results are shown in Figure 5.
It can be seen from the gure that the model has good structural validity, and there should be moderate correlation among all factors. If the correlation is too signi cant, it may indicate that there is overlap among factors. If the correlation between factors is too low, it may indicate that the  [20]. rough the analysis of the validity of the test data, the content validity, empirical validity and structural validity of the test all meet the requirements of competency measurement and have good validity, which veri es the feasibility of the competency model of high school English teachers constructed in this study.

e Overall Characteristics and Di erence Test of English
Teachers' Competence. In order to further investigate the competency characteristics of English teachers in an allround way, this study conducted a di erence test on the overall situation of the competency characteristics of English teachers and di erent demographic variables. A scienti c descriptive statistical analysis was conducted on the scores of all English teachers in each competency feature. e gender of English teachers was taken as the independent variable, and the scores of English teachers in each competency feature were taken as the dependent variable to conduct a di erence test. e speci c results are shown in Figure 6. It can be seen from Figure 6 that the overall characteristic level of English teachers is relatively high and falls within the scope of conformity. ere were significant di erences between male and female subjects in factor care, help and organization management, and there were no signi cant di erences in factor communication ability, means ability, dedication and responsibility, physical and mental health, strong self-con dence, and dedication spirit. e professional title of English teachers is taken as an independent variable, and the dependent variable is the score of each competency feature. e results are shown in Figures 7 and 8. e results showed that there were signi cant di erences in the levels of 6 factors among the participants. e scores of each factor will increase with the improvement of professional title, showing a linear relationship, which indicates that the competency level of English teachers is a ected by professional title. In the di erence test with professional title as the variable, it is found that there are signi cant di erences in all factors, indicating that with the increase of professional title, English teachers' quality in all aspects has been improved.
ere are signi cant di erences in the competence of English teachers in professional knowledge, scienti c research ability, teaching ability and innovation ability, but there are no signi cant di erences in the dedication, innovation and honesty of English teachers. Academic background has a certain in uence on the basic ability   Figure 7: A comparison of English teaching competence characteristics and titles. of English teachers, so academic background can be considered as a screening condition in the selection and recruitment of English teachers. With the length of teaching as the independent variable and the scores of English teachers in each competency feature as the dependent variable, the results of variance analysis are shown in Figure 9. It can be seen from the gure that the scores of all factors of the subjects increased with the increase of teaching years. Among them, the competency characteristics of English teachers showed signi cant di erences in seeking innovation and change, sincerity and integrity, sense of responsibility, and achievement motivation, while there were no signi cant di erences in the means ability and dedication and responsibility. is has a certain relationship with the individual development of English teachers and also has a certain in uence on the psychological quality of teachers or the way of solving problems. With the growth of working hours, English teachers' basic abilities are improving, and their teaching methods and abilities are also increasing.

Conclusion
e competency assessment can comprehensively and objectively evaluate the competency of English teaching posts. Based on the iceberg competency model, an English teacher competency evaluation model is established. e model takes in-service senior high school English teachers in four cities as the empirical research subject to evaluate the job competency of English teachers. e competency characteristics take teaching experience, professional title, gender, and educational background as independent variables and the scores of English teachers in each competency characteristics as dependent variables. e evaluation results show that there are signi cant di erences in the competency characteristics of English teachers in the factors of innovation and change, honesty and integrity, responsibility, and achievement motivation, but there are no signi cant differences in the factors of means ability, dedication, and responsibility. e scores of each factor will increase with the improvement of professional title, showing a linear relationship. ere is no signi cant di erence in communication ability, means ability, dedication and responsibility, physical and mental health, strong self-con dence, and dedication. e assessment of English teachers' job competency helps English teachers' job competency, provides support for performance management, sta motivation, and training, and thus improves the quality of English teaching and promotes the stable development of English teaching.
e sample size of this study is not convincing compared with the position, and the competency index needs to be adjusted according to the di erent in uencing factors of the evaluation work. Due to the particularity of English education teachers' work, in-depth and detailed studies should be carried out from di erent levels and perspectives in the future, so as to reach a consensus on the progress of education reform and development in the new era.
Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no con icts of interest or personal relationships that could have appeared to in uence the work reported in this paper.  Mathematical Problems in Engineering