Research on Teacher Teaching Quality Evaluation System Based on Grey System Model

To facilitate the rapid advancement of China’s initiatives, the education sector has introduced new standards for existing educational resources while increasing college enrollment numbers. To align with these changes, it is crucial to ensure that the modernization of educational infrastructure, such as teaching equipment, keeps pace with enrollment growth, thereby better fulfilling the requirements for effective education delivery. Additionally, enhancing the teaching proficiency of college faculty is essential. The goal is to cultivate qualified builders and successors for socialism. Traditionally, teaching activities lacked standardized evaluation criteria, leading to practical classroom management being characterized by a lack of direction and inconsistency. Outdated teaching methods further hindered improvements in teaching quality. Consequently, in the context of educational reform, universities should establish comprehensive teaching quality assessment systems. This will guide teachers in developing a proper understanding of educational management principles. They should continuously seek innovative teaching content and methodologies, ensuring that the evaluation metrics for teaching quality are more objective and refined. This approach aims to elevate the overall teaching standards and implement systematic educational guidance effectively.

The hypothetical variable R⁽⁰⁾ = {y⁽⁰⁾(i), i= 1, 2,..., n}refers to the non-negative monotonic raw data of a prediction target, from which a grey prediction model is constructed, and the variable y(0) is first accumulated, and a one-time accumulation sequence as shown below is generated 1 $y^{(1)} = {y^{(1)} (k), k = 1, 2, \dots, n}$ \[{{\text{y}}^{(1)}}=\{{{\text{y}}^{(1)}}(k),k=1,2,\ldots ,\text{n}\}\]

moreover 2 $y^{(1)} (k) = \sum_{i = 1}^{k} y^{(0)} (i) = y^{(1)} (k - 1) + y^{(0)} (k)$ \[{{\text{y}}^{(1)}}(k)=\underset{i=1}{\overset{k}{\mathop \sum }}\,{{\text{y}}^{(0)}}(\text{i})={{\text{y}}^{(1)}}(k-1)+{{\text{y}}^{(0)}}(k)\]

Based on the X variable, the albino form differential equation is constructed as follows: 3 $\frac{d X^{(1)}}{d t} + a y^{(1)} = u$ \[\frac{d{{X}^{(1)}}}{dt}+a{{\text{y}}^{(1)}}=\text{u}\]

The above equation is the GM(1,1) model.

The solution of the albino differential equation above can also be regarded as a discrete response, and the specific formula is as follows: 4 $y^{^(1)} (k + 1) = (y^{(0)} (1) - \frac{u}{a}) e^{- a k} + \frac{u}{a} y^{^(1)} (k) = (y^{(0)} (1) - \frac{u}{a}) e^{- a (k - 1)} + \frac{u}{a}$ \[{{\text{\hat{y}}}^{(1)}}(k+1)=\left( {{\text{y}}^{(0)}}(1)-\frac{u}{a} \right){{e}^{-ak}}+\frac{u}{a}{{\text{\hat{y}}}^{(1)}}(k)=\left( {{\text{y}}^{(0)}}(1)-\frac{u}{a} \right){{e}^{-a(k-1)}}+\frac{u}{a}\]

In the above formula, k represents the time series, which usually contains the year, quarter, and month.The sequence of parameters is,â = [a,u]^Tthen the â actual solution formula is as follows:â = (B^TB)^–1B^TY_n

In the above formula, B represents the data matrix and Yn represents the data column, and the specific algorithm is as follows: 5 $B = [\begin{array}{r} - \frac{1}{2} (X^{(1)} (1) + X^{(1)} (2)) \\ - \frac{1}{2} (X^{(1)} (2) + X^{(1)} (3)) \end{array} ⌊ - \frac{1}{2} (y^{(1)} (n - 1) + y^{(1)} (n)) ⌋ 1$ \[\text{B}=\left[ \begin{array}{*{35}{r}} -\frac{1}{2}({{X}^{(1)}}(1)+{{X}^{(1)}}(2)) \\ -\frac{1}{2}({{X}^{(1)}}(2)+{{X}^{(1)}}(3)) \\ \end{array}\left\lfloor -\frac{1}{2}\left( {{\text{y}}^{(1)}}(\mathbf{n}-1)+{{\text{y}}^{(1)}}(\mathbf{n}) \right) \right\rfloor \right.\quad 1\] 6 $Y_{n} = {(y^{(0)} (2), y^{(0)} (3), \dots, y^{(0)} (n))}^{T}$ \[{{Y}_{n}}={{({{\text{y}}^{(0)}}(2),{{\text{y}}^{(0)}}(3),\ldots ,{{\text{y}}^{(0)}}(\text{n}))}^{T}}\]

Because the GM model obtains the k ϵ {n + 1, n + 2,….} predicted value of the cumulative quantity and time at one time, the data obtained by the GM model must be reversed and restored $y^{^(0)} (k) = y^{^(1)} (k) - \sum_{i = 1}^{k - 1} y^{^(0)} (i)$ \[{{\text{\hat{y}}}^{(0)}}\text{(k)=}{{\text{\hat{y}}}^{(1)}}(k)-\underset{i=1}{\overset{k-1}{\mathop{\mathop{\sum }^{}}}}\,{{\text{\hat{y}}}^{(0)}}(\text{i})\], as follows: $y^{^(1)} (k - 1) = \sum_{i = 1}^{k - 1} y^{^(0)} (i)$ \[{{\text{\hat{y}}}^{(1)}}(k-1)=\underset{i=1}{\overset{k-1}{\mathop{\mathop{\sum }^{}}}}\,{{\text{\hat{y}}}^{(0)}}(\text{i})\],so ŷ⁽⁰⁾(k) = ŷ⁽¹⁾(k) – ŷ⁽¹⁾(k – 1)The test levels of the grey system model are shown in Table 1 below: Table 1.

Reference table for inspection grades

accuracy level	Relative error	Correlation degree	Mean square error ratio	Small error probability
first-order	0.02	0.80	0.45	0.85
Second level	0.04	0.70	0.40	0.70
three-level	0.10	0.60	0.55	0.60
Band four	0.30	0.50	0.70	0.40

2

Research Analysis and Application Scenarios of Teacher Quality Evaluation Models

2.1

Evaluation model

In the construction of the teaching quality evaluation system for college teachers, the basic needs of users for system operation, including functional needs, data needs and performance needs, are comprehensively studied, and a logical model expression software from abstract to concrete is constructed. On this basis, the design and processing of software and hardware are completed. On the one hand, the timeliness and accuracy of system processing are the basic requirements that must be considered in practice design, so as to truly meet the basic needs of teachers and experts in evaluating information processing. On the other hand, the teacher teaching quality evaluation system has a certain openness, and on the basis of following the relevant technical specifications, the system modules are added and subverted, the system is upgraded and updated in an orderly manner, and the user's familiarity with the system is shortened as much as possible. The final system module consists of four parts: first, questionnaire management; Secondly, personnel management; Thirdly, statistical query; Finally, report output. The corresponding structure is shown in Figure 1 below:

2.2

Evaluation methods

From a practical application perspective, grey relational analysis within grey system theory serves as a key method for examining the correlations among various factors. Building upon this foundation allows for improvements in fuzzy comprehensive evaluation methods, effectively addressing issues where adherence to maximum benefit principles may result in significant information loss. Consequently, integrating grey system theory with fuzzy comprehensive evaluation methods is proposed for educational assessment [5]. The specific steps involved include:In order to accurately evaluate the teaching quality of educators, we propose an evaluation framework as illustrated in Figure 2. This framework primarily utilizes relevant theories from grey system theory to enhance the fuzzy comprehensive evaluation method, while employing the Analytic Hierarchy Process (AHP) to determine weight values. This approach addresses the limitations of traditional evaluation systems that rely solely on quantitative analysis and logical reasoning, thereby assisting higher education faculty and administrators in obtaining targeted outcomes supported by multiple pieces of evidence [6].

The set of factors is constructed, which is mainly composed of evaluation indicators, and the specific set is as follows: 7 $U = [u_{1}, u_{2}, \dots, u_{n}] .$ \[\text{U}=[{{\text{u}}_{1}},{{\text{u}}_{2}},\cdots ,{{\text{u}}_{\text{n}}}].\]

Construct an evaluation set, which is composed of a set representing the merits of the evaluation objectives, as follows: 8 $C = [c_{1}, c_{2}, \dots, c_{m}]$ \[\text{C}=[{{\text{c}}_{1}},{{\text{c}}_{2}},\cdots ,{{\text{c}}_{\text{m}}}]\]

The weight matrix of the index is obtained by using the analytic hierarchy process, as follows: 9 $W = [w_{1}, w_{2}, \dots, w_{m}] .$ \[\text{W}=[{{\text{w}}_{1}},{{\text{w}}_{2}},\cdots ,{{\text{w}}_{\text{m}}}].\]

In the above set, wi represents the weight value of each indicator, and the following formula can be used to complete the consistency test: 10 $CR = \frac{{CI}_{n}}{{RI}_{n}}$ \[\text{CR}=\frac{\text{C}{{\text{I}}_{\text{n}}}}{\text{R}{{\text{I}}_{\text{n}}}}\]

In the above formula, CIn represents the evaluation consensus index of the nth-order judgment matrix, and RIn represents the average consistency index of the nth-order reciprocal matrix. If CIn≤0.1 is met, the evaluation is generally considered to be roughly the same and the analysis results are credible, but conversely, the degree of inconsistency is too high and the evaluation procedure needs to be revised [7].

Construct a single-factor evaluation matrix R, which refers to the evaluation results of the ith factor, and the specific formula is as follows: 11 $R = [\begin{matrix} r_{10} & r_{11} & \dots & r_{1 n} \\ r_{20} & r_{21} & \dots & r_{2 n} \\ ⋮ & ⋮ & ⋮ \\ r_{m 1} & r_{m 2} & \dots & r_{mn} \end{matrix}]$ \[\text{R}=\left[ \begin{matrix} {{\text{r}}_{10}} & {{\text{r}}_{11}} & \cdots & {{\text{r}}_{1\text{n}}} \\ {{r}_{20}} & {{\text{r}}_{21}} & \cdots & {{\text{r}}_{2\text{n}}} \\ \vdots & \vdots & {} & \vdots \\ {{\text{r}}_{\text{m}1}} & {{\text{r}}_{\text{m}2}} & \cdots & {{\text{r}}_{\text{mn}}} \\ \end{matrix} \right]\]

The weighted average comprehensive evaluation model is used, as follows: 12 $M (\begin{matrix} , ⊙ \end{matrix}) = \sum_{i = 1}^{n} (\begin{matrix} W_{i} & r_{mn} \end{matrix})$ \[\text{M}(\begin{matrix} {} & ,\odot \\ \end{matrix})=\underset{\text{i}=1}{\overset{\text{n}}{\mathop \sum }}\,(\begin{matrix} {{\text{W}}_{\text{i}}} & {{\text{r}}_{\text{mn}}} \\ \end{matrix})\]

Three models are usually used in fuzzy mathematics to calculate and analyze the comprehensive evaluation matrix, and the weighted average type is the most widely used in the teaching evaluation of college teachers, which can make full use of the information provided by the factor fuzzy matrix to ensure that the weight coefficient plays a real role. The details are as follows: 13 $η_{ij} (k) = \frac{\min_{i} {\min_{i}}_{i}^{Δ} (k) + ϱ max_{i} {m {ax}_{i}}_{k}^{Δ} (k)}{Δ_{i} (k) + ϱ max_{i} {m {ax}_{i}}_{k}^{Δ} (k)}$ \[{{\text{ }\!\!\eta\!\!\text{ }}_{\text{ij}}}(\text{k})=\frac{\underset{\text{i}}{\mathop{\min }}\,\underset{\text{i}}{\overset{\text{ }\!\!\Delta\!\!\text{ }}{\mathop{{{\min }_{\text{i}}}}}}\,(\text{k})+\varrho \underset{\text{i}}{\mathop{\max }}\,\underset{\text{k}}{\overset{\text{ }\!\!\Delta\!\!\text{ }}{\mathop{\operatorname{m}\text{a}{{\text{x}}_{\text{i}}}}}}\,(\text{k})}{{{\text{ }\!\!\Delta\!\!\text{ }}_{\text{i}}}(\text{k})+\varrho \underset{\text{i}}{\mathop{\max }}\,\underset{\text{k}}{\overset{\text{ }\!\!\Delta\!\!\text{ }}{\mathop{\operatorname{m}\text{a}{{\text{x}}_{\text{i}}}}}}\,(\text{k})}\]

Calculate and analyze the gray correlation degree and clarify the association order, as follows: 14 $\begin{array}{l} ϱ \in (0, 1) \\ Δ_{ij} (k) & = & | A_{j}^{'} (k) - A_{i}^{'} (k) | \end{array}$ \[\begin{array}{*{35}{l}} {} & {} & \varrho \in (0,1) \\ {{\Delta }_{\text{ij}}}(\text{k}) & = & |\text{A}_{\text{j}}^{\prime }(\text{k})-\text{A}_{\text{i}}^{\prime }(\text{k})| \\ \end{array}\] 15 $η_{ij} = \frac{1}{k} \sum_{1}^{k} η_{ij} (k) k = 1, 2, \dots, n$ \[{{\text{ }\!\!\eta\!\!\text{ }}_{\text{ij}}}=\frac{1}{\text{k}}\underset{1}{\overset{\text{k}}{\mathop \sum }}\,{{\text{ }\!\!\eta\!\!\text{ }}_{\text{ij}}}(\text{k})\text{k}=1,2,\cdots ,\text{n}\]

In the above formula, A′_j the initial value image of A is described, and Q is the resolution coefficient, which η_ij represents the degree of relevance.

2.3

Quality analysis

The entire teaching process is collaboratively completed by both educators and learners. The quality of instruction provided by teachers significantly influences student outcomes, which in turn directly reflects the effectiveness of the learning process. Based on the analysis of the college teacher teaching quality monitoring system illustrated in Figure 3, the evaluation criteria can be categorized into three main dimensions. Firstly, it encompasses the assessment outcomes of teachers' instructional design and implementation. Secondly, it involves the evaluation results concerning teachers' guidance in teaching, examination organization, and homework correction. Lastly, it includes the evaluation outcomes related to teachers' research activities.In selecting various evaluation indicators, it is challenging to apply precise quantitative values for measurement and analysis due to the inherent fuzziness in grading criteria. Therefore, comprehensive evaluation methods such as artificial neural networks, fuzzy comprehensive evaluation, and hierarchical analysis can be utilized. Practical research should explore appropriate evaluation mechanisms using fuzzy membership functions, analytic hierarchy processes, and fuzzy comprehensive evaluation methods, in conjunction with the implementation of the teacher teaching quality evaluation system, ensuring its smooth operation based on a grey system model.In practice, the teaching quality evaluation system, being a complex index system, exhibits diverse characteristics in terms of both indicator content and evaluators. It is essential to integrate qualitative and quantitative evaluations organically, as some evaluation contents cannot be easily represented with accurate data. Consequently, scientific methods should be selected for quantitative judgment in practical operations. This study employs the analytic hierarchy process and fuzzy comprehensive evaluation method to clarify the weight values of the index system and uses fuzzy membership functions to assess student achievements, thereby avoiding operational inefficiencies and providing robust support for subsequent educational reforms.Teaching methods, which are key determinants of classroom teaching processes and implementation effects, typically encompass three aspects: specific methodologies, media utilization, and organizational formats [12]. The overall design of the quality evaluation system is depicted in Figure 3 below.

3

Case analysis

3.1

Assessment tools

According to the comprehensive evaluation system of teaching quality of college teachers studied in this paper, the gray system method is used to construct the competency and quality evaluation type of efficient teachers' distance teaching, and the multi-dimensional ability assessment technology is used to systematically study the specific performance of college teachers, so as to judge their basic talents and development potential in the post ^[13]·. The assessment tools used by the evaluation center are situational exercise tools, that is, highly simulating or reproducing actual work tasks, understanding the test behavior responses of college teachers, and selecting three assessment tools for design, such as simulated behavior test, briefcase test, and case analysis, according to the actual requirements of college teaching.

3.2

Case introduction

Taking the teaching evaluation of a teacher in a certain university as an example, using the evaluation model and framework of teacher teaching quality proposed by this paper, 10 expert groups were invited to evaluate 3 excellent teachers. Overall model system is the grey system theory method as basic basis, after building the dynamic equation of system simulation, the use of historical data fitting analysis system of dynamic equations, using empirical data test determine the reliability of the model, at the same time the system design has the relationship between input and output, can use a variety of evaluation index data and teaching quality evaluation results clearly the main reason affecting the teaching quality. The evaluation of teaching quality is regarded as a system, which includes state variables and control variables, where the former is X (t) = (x1 (t)) T, and the latter is U (t) = (u1 (t), u2 (t), L, un (t)) T.Among, X (t) refers to the teaching quality of predictive analysis during the study, The x1 (t) represents the teaching quality in the case, The t represents the student number of the evaluation; U (t) represents the list of all factors affecting the quality of teaching, The u1 (t) represents the faculty ability to implement teaching instruction, U 2 (t) represents the scientific research ability and practical achievements of university teachers, The u3 (t) represents the subject knowledge and professional quality mastered by university teachers, The u4 (t) represents the responsibility of university teachers during teaching, The u5 (t) represents the rich amount of information contained in the teaching instruction and its scientific research nature, The u6 (t) represents whether the teachers have the appropriate professional personality and teaching characteristics, The u7 (t) represents the degree of adaptation between the teaching content and the students' needs, Whether u8 (t) represents the teaching method is scientific and its degree, The u9 (t) represents the cultivation of students' interest in learning, The u10 (t) represents the compliance of school rules and regulations and discipline, The u11 (t) represents the students' learning abilities and self-development abilities, U 12 (t) represents the optimization of students' moral literacy, The u13 (t) represents the basic information of the students in acquiring various professional knowledge and daily knowledge, The t represents the serial sequence of the participating evaluators.

Combined with the above, you can build a model that looks like this: 16 $\frac{d X^{(j)} (t)}{d t} = A X^{(j)} (t) + B U^{(j)} (t)$ \[\frac{d{{X}^{(j)}}(t)}{dt}=A{{X}^{(j)}}(t)+B{{U}^{(j)}}(t)\]

In the above model, A and B represent the coefficient matrix, X^(j)(t) represents the number of state outputs accumulated j times, and U^(j)(t) represents the number of controls accumulated j times.

3.3

Assessment results

Analyzing the results of teacher teaching quality evaluation, it is found that the correlation of the first-level indicators can accurately see the ranking results of the three tested teachers with the same ability. When analyzing the teaching cognitive level of teachers, the second tested teacher had a higher level, and the first tested teacher had the lowest level. At the same time, the ranking results of the tested teachers within the group are analyzed according to the overall relevance, so as to provide a reference for the subsequent optimization of teachers' teaching quality. The results are shown in Table 2 below: Table 2.

Results of first-level index analysis

testee	No 1	No 2	No 3
Teaching cognition	0.7038	0.8282	0.6293
Information processing	0.7797	0.6297	0.6013
Teaching implementation	0.8936	0.7991	0.6866
Process management	0.7923	0.6728	0.6102
Total correlation degree	0.7817	0.7278	0.6227

After obtaining the ability assessment results of the tested teachers, the competency assessment report shown in Table 3 below can be used to analyze and study, and the strengths and weaknesses of each teacher can be accurately understood.

Table 3.

Competency assessment report

Individual competency assessment results (Evaluator: X)
Primary index	Secondary index	Measured score	Standard score	Average score	Secondary index	Measured score	Standard score	Average score
Teaching cognition Information processing	Pattern cognition	5.0	5	6.6	selfefficacy	8.0	5	6.6
Teaching cognition Information processing	self-improvement	8.0	5	6.5	Creative thinking	6.0	5	6.0
Teaching implementation Process management	Information literacy	6.5	5	6.1	Interactive capability	8.0	6	6.6
Teaching implementation Process management	Media expression	6.0	5	6.0
Primary index Teaching cognition	Discipline literacy	6.0	6	6.6	Course design	6.5	6	6.6
Primary index Teaching cognition	Teaching skill	5.0	5	5.8	Learning evaluation	5.0	5	5.9
Information processing	Sense of responsibility	8.0	6	6.8	Problem solving	6.0	5	5.8
Information processing	teamwork	6.0	5	6.0

For example, a teacher has good computer technology skills and information literacy, can process and produce multimedia teaching materials that meet the requirements in the process of educational guidance, and can skillfully use network technology tools to establish a good interactive relationship with students; A teacher has a strong sense of responsibility, can solve classroom teaching problems through teamwork, and has a strong sense of achievement and professional development ability in the classroom teaching process. Compared with other teachers, the comprehensive quality and ability of a teacher who lacks the ability to control the learning process and distance teaching experience and have a deficient understanding of distance teaching are still at a medium level, and can be optimized and improved in these aspects in the future [14]. In this process, it is possible to accurately determine whether the teacher group is qualified for the teaching position, which teachers need to focus on improving their professional knowledge and ability, and which teachers need to participate in special training to strengthen their own competence and literacy, which will provide an important basis for teachers' own development and future reform [15].Combined with the research content and experimental results of this paper, it is found that the future teacher teaching quality evaluation system with the gray system model as the core needs to be improved, and the gray system modeling and calculation methods still have defects, and the final analysis results are not unique, and the real life and simulation content are different, and the results of this paper can provide strong support for future research.

4

Conclusion

In summary, using the gray system theory as a methodological foundation for evaluating and analyzing teaching quality, this research constructs an assessment model and develops a software system for evaluating the teaching quality of university faculty based on modern technological advancements. The entire evaluation process for teaching quality in higher education is simulated and analyzed, which not only uncovers more valuable data and insights but also addresses teaching challenges through evaluation data. This approach optimizes the skills and quality of university educators and enhances the overall standard of classroom instruction in higher education institutions.

Langue:: Anglais

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Sujets de la revue:: Sciences de la vie, Sciences de la vie, autres, Mathématiques, Mathématiques appliquées, Mathématiques générales, Physique, Physique, autres

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Research on Teacher Teaching Quality Evaluation System Based on Grey System Model

Yamin Wang

Publié en ligne: 27 févr. 2025

Reçu: 05 oct. 2024

Accepté: 21 janv. 2025

DOI: https://doi.org/10.2478/amns-2025-0140

Mots clésGrey system model, Teaching, Teacher, quality of teaching, Assessment

© 2025 Yamin Wang, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
Grey system model, Teaching, Teacher, quality of teaching, Assessment