A Quantitative Assessment of Teachers’ Intercultural Competence in Higher Vocational Education in the Context of Internationalization at Home with a Downward Logistic Regression Model

The General Office of the Ministry of Education requires the key task of accelerating the construction and reform of the modern vocational education system, among which the construction of vocational schools with a high level of internationalization is an important task, and the two-line development of “going out” and “bringing in” is required to focus on improving the internationalization level of vocational schools as a whole [1–3]. In this context, China’s higher vocational colleges have set off a new round of internationalization [4].

From a cross-cultural perspective, the internationalization of education is essentially a two-way exchange and development between domestic and foreign education based on their own concepts, systems and different cultural differences [5–6]. From the successful experience of the Chineseization of Marxism, it is known that the best mode of internationalization of education is the combination of “internationalization based on local practice and localization based on internationalization”. In this process, internationalization at home is an important part [7–8]. The internationalization at home of education, as a form of internationalization of education, focuses on the implementation of international talent cultivation in local education, and the process is expressed as “schools use the existing international quality educational resources to build international campuses rich in local characteristics, and provide opportunities for teachers and students to be exposed to cross-cultural and international affairs on campus” [9–10].

The integration of internationalized education in the local educational environment is mainly carried out in the following aspects of internationalization at home, including offering courses on intercultural communication or introducing international cases and materials, hiring foreign teachers, recruiting international students, then providing international training and exchanges for local teachers and students, and organizing exchange programs for international students on campus, as well as cooperating in projects with overseas educational and research institutes on domestic campuses. There are also activities such as organizing international cultural festivals on campus [11–14]. For students, internationalization at home not only allows domestic students to receive an education with international elements in their home country, which enhances their international competitiveness, but also allows foreign students to better adapt to the education model and culture of the host country by participating in international courses and programs provided by schools in the host country [15–17].

In this process, teachers, as the main body of educational practice, have a direct impact on the quality of education and teaching and the international competitiveness of students, and their intercultural competence is an important symbol to test the internationalization level of the school in the field [18]. Therefore, tracking the development of teachers’ intercultural competence is not only conducive to promoting the internationalization at home of higher vocational education at a higher level, but also conducive to raising the international profile of the host country’s higher vocational education and helping to promote the high quality development of the “One Belt and One Road” [19–20]. In this sense, the study of teachers’ intercultural competence in cross-cultural communication is an unavoidable issue when discussing their roles in the internationalization at home in higher vocational education.

For teachers, intercultural competence is first of all the ability to accept different cultures. Teachers need to understand the deeper characteristics of their own culture and different cultures, and make necessary adjustments to the worldview, outlook on life, values and way of thinking of their own personalities in order to adapt to the needs of intercultural communication. intercultural competence is also a kind of output ability with subjective initiative. In the process of teaching, teachers should actively exert this ability to create and reflect another culture---that is, the culture of the targetlanguage in the classroom, so as to cultivate students’ awareness, acceptance and communicative competence of the foreign culture [21–23].

In this paper, starting from the quantitative assessment system of teachers’ intercultural competence, the comprehensive evaluation index system of intercultural competence was constructed and the connotation of the comprehensive evaluation index was explained. After that, a logistic regression model based on the assessment of teachers’ intercultural competence is constructed on the basis of k-means clustering algorithm and logistic regression function. The model started with the six dimensional comprehensive evaluation indexes of intercultural competence, clustered teachers’ intercultural competence, and calculated the correlation between variables. Afterwards, the model was used to calculate the baseline scores of intercultural competence and to analyze and evaluate the attributes related to intercultural competence.

2

Quantitative assessment system and assessment method for teachers’ intercultural competence

2.1

Establishment of a comprehensive evaluation index system for intercultural competence

2.1.1

Principles for setting up a comprehensive evaluation index system

1)

Principle of systemic comprehensiveness

The evaluation indicator system must include indicators that can comprehensively reflect all aspects of the evaluation of intercultural competence, and the evaluation objectives and evaluation indicators are organically linked to form a hierarchical whole.

2)

Principle of conciseness and scientificity

The evaluation index system must clearly reflect the strict dominant relationship between the evaluation objectives and the subordinate indicators, and the size of the evaluation index system must be appropriate, that is to say, the construction of the evaluation index system should have a certain degree of scientificity. Because if the evaluation index system is too large, the attention of the evaluator will be scattered to the details of the problem; while the evaluation index system is too small, or the upper and lower levels of indicators are too small, or each level of indicators is too coarse, it will not be able to comprehensively and systematically reflect the real situation of the evaluation target intercultural competence.

3)

Principle of flexibility and operability

The evaluation index system should be flexible and operable in practical application, so as to facilitate the use of learners who do not understand the process of establishing the index system, and at the same time, the evaluators can make corresponding adjustments and changes to the index system according to their different evaluation objectives.

2.1.2

Establishment of a comprehensive evaluation index system for intercultural competence

Based on the above setting principles and with reference to the research results on intercultural competence at home and abroad, the questionnaire scale used in this study was designed to evaluate the level of teachers’ intercultural competence based on the proposed multidimensional model of intercultural competence (knowledge, skills, critical cultural awareness, and intercultural attitudes), with reference to the self-assessment questionnaire for intercultural competence compiled and the Self-Assessment Questionnaire for Intercultural Competence for Federal Research Programs, and with the actual situation of teachers’ intercultural competence level in mind. teachers’ intercultural competence self-assessment scale (containing 6 main factors), using Exploratory Factor Analysis (EFA) and Validated Factor Analysis (CFA) [24] and validity and reliability tests such as scale test of internal consistency, and the results proved that the self-assessment scale has a good level of reliability and validity, and that it is a new, localized assessment scale for evaluating teachers’ intercultural competence, and that it has reliability in the actual measurement process and validity in the actual measurement process.

The improved scale consists of the following six factors: (1) knowledge related to national culture; (2) knowledge related to foreign culture; (3) attitude; (4) intercultural communication skills; (5) intercultural cognitive skills; and (6) awareness. The above six factors can be finally summarized into four main dimensions, namely, knowledge, attitude, skills and awareness. This division of dimensions roughly coincides with the viewpoint of foreign scholars of intercultural competence research that intercultural competence mainly includes knowledge, skills, attitudes and awareness.

2.1.3

Interpretation of the meaning of integrated evaluation indicators

1)

Knowledge related to national culture. Knowledge of the national culture refers to the ability to understand knowledge of the national culture, which involves knowledge of the country’s history, geography, lifestyle and values, social etiquette, religious etiquette, and cultural taboos, and is a first-level evaluation indicator for assessing intercultural competence.

2)

Knowledge related to foreign cultures. Knowledge related to foreign cultures refers to the ability to understand knowledge of foreign cultures, which involves the history, geography, lifestyles and values, social etiquette, religious etiquette and cultural taboos of each country, and is a first-level evaluation indicator for evaluating intercultural competence.

3)

Attitude. Attitude refers to people’s positive attitudes towards different cultures, such as strong willingness and interest in intercultural communication, respect for other cultures, strong patience and tolerance, acceptance of cultural differences, and the ability to overcome barriers to communication such as ethnocentrism, racism, etc., when they view and understand their own cultures and those of other countries from different perspectives with an enlightened attitude. The attitude indicator is the first level evaluation indicator of intercultural competence.

4)

Intercultural communication skills. Intercultural communication skills refer to the ability of people with different cultural backgrounds to communicate with each other across differences between cultures, to preserve and spread their own cultures, to respect and accept foreign cultures, to be sensitive to the differences between cultures, to avoid and clarify misunderstandings, and to make intercultural communication ultimately successful, and are the first level of evaluation indicators for intercultural competence.

5)

Intercultural cognitive skills. Intercultural cognitive skills refer to the ability to learn and acquire various methods, techniques and strategies to communicate with foreigners from different cultures, and the ability to reflect on and learn from cultural differences so that intercultural communication can be carried out successfully, which is the first level of evaluation index for intercultural competence.

6)

Awareness. Awareness refers to people’s ability to understand and recognize the differences between different cultures. When communicating with foreigners, it is the first level of evaluation of intercultural competence due to the differences in the natural geographic environment in which each person lives, his or her own cultural literacy, and the literacy of national cultures, thus creating differences in intercultural communication skills.

2.2

k-means clustering algorithm based on teachers’ intercultural competence

2.2.1

Clustering algorithm process

Cluster analysis is a collective term for a group of classification methods, a statistical method of categorizing variables or observed individuals, i.e., similar variables or observed individuals are grouped into one category, also called a cluster, while those with large differences are grouped into different categories. Specifically, it is based on known data, calculating the statistics of the affinity between the observed individuals or variables, and then according to some criteria, combining the observed individuals or variables, so that the smaller within the same class, and the larger differences between classes, and ultimately, the observed individuals or variables into a number of categories.

The classification process of cluster analysis relies entirely on the data itself and does not rely on any pre-existing or external classification criteria. k-means algorithm [25–26] belongs to one of the basic and most widely used segmentation algorithms in cluster analysis methodology, which is a clustering algorithm with a known number of clustering categories. Specify the number of categories for k, the sample set for clustering, the clustering result is expressed by the k clustering center, based on the given clustering objective function (or clustering effect criterion), the algorithm adopts an iterative updating method, each iteration process is carried out in the direction of the decreasing value of the objective function, and the final clustering result makes the objective function value to obtain the smallest value, and achieves the better clustering effect. According to the expression of clustering results can be divided into hard k-means (HCM) algorithm, fuzzy k-means algorithm (FCM) and probabilistic k-means algorithm (PCM). k-means algorithm: k-means algorithm used for the division of the center of each cluster is expressed by the average value of the objects in the cluster.

Input: k:

Number of clusters

D:

Dataset containing n objects

Output: Set of k clusters with the criterion of minimizing the sum of squares error.

Algorithm steps: 1)

Choose any k initial clustering center: $z_{1}^{(1)}, z_{2}^{(0)}, \dots z_{k}^{(1)}$ , where the superscript indicates the number of iterative operations in the clustering process.

2)

Assume that the r st iteration has been performed. If for a given sample x there is $d (x, z_{j}^{(r)}) =^{*} m i n {d (x, z_{i}^{(r)}), i = 1, 2, \dots k}$ , then $x \in S_{j}^{(r)}$ . where $S_{j}^{(r)}$ is a subset of samples with $z_{j}^{(r)}$ as the clustering center. In this way, i.e., the minimum distance principle, all samples are assigned to k cluster centers

3)

Calculate each cluster center after reclassification: $z_{j}^{(r + 1)} = \frac{1}{n_{j}^{(r)}} \sum_{x \in S_{j}^{(r)}} x, (j = 1, 2, \dots K)$ , where, $n_{j}^{(r)}$ is the number of samples contained in $S_{j}^{(r)}$ .

4)

If $z_{j}^{(r + 1)} = z_{j}^{(r)}, j = 1, 2, \dots K$ , then end; otherwise go to 2)

It is called the mean k algorithm because the sample means of the k clusters are computed in step 3). The characteristics of this algorithm are: after a batch of representative points (initial clustering center), calculate the distance of all samples to the clustering center, divide all samples into categories according to the principle of minimum distance to form the initial classification, and then recalculate the center of each cluster, which is a batch processing method. Another method is the processing method one by one, every read in a sample will be classified in the nearest class, form a new classification and calculate the new clustering center, and then read in the next classification of samples, that is, the classification of each sample is changed once the clustering center.

2.2.2

Clustering algorithm statistics

How to measure the degree of proximity or similarity between classes requires the definition of some categorical statistics to be used as quantitative indicators of clustering so that clustering can be performed quantitatively. Commonly used categorical statistics are matching coefficient, distance and similarity coefficient, and their definitions are related to the type of cluster analysis. Common statistics that measure the similarity between points are: 1)

Distance

Sum-of-squares distance (Euclidean distance): 1 $d_{i j}^{2} = \sum_{k = 1}^{p} {(x_{i k} - x_{j k})}^{2} or d_{i j} = {(\sum_{k = 1}^{p} {(x_{i k} - x_{j k})}^{2})}^{\frac{1}{2}}$

2)

Similarity coefficient

(1)

Correlation coefficient: 2 $r_{i j} = \frac{\sum_{k = 1}^{p} (x_{i k} - \bar{x_{i}}) (x_{j k} - \bar{x_{j}})}{\sqrt{\sum_{k = 1}^{p} {(x_{i k} - \bar{x_{i}})}^{2} \sum_{k = 1}^{p} {(x_{j k} - \bar{x_{j}})}^{2}}}$ where $\bar{x_{i}} = \frac{1}{n} \sum_{i = 1}^{p} x_{i}, \bar{x_{j}} = \frac{1}{n} \sum_{i = 1}^{p} x_{j k}$ , it is easy to see that r_ij is actually the cosine of the pinched angle after centering the data, hence –1 ≤ r_ij ≤ 1, and the closer |r_ij| is to 1, the more similar the samples are.

(2)

Exponential similarity coefficient

The exponential similarity coefficient is defined as: 3 $c_{i j} = \frac{1}{n} \sum_{k = 1}^{n} \exp [- \frac{3 {(x_{i k} - x_{j k})}^{2}}{4 s_{k}^{2}}]$ where $s_{k}^{2}$ is the variance of the corresponding component. These statistics can be used for correlation analysis, and the most used in this paper are the correlation coefficient and the exponential similarity coefficient.

2.3

Logistic regression model based on the assessment of teachers’ intercultural competence

2.3.1

Logistic regression in a nutshell

Logistic regression is convenient, accurate, practical, good performance, good expansion and other advantages, a large number of applications in industrial research, stock market prediction, medical research and data mining. The flow chart of logistic regression in brief is shown in Figure 1.

2.3.2

Logistic regression function

Logistic regression analysis [27] has the following properties (1) Linear regression: y is a quantitative variable, when y has corresponding values for different independent variables. (2) Logistic regression: y is a qualitative variable, for example, y can only be equal to 0 or 1.

Logistic regression can actually be described as the output of a linear regression function taken as input to a Sigmoid function.

For example, we have a function of the model is part of the binary classification problem and the output is y ∈ {0,1}, at this time expect to obtain such a step function, it can realize the z value to 0/1 conversion. Then there is: 4 $ϕ (z) = {\begin{array}{l} 0, & if z < 0 \\ 0.5, & if \hat{u} z = 0 \\ 1, & if \hat{u} z > 0 \end{array}$

A sigmoid function, a step function, is a function that can jump from 0 to 1 instantaneously at different horizontal coordinate scales. That is, when 1, the sigmoid function value is between infinitely close to 0 or infinitely close to x > 0. x has no latitude. Scalar formulas, not vectors. The function form is as follows: 5 $σ (z) = \frac{1}{1 + e^{- w^{t} x}}$

Here z = w^tx.

Assume that the definition threshold is 0.5, i.e., categorize objects greater than 0.5 in the above function calculations as 1; those less than 0.5 are categorized as 0: 6 $y = {\begin{matrix} 1, & if σ (z) \geq 0.5 \\ 0, & other \end{matrix}$

The logistic regression model with dichotomization is as follows: 7 $\begin{matrix} P = (y = 1 ∣ x) = \frac{1}{1 + e^{- w^{t} x}} = \frac{1}{1 + e^{- φ}} \\ among φ = b + \sum β_{k} x \end{matrix}$

For the training dataset, w corresponds to the attribute vector feature data x = {x₁, x₂, x₃, …, x_p} and the corresponding categorized data β = β₁, β₂, β₃, …, β_p}, b is a bias term, and P(y = 1| x) denotes the posterior probability that input x belongs to class 1.

Its parameters are estimated using the method of great likelihood.

It is assumed that the whole population {Y₁, Y₂, …, Y_N} consists of N individuals, and then n samples, denoted as {y₁, y₂, …, y_n}, are taken using random sampling.

The conditional probability of obtaining the outcome y_i = 1 under the set {x₁, x₂, …, x_i} conditions is denoted as: P_i = P(y_i = 1|x,ω) = ∅(ω^Tx + b) = ∅(z)

The conditional probability of y_i = 0 is then: p_i = P(y_i = 0 | x, ω) = 1 – ϕ(z).

Thus, the probability of the observation is: 8 $P (y_{i}) = p_{i}^{y_{i}} {(1 - p_{i})}^{1 - y_{i}}$

The following great likelihood function can be obtained: 9 $L (θ) = \prod_{i = 1}^{n} p_{i}^{y_{i}} {(1 - p_{i})}^{1 - y_{i}}$

To better maximize the above equation, take a natural logarithm for each side of the equation: 10 $\begin{array}{l} l (θ) & = \ln [\prod_{i = 1}^{n} p_{i}^{y_{i}} {(1 - p_{i})}^{1 - y_{i}}] \\ = \sum_{i = 1}^{n} y_{i} \ln p_{i} + (1 - y_{i}) \ln (1 - p_{i}) \\ = y_{i} \ln (\frac{p_{i}}{1 - p_{i}}) + \ln (1 - p_{i}) \\ = \sum_{i = 1}^{n} [y_{i} (b + \sum_{j = 1}^{m} β_{j} x_{i j}) - \ln (1 + e^{b + \sum_{j = 1}^{m} β_{j} x_{i j}})] \end{array}$

Taking the maximum value of the above equation, taking partial derivatives with respect to parameters b and β, respectively, and making the above equation 0; we have: 11 $\frac{\partial l (θ)}{\partial b} = \sum_{i = 1}^{n} [y_{i} - \frac{e^{b + \sum_{j = 1}^{m} β_{j} x_{i j}}}{1 + e^{b + \sum_{j = 1}^{m} β_{j} x_{i j}}}] = 0$ 12 $\frac{\partial l (0)}{\partial β_{j}} = \sum_{i = 1}^{n} [y_{i} - \frac{e^{b + \sum_{j = 1}^{m} β_{j} x_{i j}}}{1 + e^{b + \sum_{j = 1}^{m} β_{j} x_{i j}}}] x_{i j} = 0$

The above equation is called the likelihood equation. Linear regression due to the parameter to be estimated for linear, can be used to find the deviation value of the square and respectively for the value of the partial derivative function of the combination of the two methods used to solve this particular parameter directly, although we can take the logistic explicit regression solution directly: but due to the iterative logistic explicit regression process of the likelihood function of the equation in fact most of the reasons for the nonlinear, can not be solved directly to obtain a solution with a display of the value of the solution. Must be through the logic computer applications iterative replacement of various ways to solve it directly, in today’s rapid development of computer engineering science and information technology in our country, iterative replacement of logic computer applications has been very common, promoting the iterative logistic regression plant wide application.

For logistic regression using the great likelihood method of model fit is high. We can estimate the parameters in the model through the existing samples and indicator methods, and these parameters have been related to statistical and analytical tests, in order to finally get a more nearly accurate model.

3

Results and discussion

3.1

Cluster analysis of teachers’ intercultural competence

The samples of this study were mainly from 200 teachers randomly selected from 15 higher vocational colleges of international exchange in China, and the intercultural competence of the 200 teachers was quantitatively assessed during the period of 2021-2023. The results of the cluster analysis of teachers’ intercultural competence are shown in Table 1. In this paper, the scores of teachers’ intercultural competence were clustered according to four categories, and the scores of knowledge related to the home culture were 88.93, 90.52, 70.16, and 75.39 in categories 1-4 of the initial clustering centers set automatically by SPSS, and the scores of knowledge related to foreign cultures were 75.42, 84.32, 73.44 and 94.36; attitude scores in the four categories were 60.13, 62.75, 70.14, and 96.35, respectively; intercultural communication skills scores in the four categories were 90.52, 68.89, 59.43, and 87.52, respectively; intercultural cognitive skills scores in the four categories were 44.87, 61.23, 64.36, and 75.95, respectively; and awareness scores in the four Awareness scores in the categories were 68.43, 60.79, 67.98 and 90.19. The comprehensive analysis found that Category 1 teachers scored higher on intercultural competence in terms of knowledge of their own culture and intercultural communication skills than in terms of other competencies. Therefore, teachers in this category belonged to the communication-oriented category with high intercultural competence. Teachers in clustering centers of category 2 have a high level of knowledge of both national and foreign cultures, but their scores on attitudes, communication skills, cultural cognitive skills, and awareness are lower, and this category of teachers has a weak intercultural teaching pedagogical competence, which is referred to as the weak in all competencies type of clusters. Type 3 clustering centers in the performance of teachers’ competence in intercultural are all remaining average, Gu this paper called the average clusters of teachers. Class 4 clustering center, teachers’ intercultural competence in the six evaluation indicators have high scores, belong to the perfect type of teachers.

Table 1.

The result of the teacher’s intercultural competence clustering analysis

The teacher’s cross-cultural evaluation index(Score)	Cluster result
The teacher’s cross-cultural evaluation index(Score)	1	2	3	4
knowledge related to the culture of the country	88.93	90.52	70.16	75.39
knowledge related to foreign culture	75.42	84.32	73.44	94.36
Attitude	60.13	62.75	70.14	96.35
Cross-cultural communication skills	90.52	68.89	59.43	87.52
Cross-cultural cognitive skills	44.87	61.23	64.36	75.95
Consciousness	68.43	60.79	67.98	90.19

The results of clustering teachers’ competence based on this initial clustering center are shown in Table 2. The cluster analysis of the samples of this paper using SPSS yielded: 39 teachers of type 1 intercultural communication (CCT), 43 teachers of type 2 incompetence (IT); 82 teachers of type 3 common type (CT); and 36 teachers of type 4 excellent type (ET). From the results of the analysis, the number of excellent teachers is the least, and its percentage in the total number is 18.00%, the data shows that teachers whose intercultural competence is poor in terms of both knowledge and communication skills cannot meet the requirements are only a very small number of teachers. This is because excellent teachers are very important in intercultural teaching and cultural communication in the context of internationalization. This type of teachers has strong teaching ability and rich knowledge reserves, which can contribute to the improvement of the quality of higher vocational college teaching in the context of internationalization at home. In contrast, general type teachers account for the largest proportion (41%), and this finding is consistent with the actual situation in society. In the context of intercultural teaching, the number of communicative teachers and teachers with weak competence accounted for 19.5% and 21.5%, respectively, which were comparable, and the total number of both was not more than half of the total sample size (82). Therefore, in the context of local nationalization of higher vocational education, the excellent type of teacher talent is a very important human resource, which has an important role in intercultural teaching.

Table 2.

Teachers’ ability clustering results based on the initial cluster center

Cluster result	Teacher type	Number	Proportion (%)
1	Communication teacher	39	19.50
2	Incompetent teacher	43	21.50
3	Common teacher	82	41.00
4	Excellent teacher	36	18.00

3.2

Correlation analysis between variables

3.2.1

Univariate analysis

In order to have an overall grasp of the data, we selected some key features to do univariate analysis. Univariate analysis is the most basic form of data analysis, which is to describe the discrete or concentrated trend of the data in our hands through a simple generalization, and to judge its reasonableness by applying the method of mathematical analysis of statistics. The results of the univariate distribution of the mastery of foreign cultural knowledge are shown in Fig. 2. It is found that in the context of the internationalization at home of higher vocational education, the teachers’ mastery of foreign cultural knowledge is generally in the form of normal distribution, which is in line with the law of statistical analysis. Their mastery is mainly distributed between 65% and 85%.

3.2.2

Correlation modeling between variables

Before modeling, the correlation between each variable has to be examined first, which is also to make the model more scientific and reduce the statistical error after the model is established, if the correlation between each variable is strong, it will bring different degrees of impact on the generalization ability of the model.The results of the correlation analysis between the six variables are shown in Fig. 3. The knowledge of correlation analysis of variables carried out in this section provides a preliminary analysis of each variable, and since the maximum correlation coefficient between the six variables is less than 0.42, it is judged that there is no problem of multicollinearity between the variables. For ease of representation, the original six factor indicators were re-labeled as “Knowledge related to home culture (KRCC); Knowledge related to foreign culture (KRFC); Attitude (A); Cross-cultural communication skills (CCComS); Cross-cultural Cognitive skills (CCCogS); and Consciousness (C)”.

3.3

Teachers’ intercultural competence assessment experiment

3.3.1

Baseline distribution of teachers’ intercultural competence scores

The baseline distribution of teachers’ intercultural competence scores is shown in Figure 4. It can be seen that the largest number of teachers in the distribution is 90-95, with teachers concentrated between scores of 80 and 95. The number of teachers below 85 shows a smooth sub-linear decline, while the number of teachers between 95 and 90 decreases by more than half. A peak occurs around the 90th percentile, indicating the highest numbers near that score. And a particularly steep spike occurs within the 10-point score range on either side of the peak, which characterizes the concentration of teachers in the 80 to 90 score range. Meanwhile, the distribution of teachers below 75 points is relatively smooth and even. Taken together, the above analysis shows that the number of people with good intercultural teaching skills is higher than the number of people with poor skills, and the vast majority of them are concentrated in the upper middle level.

The density distribution of teachers’ intercultural competence scores is shown in Figure 5. It can be seen that the peak point occurs at about 94 points rather than at the middle score as commonly thought, and this phenomenon occurs in relation to the distribution of internationalized education. First of all, internationalized education itself is intercultural teaching more people with good ability than those with poor ability, and after calculating the results, the mean value among those in good condition is close to about 95 points, which makes the appearance of a peak around 95 points easy to understand. However, the number of people who progressed to the two extremes (increase in score and decrease in score) centered on this is relatively small, and yet the number of people with an intact state of intercultural competence as measured by the attributes related to statistical intercultural competence (the methodology of this paper) in the raw data is much larger than the number of teachers with impaired competence. The reason for this phenomenon may be the addition of key influences on intercultural competence to the model, and the differences between these key influences are reflected in the impact on intercultural competence in the form of a further delineation of teachers’ intercultural competence, shifting the vast majority of those with good raw intercultural competence to lesser competence.

3.3.2

Attributes related to intercultural competence

The distribution of the attributes of this paper’s method in intercultural competence is shown in Table 3. It can be seen that the scores of this paper’s method (an assessment model of intercultural competence integrating K-Means and logistic regression algorithms) can divide the teachers into 6 groups, especially the category group with the best state of intercultural competence has 186 people, which means that no matter how the cut-off point of the scores of this paper’s method is divided, these people will be classified into the same category. And the method of this paper can divide the corresponding teachers of this group into 6 categories with the lowest division rate of 97%. In other words, by choosing the appropriate cut-point of the intercultural competence score, it is possible to divide the people who are necessarily classified into the same category by the score of this paper’s method into any group of no more than 6 categories. And among others this paper’s method category teachers, the intercultural competence score obtained by this paper’s method can divide the teachers whose scores of this paper’s method are divided into the same category into 100%. Taken together, the above analysis shows that this paper’s method can divide teachers who are difficult to divide into more detailed categories.

Table 3.

The distribution of intercultural competence in this paper

This method category group scores	Number of our method categories	The number of methods of this article	Division ratio(%)
1	186	180	97
2	97	97	100
3	62	62	100
4	47	47	100
5	40	40	100
6	17	17	100

The distribution of this paper’s method attributes across intercultural teaching competencies is shown in Table 4. It can be seen that as the score of intercultural competence increases (50-95), the mean value of the method score of this paper decreases (14.17-8.087); the score of this paper’s method in the original data ranges from 8-22. Lower scores indicate greater dependence on the help of others for intercultural competence, i.e., weak intercultural competence. Higher scores on the Intercultural Competence Score indicate stronger intercultural competence. The reverse trend of this data is in line with the same pattern of change of the two teachers. At the same time, with the increase of the intercultural teaching ability score, the standard deviation of this paper’s method score decreased from 3.85 (<50 points) to 0.27 (>95), which is related to the amount of data and the division of the score section, the lower the score the larger the division of the score section. The lower the score, the larger the score segment. Therefore, the corresponding score segment of this paper’s method is also larger, and the standard deviation naturally has to be larger. This objectively illustrates the mapping relationship of the same trend of the intercultural competence score and the attributes of this paper’s method, as well as the strong correlation. The maximum value of this paper’s method for each score band has the same decreasing trend with the increase of the intercultural competence score, and the maximum value of all scores except for the score of 95 or above does not exceed 20, which indicates that the intercultural competence score is able to separate teachers according to the completion of this paper’s method activities. And there was no significant monotonic trend with increasing intercultural competence scores in terms of minimum, median, and two quartiles, only an overall trend.

Table 4.

The distribution of intercultural competence in this paper

Measuring index	Fractional segment
Measuring index	<50	50—80	80—90	90—95	>95
Mean	14.17	9.25	8.134	8.09	8.087
Variance	3.85	1.80	0.37	0.28	0.27
Minimum value	8	8	2	2	2
First point	12	8	8	8	8
Median	13	8	8	8	8
Third point	15.86	10	8	8	8
Maximum value	22	15	12	9	8

4

Conclusion

This paper quantitatively assesses the intercultural education competence of higher vocational teachers in the context of internationalization at home using the intercultural competence assessment model of K-Means clustering and logistic regression algorithm. The main findings are as follows: 1)

This paper clusters teachers’ teaching competence into four categories, namely, communicative clusters, whose intercultural competence scores are higher than other aspects of competence in terms of knowledge of their own culture and cross-cultural communication skills; category 2 is a weak competence in all categories, whose scores are more advantageous than other aspects in terms of knowledge of their own culture and mastery of knowledge of foreign cultures; category 3 is a general category of teachers, whose competence in teachers’ cross-cultural scores are close and not outstanding enough; category 4 is called perfect teachers, whose scores are higher in all six evaluation indicators of intercultural competence. The average scores of the four categories of teachers in the six evaluation indicators are 71.38, 71.42, 67.59, and 86.63, respectively.

2)

In the context of internationalization at home of higher vocational education, teachers’ mastery of foreign cultural knowledge is mainly distributed between 65% and 85%, which is generally in the form of normal distribution, in line with the law of statistical analysis. There is no problem of multicollinearity between the six variables, and their correlation coefficients are all less than 0.42.

3)

The largest number of teachers in the baseline distribution of scores was concentrated in the 90-95 range, mainly between the 80-95 scores, and the number of teachers in the distribution of scores with a baseline of less than 85 points and more than 95 points decreased significantly. In addition, the peak point of the density of teachers’ intercultural competence scores appeared around 94 points. This shows that the number of good intercultural competence is higher than the number of poor ones, and the vast majority of them are concentrated in the upper middle level. The lower the intercultural competence score, the weaker the intercultural competence and the more dependent they are on the help of others; the higher the score, the lower the degree of help they need. The results of the survey are in line with the same pattern of change of the two teachers.

Language:: English

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A Quantitative Assessment of Teachers’ Intercultural Competence in Higher Vocational Education in the Context of Internationalization at Home with a Downward Logistic Regression Model

Chang Liu

Published Online: Jun 05, 2025

Received: Jan 07, 2025

Accepted: Apr 16, 2025

DOI: https://doi.org/10.2478/amns-2025-0969

KeywordsIntercultural competence, K-Means clustering, Logistic regression algorithm, Competence assessment model, Internationalization at home

© 2025 Chang Liu, published by Sciendo

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

Keywords
Intercultural competence, K-Means clustering, Logistic regression algorithm, Competence assessment model, Internationalization at home