Introduction

Secondary vocational education is essential to a country’s education system and plays a crucial role in national economic development. Many nations, including the United Kingdom, Canada, New Zealand (Chhetri et al., 2018), and China, have undertaken reforms to foster the development of skilled workers through secondary vocational education and thereby promote a thriving national economy. However, secondary vocational education continues to face issues including a lack of higher quality and skilled workers, an upgrade to the industrial structure (i.e., a classification or composition of the three main economic activities, the agricultural, manufacturing, and service sectors) (Atikian, 2013), and an imbalance between the supply of skills and the demands of a particular industry. Therefore, in a rapidly evolving labour market, well-constructed vocational education programmes are vital in helping students acquire the necessary abilities, and vocational education is the first choice in seeking a better match between the supply and demand of skills (European Commission, 2016). The achievements of vocational education programmes depend on graduates’ smooth entry into the labour market.

The relationship between vocational education and the industry or labour market has been examined in recent years. Tran (2021) used the dynamic network DEA model to investigate the linked efficiency between teaching and industry responsiveness. She found that the critical factor is an interaction between providers, students, industry, and employers in raising Austria’s quality outcome of vocational education. The intensity of the relationships between vocational education schools and firms is influenced by the following factors: the size of the company (more than 50 employees), belonging to the metallurgical industry, the proportion of staff with higher-tertiary-level vocational education qualifications, and external cooperation in innovation (Olazaran et al., 2019). Cui and Li (2021) investigated the relationship between culture and art talent training in SVS programmes and regional cultural industry development and they analysed the causes from the three aspects of training quantity, structure, and quality. Kemendikbudristek concretely fused vocational education with the work world by implementing the programme Link and Match 8+i (Disas, 2018; Wibisono et al., 2020). Cedefop (2013) noted that feedback mechanisms are crucial to ensure that vocational education systems are responsive to the labour market and society as a whole. Vocational schools also need to be increasingly responsive, which is essential in understanding how vocational education responds and how it could respond more effectively to the demands of the economy and labour market. Raffe and Willms (1989) discovered that industry and occupation structures matter in regional educational and occupational attainment and that the local occupation structure directly affected the occupational segment of vocational education entry for school graduates. Dummert et al. (2019) proposed that the availability of school graduates and competition within regions and sectors affect the quality of matches on the vocational education market and how well vocational education programmes and structures are matched to the needs of local economic and social development as well as changes in the industrial structure. Vocational education programmes provide students with technical expertise for work as well as personal and learning competencies to attain the desired results (Ellström, 1997); thus, it is necessary to systematically develop vocational education programmes that meet the job market’ needs (Boateng, 2012).

Despite increasing training numbers and education levels, there is still a problem with skills mismatch (Cedefop, 2015). Vocational education should invite the work world to participate in developing its programmes to prevent graduates from experiencing unemployment or job mismatch (Anam, 2021; Wardina et al., 2019). It is challenging to measure skill mismatches, especially for skill surpluses or overeducation, and there is a shortage of data that can be used to assess whether mismatches exist and to what extent they do. Additionally, the data are occasionally subject to different interpretations. The mismatch incident in the industrial world will not happen again if the notion of linking and matching vocational education can be executed as expected (Disas, 2018; Husein, 2019). According to conjugation theory, Ren et al. (2021) explored the conjugate relationship between the industrial economy and vocational education and found that it is generally good but structurally insufficient. An insufficient relationship exists between vocational education and production (Aguilar-Gonzálvez, 2015; García-Ruiz, 2008; OECD, 2012; Li and Tang, 2021). There is a lack of coupling between vocational education and industry (Cabrera-Rodríguez, 1993); thus, coordination is becoming increasingly crucial (Billet, 2009; Powell and Solga, 2010). Some scholars have used the educational approach to research this mismatch, such as the competence approach (Guillem, 2011), learning strategies (Hanafi, 2012), and educational mismatches (Badillo-Amador and Vila, 2013). However, vocational education is more strongly tied to the economy than other types of education, making it challenging to address the issues at their root merely within a theoretical framework of pedagogical research (Zhao and Liu, 2019).

Given the above context and literature review, studies on the interactive relationship between the structures of SVS programmes and industries and the use of quantitative methods are still lacking. To address this research gap, this paper aims to build a conceptual framework and a quantitative computation model of coupling and coordination to measure the relationship between the structures of SVS programmes and industries. This study also uses the method of grey relational analysis to explore influencing factors between indicators of SVS programmes and the coupling coordination degree (CCD). Investigating the coupling coordination relationship between the structures of SVS programmes and industries can help us understand their positive interactions and reduce skill mismatch. It is of great significance to the strategies of secondary vocational education and sustainable economic development. As such, this study will focus on three questions: (1) What coupling coordination relationship exists between the structures of SVS programmes and industries? (2) How can the coupling coordination relationship between the two be measured? (3) What are the important factors affecting the coupling coordination relationship between the two?

The rest of this paper is structured as follows. Section “Coupling coordination conceptual framework between the structures of SVS programmes and industries” presents the indicators and conceptual framework of coupling coordination between the structures of SVS programmes and industries. Section “Method and data sources” covers the method and data resources, and the method uses a model of quantitative computation and grey relational analysis to measure the relationship of coupling coordination. Section “Results and discussion” explores the influencing factors between SVS programmes and industries by using data from Tianjin, China. Section “Conclusion and limitations” provides limitations, conclusions, and recommendations for future research.

Coupling coordination conceptual framework between the structures of SVS programmes and industries

Coupling and coordination

Coupling is a phenomenon in physics where two or more objects interact (Lin and Li, 2021). Since the 1980s, with the advent of system theory, scientific research has increased its emphasis on the interconnections or interactions between two or more systems, and research domains such as environmental science, ecology, economics, and sociology have steadily embraced the notion of coupling (Liu et al., 2022). In general, the coupling is either good or defective. Good coupling occurs when the system elements properly coordinate and promote one another. Otherwise, the coupling is defective. Coordination refers to a consistent and good interrelationship between two or more systems or system components that ensures the system’s healthy development.

The coupling degree is a level of reciprocal influence and interaction between systems or system components (Schandl et al., 2016), regardless of the advantages and disadvantages. The CCD can be used in the development process to measure the coordination degree between systems or various elements within a system, which reflects the system’s transition from a disordered to an ordered state. As a result, there is a distinction between the two concepts. The coupling degree indicates how strongly or weakly systems interact with one another. On the other hand, the CCD focuses on the good coupling degree between two or more systems in the interaction and directly presents the coordination degree between systems.

A conceptual framework of coupling coordination between the structures of SVS programmes and industries

The industrial structure is divided into primary industry, secondary industry, and tertiary industry (Yi, 2021). The primary industry includes agriculture, forestry, animal husbandry, and fisheries. The secondary industry includes mining, manufacturing, production, construction, and supply of electricity, gas, and water. The tertiary industry covers a wide range of activities from commerce to administration, transport, financial and real estate activities, business and personal services, education, health, and social work (The French National Institute of Statistics and Economic Studies, 2019).

According to catalogues of vocational school programmes in the U.S. Department of Education (2019) and the Ministry of Education of the People’s Republic of China (2021), SVS programmes offer studies in the following occupational areas: agriculture/nature resources; construction; engineering, design, and production; health care; business, finance, and marketing; communication and communication technologies; computer and information sciences; consumer services; mechanical repair and operation; and public services. These SVS programmes are within the scope of the three major industries. Kuznets (1966) argued that indicators of an industrial structure are the share in employment and output. Atikian (2013) thought a pivotal concept was defined by the industrial structure: the share of each sector in the gross domestic product (GDP). Only if the industrial structure has the right proportions of people able to work in each of these sectors, can it be said to have an industrial structure. Therefore, in industrial structure, this study selects GDP and employees as 1st indicators and the proportions of GDP and employees by the industry as the 2nd indicators.

SVS programme structure is the proportional relationship and composition of programmes by industry according to the above industry division. Regarding the SVS programme structure, the Danish vocational education and training benchmark designed two indicators: the number of students and the distribution of programmes (Bogetoft and Wittrup, 2015). This study uses similar expressions for the 1st indicators: programme scale and programme quantity. On the programme scale, the 2nd indicators are students admitted, students enrolled, and graduates by industry. Regarding the number of programmes, we deconstruct it by industry into 2nd indicators. Sources of 2nd indicators are the Educational Statistical Yearbook of China (Development and Planning Department, 2021) and the Tianjin Statistical Yearbook (Tianjin Municipal Bureau of Statistics, 2020).

The index system of SVS programmes and industries is shown in Table 1, and the indicators are usually expressed as percentages.

Table 1 Indicators of SVS programmes and industries.
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According to the above analysis, we proposed a conceptual framework to measure the coupling coordination relationship between SVS programmes and industries, as shown in Fig. 1. SVS programmes’ structure has connectivity with the industrial structure, and both are closely related systems that support and constrain one another (Zhan and Wang, 2019).

Fig. 1
figure 1

A conceptual framework of coupling coordination between the structures of SVS programmes and industries.

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Method and data sources

A quantitative computation model of the CCD between the structures of SVS programmes and industries

The detailed design is as follows.

Determination of weighting indices

Measuring the overall CCD is critically dependent on the weight (wij) of each indicator of the system. The entropy weighting method is utilized in this study to identify the weight of every index in the system to reduce or avoid errors caused by subjective factors.

Assume that data of m years are selected as samples and the number of evaluation indicators is n. Let xij represent the jth index of the ith year (i = 1, 2, …, m; j = 1, 2, …, n).

Calculating the proportion of the jth index of xij in the ith year.

$$S_{ij} = \frac{{x_{ij}}}{{\mathop {\sum }\nolimits_{i = 1}^m x_{ij}}}$$
(1)

Calculating the jth index’s entropy value

$$e_j = - \frac{1}{{\ln m}}\mathop {\sum }\limits_{i = 1}^m \left( {s_{ij}\ln s_{ij}} \right)$$
(2)

Calculating the difference degree of the jth index

$$a_j = 1 - e_j$$
(3)

Calculating the evaluation weight of the jth index

$$w_j = \frac{{a_j}}{{\mathop {\sum }\nolimits_{j = 1}^n a_j}}$$
(4)

A larger ai means that the difference is greater and has a greater effect on the overall evaluation. If wj is larger, it means that the index’s coefficient is higher, and the importance of the evaluation result is larger.

Determination of the overall evaluation index

The power function was used to determine the contribution value. The power function serves as the foundation for building the system’s coupling coordination and indicates the contribution of changes in the system. Indicators in this study are positive, and uij is calculated by Eq. (5).

$$u_{ij} = \frac{{x_{ij} - \min \left( {x_{ij}} \right)}}{{\max \left( {x_{ij}} \right) - \min \left( {x_{ij}} \right)}}$$
(5)

In Eq. (5), uij is the jth index of the ith year, max (xij) is the maximum value and min (xij) is the minimum value in the xij index.

Calculating the index’s contribution value to the system. A linear weighting method is used to calculate the contribution value of each index, as shown in Eq. (6).

$$U = \mathop {\sum }\limits_{j = 1}^n \left( {w_ju_{ij}} \right),\mathop {\sum }\limits_{j = 1}^n w_j = 1$$
(6)

In this study, U1 represents the overall evaluation function of the SVS programmes’ structure, and U2 is the industrial structure’s overall evaluation function.

Calculating the CCD between the two

By utilizing the concept and coefficient model of capacity coupling in physics, the coupling degree (C) between the two can be calculated, as shown in Eq. (7).

$$C = 2 \times \left[ {\frac{{U_1 \times U_2}}{{\left( {U_1 + U_2} \right)^2}}} \right]^{\frac{1}{2}}$$
(7)

However, the calculation of this model makes it appear that development levels are low and the overall coupling degree obtained is high, which is usually not the case. To avoid the appearance of this type of illusion, the CCD (D) between the structures of SVS programmes and industries is designed and shown in Eq. (9).

$$T = \alpha \times U_1 + \beta \times U_2$$
(8)
$$D = \left( {C \times T} \right)^{1/2}$$
(9)

In Eq. (8), T stands for the system’s overall coordination index, which reflects the system’s contribution degree, and α and β represent undetermined coefficients. When combined with the study’s actual situation, α = 0.35 and β = 0.65.

Determining coupling coordination level

Conventional classification criteria of the coupling coordination level have some deficiencies, manifested as a discontinuity in the division interval of the CCD. For example, when D = 0.499, whether the coupling coordination level is “near incoordination” or “reluctant coordination” cannot be determined accurately, thus not providing a relatively unified and accurate judgement. Therefore, we appropriately adjust the criteria and strive to include all values shown in Table 2, which made use of evaluating the coupling coordination level (L) between the structures of SVS programmes and industries.

Table 2 Criteria of coupling coordination level for the structures of SVS programmes and industries.
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Grey relational analysis

The method of grey relational analysis is quantitative and demonstrates the two sequences’ correlations, reflecting factors’ relative changes according to the scenario (Deng, 1982).

Calculating the grey correlation coefficient

Constructing the reference sequence of the CCD between the structures of SVS programmes and industries and the comparison sequence of each index in SVS programmes’ structure, and calculating the grey correlation coefficient of the reference sequence and the comparison sequence are shown in Eq. (10).

$$\varepsilon _r\left( t \right) = \frac{{x_{{\rm {min}}} + \rho x_{{\rm {max}}}}}{{x_r\left( t \right) + \rho x_{{\rm {max}}}}}$$
(10)

In Eq. (10). xmax and xmin are the two-level maximum and minimum differences between the reference and comparison sequences. εr(t) is the grey correlation coefficient, ρ is the resolution coefficient, and usually 0.5. xr(t) is the comparison sequence of the rth index in year tth.

Calculating the grey relational degree

A grey relational degree is calculated by Eq. (11), and m is the total number of sample years.

$$\gamma _r = \frac{1}{m}\mathop {\sum }\limits_{i = 1}^m \varepsilon _r\left( t \right)$$
(11)

Data sources

The original data of the programme scale of SVSs are publicly available in the Dataverse repository (Zhan et al., 2023) from the Tianjin Statistical Yearbook published on the website of the Tianjin Statistics Bureau in China. Data on the number of SVS programmes are publicly available in the Dataverse repository (Zhan et al., 2023) from the admission announcement of SVSs released by the Tianjin Education Admission and Examination Institute. After sorting and calculating, the SVS programme’s indicators from 2013 to 2019 are illustrated in Table 3.

Table 3 Indicators of SVS programmes’ structure.
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The original data on the structures of GDP and employees are publicly available in the Dataverse repository (Zhan et al., 2023) from the Tianjin Statistical Yearbook (2020) provided by the Tianjin Municipal Statistics Bureau. Table 4 shows the index data selected and organized.

Table 4 Indicators of industry structure.
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Results and discussion

The interaction between SVS programmes and industries

Before exploring the coupling coordination relationship between the structures of SVS programmes and industries, it is necessary to check whether there is an interaction between the two. The programme quantity by industry, GDP by industry, and employees by industry are variables. A two-variable correlation analysis method and Pearson’s correlation coefficient are used to judge the correlation degree between the two. The results are shown in Table 5.

Table 5 Correlation between programme quantity by industry, GDP by industry, and employees by industry.
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It can be seen from Table 5 that there is a strong negative correlation between the number of SVS secondary industry-related programmes and the GDP of the corresponding industry and a strong positive correlation between the number of SVS secondary industry programmes and corresponding industry employees. P values for the relationships of the number of SVS programmes in the secondary industry with the corresponding industry’s GDP and the number of employees in the corresponding industry are −0.883 and 0.893, respectively. The sig. (2-tailed) values of the irrelevance are all <0.01. That is, the relationship between the number of secondary industry-related programmes offered in SVSs and their corresponding industry’s GDP exhibits a negative correlation at the 0.01 significance level, and the relationship between the number of SVSs offering secondary industry-related programmes and the number of employees working in the corresponding industry exhibits a positive correlation at the 0.01 significance level. The skilled talents cultivated under the number of secondary industry-related programmes are closely related to the demands for talent in the corresponding industries and can meet the demands of the number of employees.

P values for the relationships of the number of SVS tertiary-industry-related programmes with the corresponding industry’s GDP and the number of employees in the corresponding industry are −0.939 and −0.978, respectively. The relationships between the number of tertiary industry-related programmes with GDP and with the number of employees in the corresponding industry exhibit a negative correlation at the 0.01 significance level. Knowledge and skills of workers available in the labour supply are key determinants for both business and economic growth (Radcliffe, 2022). However, from 2013 to 2019, the GDP growth rate of the tertiary industry slowed, and the development of the tertiary industry reached a stable stage during this study. It showed that SVS tertiary industry-related programmes did not strengthen students’ transition from school to work and that the programmes needed to develop skilled talent by improving the quality of their training and not expanding the number of students.

With the scale of SVS programmes, industrial GDP, and employees as variables, the correlation degree of SVS programmes and industry was judged by the bivariate correlation analysis method and Pearson correlation coefficient. The results are shown in Table 6.

Table 6 Correlation analysis of programme scale in SVSs and industrial structure.
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It can be seen from Table 6 that there is a strong negative correlation between the number of students admitted and enrolled in SVS programmes related to the primary and secondary industry and the GDP of the corresponding industry. P values for the relationships of the number of students admitted to the primary and secondary industry with the GDP of the corresponding industries are −0.792 and −0.864, respectively. The sig. values (2-tailed) of the irrelevance are all less than 0.05, indicating that there are negative relationships between the number of students admitted in the primary industry and in the secondary industry with the GDP of the corresponding industry. P values for the relationships between the number of students enrolled in the primary industry-related programmes and the secondary industry-related programmes with the GDP of the corresponding industry are −0.886 and −0.940, respectively, indicating that there are negative relationships between the number of students enrolled in the primary industry-related programmes and the secondary industry-related programmes with the GDP of the corresponding industry at the 0.01 significance level.

There is a strong negative correlation between the number of students enrolled in programmes related to the primary and secondary industries and the growth of the GDP of the corresponding industries. P values for the relationships of the number of students enrolled in primary industry-related programmes, those enrolled in secondary industry-related programmes, and the number of graduates in secondary industry-related programmes with employees working in corresponding industries were 0.882, 0.883, and 0.937, respectively. The sig. values (2-tailed) of all are <0.01, indicating significant positive relationships at the 0.01 significance level. The supply of skilled talent is closely related to the demand for employees. The scale of students in SVSs can meet the demand for skilled talent in the rapid development of the secondary industry.

It showed that the relationship between the number of primary industry-related programmes in SVSs and the development of the corresponding industrial GDP is not close enough to meet the needs of employers. The number of primary industry-related programmes is out of line with the developmental needs of industrial GDP; thus, the low contribution of programmes to GDP development and the skilled talent supply cannot meet the demands for economic development. There is a relatively low relationship between tertiary industry-related programmes and the development of the corresponding industrial GDP. Therefore, the tertiary industry-related programmes did not contribute much to the development of industries or the supply of skilled workers.

Comprehensively considering the correlation analysis results of SVS programmes’ structure and industrial structure regarding the three main industries, it can be found that compared with the primary and tertiary industries, SVS programmes’ structure is more closely related to the structure of the secondary industry. An economy’s productivity rises as the number of well-educated workers increases (Radcliffe, 2022). According to this viewpoint, primary and tertiary industry-related programmes produce workers with mostly lower-level skills. Vocational students’ high-level job skills are a vital source of human resource development for increasing productivity and incomes and achieving industry economic growth and even excellence (Zin, 2005; Tripathi et al., 2010). Therefore, SVSs should improve programmes in primary and tertiary industries to enhance students’ skills, prepare them for the competitive labour market and develop the GDP.

Analysing CCD

Based on the calculation methods of Eqs. (1)–(6), the overall evaluation values of the structures of SVS programmes and industries are obtained, as shown in Table 7, and the change process is shown in Fig. 2.

Table 7 Overall evaluation values of the structures of SVS programmes and industries.
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Fig. 2
figure 2

Changes in the overall evaluation values of the structures of SVS programmes and industries.

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Figure 2 shows that the changes fluctuated greatly in the overall values of the SVS programme structure, but the overall trend was declining. The change also showed a downward trend in the overall values of the industrial structure. Comparing U1 and U2, the development of the SVS programmes’ structure and industrial structure was divided into three situations: U1 > U2, which is the lagging type of industrial structure development; U1 = U2, which is the type of simultaneous development of SVS programmes’ structure and industrial structure; U1 < U2, which is the lag type of development of the SVS programmes’ structure. In 2013 and 2019, U1 was smaller than U2, so 2013 and 2019 were the lag type of development of the SVS programmes’ structure. From 2014 to 2018, U1 was larger than U2, so these 5 years were the lag type of industrial structure development. During the sample period, the average of the overall values of the SVS programmes’ structure was 0.5699, and the average value of the overall values of the industrial structure was 0.4626. The two did not achieve a good state of promoting development.

Figure 2 also shows that in 2013–2014, the SVS programmes’ structure increased significantly. This is because Tianjin implemented the Pilot Project of Systematic Skilled Talents Cultivation and expanded admissions. In 2018–2019, the SVS programmes’ structure sharply declined. There are two reasons for this: one is that five SVSs stopped admitting students; the other is that the Tianjin Municipal Education Commission reduced the number of admitted students so that the proportion of students in high schools and SVSs was roughly the same.

Table 8 shows the coupling degree and the CCD between the structures of SVS programmes and industries from 2013 to 2019, and the overall level was general. The average value of coupling coordination between the two during the sample period was 0.6794, which is primary coordination. In 2013 and 2014, the CCD achieved good coordination. In 2015 and 2016, the CCD was at the intermediate coordination level. In 2017 and 2018, the CCD was primarily coordinated and reluctant to coordinate. Until 2019, the CCD was reduced to mild incoordination, which should have raised awareness among schools and relevant sectors.

Table 8 Coupling and coordination between the structures of SVS programmes and industries.
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Figure 3 shows all the results of coupling coordination. The coupling degree between the structures of SVS programmes and industries was more significant than 0.8, indicating that the interaction had a high degree of influence from 2013 to 2019. The CCD generally showed a relatively large fluctuation and declining trend. By observing the changing trend, the CCD is found to have peaked in 2014. The CCD 2019 fell into a trough period during 2013–2019.

Fig. 3
figure 3

Coupling coordination of the structures of SVS programmes and industries.

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In 2014, the CCD between the structure of SVS programmes and industries reached a state of good coordination with D = 0.8596, the SVS programmes’ structure contributed maximally to the coupling coordination with U1 ≈ 0.9792, and the CCD between the two greatly increased. After 2014, the CCD gradually decreased. In 2019, the SVS programmes’ structure contributed minimally to the coupling coordination between the two, U1 ≈ 0.0720. The CCD fell to a low point, D = 0.3857, thus resulting in a state of mild incoordination.

Analysis of the correlation between the indicators of SVS programmes’ structure and the CCD

The correlation between the 12 indicators of SVS programmes’ structure and the CCD is calculated by the method of grey relational analysis. The results are shown in Table 9.

Table 9 Correlation and ranking of each indicator in SVS programmes with the CCD.
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From Table 8, the 12 indicators of the programmes’ structure have different influences on the CCD between the structures of SVS programmes and industries. The top 5 are the proportion of students enrolled in primary industry-related programmes (%), the proportion of students enrolled in secondary industry-related programmes (%), the proportion of students admitted to secondary industry-related programmes (%), the proportion of the number of secondary industry-related programmes (%), and the proportion of graduates in secondary industry-related programmes (%). The related indicators of secondary industry-related programmes have a more significant impact on the CCD, and schools should pay attention to the admissions and development of students in secondary industry-related programmes.

As the contribution of the SVS programmes’ structure to the coupling system increases, the CCD between the structures of SVS programmes and industries also increases. It is clear that the industrial structure and SVS programme structure are closely related, and the development of the programme structure significantly impacts the CCD between the two. It is also found that the correlation is relatively high between the indicators of secondary-industry programmes and the CCD in SVSs. This is because Tianjin names the manufacturing sector as its main economic pillar and is the only area among the country’s municipalities and provinces to designate it as a chief economic pillar (Tianjin Municipal Government, 2022). The manufacturing sector is also skilled labour intensive, providing more employment opportunities for vocational school graduates. Therefore, reasonably adjusting the programme scale and quantity structure is necessary to realize the close correlation between the programmes’ structure and the industrial structure. The specific adjustment of admission programmes should be determined according to the local industrial GDP and employer demands.

Previous research has highlighted the significance of coupling and coordination between vocational education and industry (Cabrera-Rodríguez, 1993; Billet, 2009; Powell and Solga, 2010). This study advances this research by taking into account interaction, coupling, and coordination and thus develops a coupling coordination conceptual framework (CCCF) with an index system for the structures of SVS programmes and industries and a quantitative computation model to conduct accurate performance analysis. In doing so, CCCF presents an alternative conceptual framework of skills mismatch and challenges the normative premises and existing implementations of the classical adequationist framework (CAF). CAF distinguishes between skill match and mismatch, namely, that there is a binary relationship between the various types of training and the various types of jobs based on the adequacy of the professional skills (Guillem, 2011). CAF is less accurate for describing industrial structure more dynamically, and it does not result in precise performance analysis because of the lack of precise indicators on match quality.

This study found that the coupling coordination relationship between the structures of SVS programmes and industries is affected by the following crucial factors: interaction between the two, the contribution of programmes’ structure, regional featured or key industries, and changes in admission policies by the local education authority. Our finding that interaction is a crucial impact factor aligns with the studies by Olazaran et al. (2019) and Tran (2021). Our result that links the development of SVS programmes to industry sectors in specific geographical areas is consistent with the findings of other researchers (Raffe and Willms, 1989; Olazaran et al., 2019; Dummert et al., 2019). According to Olazaran et al. (2019), the good match between industrial specialization and vocational education in Basque may be the reason for the greater intensity of the relationship with the metallurgical industry.

Conclusion and limitations

Conclusion

The structure of SVS programmes is closely linked to the industrial structure, and the coupling coordination development of the two is a dynamic rather than a static process. This paper builds a conceptual framework and a quantitative computation model for the CCD between the structures of SVS programmes and industries. Taking Tianjin in China as an example, this paper found that SVS programmes’ structure interacted with the industrial structure as follows: As the contribution of SVS programmes’ structure to the coupling system increases, the CCD between the structures of SVS programmes and industries also increases. Compared with the primary and tertiary industries, the secondary industrial structure is more closely related to SVS programmes’ structure, the interaction between the two has a high degree of influence, and the correlation is relatively high between the indicators of secondary-industry programmes in SVSs and the CCD. It is necessary to adjust the number of programmes, increase the number of students in the secondary industry-related programmes and reduce the number of students in the programmes of the primary and tertiary industries to adapt to the needs of the dynamic industrial structure gradually. At the same time, SVSs should improve programmes in primary and tertiary industries to enhance students’ skills and prepare them for the competitive labour market, develop the GDP and strengthen students’ transition from school to work. Studying the coupling coordination relationship helps explain the CCD between the structures of SVS programmes and industries and is significant for guiding the future policy formulation of secondary vocational education and promoting regional economic development.

There are ten levels of coupling coordination relationship between the structures of SVS programmes and industries: extreme incoordination, serious incoordination, intermediate incoordination, mild incoordination, near incoordination, reluctant coordination, primary coordination, intermediate coordination, good coordination, and excellent coordination. The specificity between the two can be measured by the computation model of the CCD. This study found that the coupling coordination relationship between the two is affected by the following crucial factors: interaction between the two, the contribution of programmes’ structure, regional featured or key industries, and changes in admission policies by the local education authority.

Limitations

Samples are not enough

This study only uses Tianjin as the sample and does not cover more provinces in China. Different regions have different industries and SVS programmes, and they may have some differences in the coupling coordination relationship between the two. Because there are no similar studies in the literature, it is difficult to conduct comparative studies and differential analyses.

The tendency of data selection

We selected SVS students being prepared for the labour market in Tianjin. This study did not include students from vocational high schools and the third and second divisional system (3 + 2-year) in SVSs because they will matriculate to higher vocational education institutions. The third and second divisional system requires admitted students to first study in SVSs for 3 years and then pass the transition assessment test to enter the corresponding programmes in the higher vocational education institutions for 2 years of study.

Future research should collect data from other provinces and municipalities in China to verify the conceptual framework and methods in this paper. Further, studies should explore the differences in relationships between the structures of SVS programmes and industries in various provinces and municipalities, the evolutionary trend of the coupling coordination between them, and the factors driving those relationships.