Measurement of the coupling coordination relationship between the structures of secondary vocational school programs and industries in China

The paper addresses persistent challenges in secondary vocational education (SVE): improving quality, aligning with industrial upgrading, and reducing skill mismatches between graduates and labor market needs. Prior work highlights the value of close ties between vocational education and industry and the importance of responsive curricula and feedback mechanisms. However, quantitative analyses of the interaction between the structures of SVS programmes and industrial structures are scarce. This study proposes a coupling-coordination perspective to examine how the proportional structure of SVS programmes (by primary, secondary, tertiary industries) aligns with regional industrial structures (by GDP and employment shares). The research questions are: (1) What coupling coordination relationship exists between the structures of SVS programmes and industries? (2) How can this relationship be quantitatively measured? (3) What factors affect the coupling coordination relationship? Using Tianjin, China as a case, the study aims to build a conceptual framework, develop a quantitative computation model for the coupling coordination degree (CCD), and identify key influencing programme indicators via grey relational analysis. The work is motivated by the need to reduce mismatches, enhance graduates’ transitions to work, and support sustainable economic development.

The study synthesizes literature on vocational education–industry linkages, responsiveness, and skill mismatch. Prior research indicates: (a) linkages and interaction among providers, students, industry, and employers improve outcomes (Tran, 2021; Cedefop, 2013); (b) relationship intensity is shaped by firm size, sector (e.g., metallurgical), staff qualifications, and innovation cooperation (Olazaran et al., 2019); (c) regional industrial and occupational structures influence educational participation and programme placement (Raffe & Willms, 1989); (d) regional/supply-side determinants affect match quality (Dummert et al., 2019); (e) despite expanded training, skill mismatches persist (Cedefop, 2015). Conceptual approaches include competence-based frameworks, learning strategies, and mismatch typologies (Guillem, 2011; Hanafi, 2012; Badillo-Amador & Vila, 2013), yet purely pedagogical perspectives may underaddress economic linkages (Zhao & Liu, 2019). Coupling/coordination perspectives have been applied in related domains (e.g., industrial economy–vocational education conjugation: Ren et al., 2021; general coupling in systems: Lin & Li, 2021; Liu et al., 2022). The authors identify a gap: quantitative, indicator-based evaluation of the coupling and coordination between SVS programme structures and industrial structures, prompting their conceptual framework and CCD model.

Conceptual framework: The industrial structure is categorized into primary, secondary, and tertiary sectors. SVS programme structure is aligned to these sectors via two first-level dimensions: programme scale (shares of admitted, enrolled, and graduating students by industry) and programme quantity (share of programmes by industry). Industrial structure is represented by two first-level dimensions: GDP and employment (shares by industry). Indicators are measured as percentages. Data sources include Tianjin Statistical Yearbook (GDP, employment; 2013–2019) and SVS programme data (admissions announcements and yearbooks) compiled in Zhan et al. (2023). Indicator sets are summarized in Tables 1, 3, and 4 in the article. Computation of coupling coordination degree (CCD): 1) Indicator weighting: Entropy weighting method determines weights w_j for each indicator to reduce subjectivity. Steps: compute S_ij (proportions of indicator values across years), entropy e_j = -(1/m) Σ S_ij ln S_ij, difference a_j = 1 - e_j, and weights w_j = a_j / Σ a_j. 2) Normalization and contribution: For positive indicators, u_ij = (x_ij - min(x_j)) / (max(x_j) - min(x_j)) (note: the paper presents the equivalent form). Linear aggregation yields system evaluation: U = Σ w_j u_ij, with Σ w_j = 1. U1 denotes SVS programme structure evaluation; U2 denotes industrial structure evaluation. 3) Coupling degree (C) and CCD (D): C = 2 U1 U2 / (U1 + U2)^2. Overall coordination index T = α U1 + β U2 with α = 0.35, β = 0.65. CCD D = sqrt(C × T). The authors adjust coordination level categories to avoid interval gaps, defining ten levels from extreme incoordination to excellent coordination (Table 2). 4) Grey relational analysis (GRA): To identify which SVS programme indicators most influence CCD, the CCD time series is the reference sequence; each SVS indicator time series is a comparison sequence. Grey correlation coefficient ε_r(t) = (X_min + ρ X_max) / (x_r(t) + ρ X_max), with ρ = 0.5; relational degree γ_r = (1/m) Σ ε_r(t). Data and period: Tianjin, China, 2013–2019. Programme scale and quantity data (Table 3); industrial GDP and employment shares (Table 4). The model computes annual U1, U2 (Table 7), C and D (Table 8), and GRA rankings (Table 9).

- Interaction and correlations: Programme quantities and scales by industry correlate with industrial GDP and employment structures. • Secondary industry programmes: strong negative correlation with secondary-industry GDP (P = -0.883, Sig < 0.01) and strong positive with secondary-industry employment (P = 0.893, Sig < 0.01). For programme scale in secondary industry: enrolled vs GDP P = -0.940 (Sig 0.002); graduates vs employment P = 0.937 (Sig 0.002). Admitted vs GDP P = -0.864 (Sig 0.012); enrolled vs employment P = 0.883 (Sig 0.008). • Tertiary industry programmes: strong negative correlations with both GDP (P = -0.939, Sig 0.002) and employment (P = -0.978, Sig < 0.001), suggesting expansion in programme counts did not translate into better alignment with labor demand. • Primary industry: mixed/weaker relationships; in several cases correlations are significant but lower in magnitude (e.g., enrolled vs GDP P = -0.886, Sig 0.008; enrolled vs employment P = 0.882, Sig 0.009). - System evaluation values (Table 7): • U1 (SVS programmes) averages 0.5699 across 2013–2019 and shows fluctuation with overall decline; notable peaks in 2014 (U1 = 0.9792) due to policy-driven admissions expansion; sharp decline in 2019 (U1 = 0.0720) linked to schools ceasing admissions and enrollment caps. • U2 (industrial structure) averages 0.4626 and declines over time (2013: 0.7703 → 2019: 0.2297). • Development types: 2013 and 2019 U1 < U2 (SVS lag); 2014–2018 U1 > U2 (industry lag). - Coupling and coordination (Table 8): • Coupling degree C remains high (>0.8) throughout (0.9418–0.9874), indicating strong interaction. • CCD D fluctuates downward over time; average D = 0.6794 (primary coordination). - 2013: D = 0.8024 (good coordination) - 2014: D = 0.8596 (good coordination, peak) - 2015: D = 0.7823 (intermediate coordination) - 2016: D = 0.7250 (intermediate coordination) - 2017: D = 0.6082 (primary coordination) - 2018: D = 0.5923 (reluctant coordination) - 2019: D = 0.3857 (mild incoordination, trough) - Grey relational analysis (Table 9): Top influencing indicators on CCD are: 1) Enrolled students in primary industry (γ = 0.816) 2) Enrolled students in secondary industry (γ = 0.744) 3) Admitted students in secondary industry (γ = 0.731) 4) Programmes in secondary industry (γ = 0.713) 5) Graduates in secondary industry (γ = 0.682) Lower-ranked indicators include graduates in primary industry (γ = 0.554) and programme distribution in primary industry (γ = 0.577). - Policy and context effects: 2014 increase in U1 and CCD linked to Tianjin’s Pilot Project for Systematic Skilled Talents Cultivation and admissions expansion; 2018–2019 declines linked to five SVSs halting admissions and city-level enrollment reductions. Tianjin’s designation of manufacturing as a main economic pillar increases the influence of secondary-industry-related programme indicators on CCD. - Implications: The secondary industry structure shows the closest relationship with SVS programme structure. Adjusting programme numbers and student allocations—expanding secondary-industry programmes and carefully managing primary/tertiary—can improve coordination. Quality improvements in primary and tertiary programmes are needed to enhance employability and labor-market alignment.

The findings confirm that SVS programme structures and industrial structures are tightly coupled, but coordination quality varies over time and is sensitive to policy and structural economic shifts. High coupling degrees indicate persistent interaction; however, declining CCD reflects a mismatch in development speeds and contributions (U1 vs U2), especially after 2014. The strong alignment with the secondary industry in Tianjin, where manufacturing is a key pillar, demonstrates the importance of regional industrial specializations in shaping effective SVS–industry coordination. The negative associations of programme counts or student shares with GDP in primary/secondary sectors likely capture countercyclical or structural adjustment dynamics and the need to align not just scale but also skill quality. The grey relational results highlight that student flows (admissions/enrollments/graduations) in secondary industry, as well as the number of secondary-industry programmes, most strongly influence CCD—suggesting that optimizing intake and progression in these areas yields the greatest coordination gains. These results address the research questions by: (1) documenting a measurable, dynamic coupling–coordination relationship; (2) providing a CCD model with entropy weighting and normalization to quantify it; and (3) identifying key programme indicators that drive coordination outcomes. Practically, SVSs should align enrolment and curricula with industrial employment demands (particularly in secondary industry), while upgrading the skill quality of primary and tertiary programmes to enhance employability and GDP contributions. Policymakers should consider how admissions caps, school closures, and sectoral priorities affect CCD and continuously calibrate programme structures to the evolving industrial mix.

The study proposes a coupling coordination conceptual framework (CCCF) and a quantitative computation model to assess how SVS programme structures align with industrial structures. Using Tianjin (2013–2019) data, it shows that: (a) SVS programme structures and industrial structures are strongly interactive (high coupling), but coordination (CCD) fluctuates and trended downward, peaking in 2014 and reaching mild incoordination by 2019; (b) secondary-industry-related programme indicators exhibit the highest influence on CCD; and (c) the relative contributions of programme and industrial structures (U1, U2) determine whether SVSs or industry are lagging in a given year. Policy and management implications include adjusting programme numbers and student allocations toward secondary industry, improving skill quality in primary and tertiary programmes, and calibrating admissions to local GDP and employer demand. The ten-level CCD classification provides a practical tool for monitoring coordination status. Future research should validate the framework with broader regional datasets, analyze inter-provincial differences, track evolutionary trends, and identify drivers of change to guide national-level SVS planning and economic development strategies.

- Geographic scope: Single-case study of Tianjin; results may not generalize across provinces with different industrial and SVS profiles, limiting comparative analysis. - Data scope: Focus on SVS students entering the labor market; excludes vocational high schools and 3+2 (secondary-to-higher vocational) tracks that matriculate to higher vocational institutions, potentially biasing programme scale indicators. - Comparative literature: Lack of similar quantitative studies constrains benchmarking and differential analyses. Future work should expand to other provinces/municipalities, investigate regional differences in SVS–industry coordination, examine temporal evolution, and identify causal drivers.