Performance evaluation of industry-education integration in higher education from the perspective of coupling coordination-an empirical study based on Chongqing

Based on the synergy theory, the industry education composite system is constructed. Under the framework of the industry education composite system, the industry-education integration refers to the evolution and development trend of the elements of the industry sub- system and the education subsystem infiltrating, crossing, coupling and complementing each other in the process of achieving the common goal, from disorder to order, from chaos to con- sistency. From this perspective, the key to achieving good performance of the industry-educa- tion integration lies in the complementary advantages of industry and education, collaborative development, and the synergistic effect of 1+1>2. This requires the education sector and the industrial sector to rely on their respective advantageous resources, based on mutual trust con- tracts, to serve economic and social development as the starting point, to take mutual benefit and win-win as the driving force, and to take school enterprise cooperation, project coopera- tion, technology transfer and joint development as the carrier, to teach in production and pro- duce in teaching [35], and to cooperate closely to cultivate people, forming an optimized combination and highly integrated mode [36]. The integration of production and education is the organic combination of "productive learning" and "learning production", "productive teaching" and "teaching production" [37]. The performance of the industry-education integra- tion shows the interactive coupling and collaborative development of industry and education

in terms of scale and structure at the macro level, and the collaborative education of school enterprise cooperation at the micro level. In a complex system, coupling refers to the phenomenon that two or more systems or forms of motion influence each other through various interactions, and this coupling effect can be reflected by the degree of coupling. Collaboration refers to the harmony and consis- tency between systems or their components during their development and evolution, and this degree of collaboration can be described by the degree of collaboration. At the phase transition point, the internal variables of the system include fast relaxation variable and slow relaxation variable, and the slow relaxation variable, that is, the order parameter of the system, plays a decisive role in the phase transition process of the system. The synergistic effect between the order parameters within the system dominates the trend of the system’s evolution from disor- der to order, and determines the characteristics and laws of the system’s phase transition. The degree of coupling and coordination determines the type of order and structure that the sys- tem will adopt when it reaches the critical region [38]. Based on the complex system of industry and education, a performance evaluation model for the industry-education integration is constructed from three aspects: the efficacy coeffi- cient of order parameters, the order degree of subsystems, and the coupling collaboration degree of the complex system. Assume that the order parameter in the evolution process of the

industrial education composite system is ui(i = 1,2), that uij(j = 1,2,3,. . .,n) is any component of the order parameter ui, and that the value is Xij. The upper and lower limits of the order parameter are αij and βij, respectively, and the contribution that this order parameter promotes the orderly development of the composite system can be expressed as UðuijÞ ¼ Xij bij aij bij ; uij has positive effect aij Xij aij bij ; uij has negative effect 8 > > > < > > > : ð1Þ In formula (1), U(uij) is the order degree of the order parameter uij, and U(uij) 2 [0,1]. The larger the value is, the greater the contribution of the order parameter to the system. The total contribution of the order parameter to the system can be achieved by integration, and the PLOS ONE Performance evaluation of industry-education integration in higher education based on coupling coordination PLOS ONE | https://doi.org/10.1371/journal.pone.0308572 September 18, 2024 6 / 22