The teacher education management system is crucial to the operation of the teacher education system (TES). It is the core institutional system of the TES, which stipulates the management authority and functional scope of the relevant departments of the TES. After the new pluralistic and open TES is formed, the original management system must be adjusted accordingly. In this context, this article integrates public mental health (PMH) into the diversified and open management system of TES and then uses a neural network to evaluate and complete the following tasks: (1) this article introduces the development status of diversified and open TES management systems at home and abroad and the importance of public psychology courses to teacher education. (2) The framework of TES integrating PMH is proposed, and then the principles of BPNN and gray wolf optimization (GWO) algorithm are introduced, and the IGWO-BPNN model is constructed accordingly. (3) The convergence and fitness of the IGWO-BP model and the GWO-BP model are compared through experiments, which proves the superiority of the performance of the IGWO-BP model. The optimal model is constructed by selecting parameters, and then the output of the model is compared with the expert evaluation results, and the error is small. It is proved that the model has superior performance in evaluating the professional quality of teacher education. (4) This article selects three professional quality evaluation indicators of teacher education to compare the changes before and after the integration of PMH. The results show that the proposed diversified and open management system of TES integrating PMH can effectively improve the professional quality of teachers in all aspects.
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