Models and criteria for monitoring the quality of education

Introduction. The article focuses on monitoring the quality of education, analyzes the shortcomings of modern models and criteria functioning in this area. The purpose of the study is to build models and develop a criterion for their implementation in the field of education, free from these shortcomings. Materials and Methods. The methodology of solving this problem is based on the integration of mathematics and pedagogy (education studies) in the wide range of interactions of educational technologies, mathematical statistics and new results obtained by the author in the field of processing the findings of educational research investigations. Results. Achieving the goal includes three problems: the first is to build models for the study of dependent and independent samples; the second is to develop a single criterion for their implementation for the constructed models (instead of 12), free from known shortcomings; the third is to test and compare with other criteria in the process of solving specific problems in the field of education. The listed problems have been solved. Conclusions. The constructed models and the specified criterion are applicable for the study of dependent and independent samples, determine the direction of change caused by the introduction of a new educational technology, generalize almost all models and criteria known in this area.