The article reveals some findings of a study on a problem associated with developing objective criteria for evaluating the quality of general art education for basic and advanced learning of art and culture items. The article also contains an analytical review of existing methods to assess the quality of general art education (professional, fine art, problem development); shows the criteria for each of the approaches, and demonstrates their obvious advantages and some limitations. Based on the study conducted, the authors introduce optimum indicators for an objective assessment of the quality of education for schoolchildren grades 1 through 9 on such disciplines as "Music", "Visual Arts", "World Art Culture" in a modern secondary education school (such as intellect, creativity, communicability, etc.); describe the newly developed criteria to assess the quality of teaching art and culture-related disciplines (knowledge of the subject matter, methodological training and interaction with students and colleagues, creative approach to teaching and technical or artistic performance skills). The work outlines general, specific and additional criteria for assessing the quality of general art education system (educational esthetic environment in the school, participation in School Olympics on art and global art culture, presence of intra-school model of extracurricular activities on general culture education, etc.). The article draws conclusions on the necessity and possibility of assessing the education quality by a combination of three components -children's education, teaching activities for art and culture-related disciplines, and organization of the entire general art education system in the modern-day school.