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Abstract: The article discusses the idea of assessment as a diagnostic procedure of forming the final results of teaching mathematics. There is an explanation of priority, role and place of using diagnostics in teaching process. At the same time the procedure of assessment is a mechanism of diagnostics in the process of teaching mathematics, which performs the function of education quality management, realizing complex approach to the assessment of the results of learning and assessment of individual achievements of students. Multifunctionality and multifold of assessment category are in the variety of different approaches to the definition of that phenomenon. The necessity of creating a new approach to the assessment of final results based on the Federal State Educational Standard of Secondary Education is argued. Transition to the «criterion-based», substantial assessment and to learners’ individual process assessment is suggested. The meaning of the concept «universal educational activities» as «knowledge in activities» is discussed and the ability of using knowledge gained in practice is explained. The modern structure of control and assessment system is described. New ways of assessment are analyzed, such as forming assessment and summary assessment. The method of self-assessment in forming assessment is possible. The author’s structure of forming assessment and the algorithm of criteria assessment are given. The meaning, function and tools of summary assessment are described. There is a conclusion that purposeful usage of criterion assessment in teaching process lets learners become more active in assessment of their studying results.