The article defines the normative documents which regulate the assessment system in general secondary education institutions of Ukraine, in particular at the level of primary school. The views of foreign scholars (W. Stones, A. Kelly, T. Kellaghan, W. Greeny) on the essence of assessment, which means any procedure or activity used to gather information about the knowledge, skills, attitudes of a student or groups of students. The attention is focused on the fact that in the Ukrainian school, assessment is considered as a process of obtaining data on the state of formation students’ learning outcomes, analysis of these data and its formulation based on judgments about the object being evaluated. The purpose of assessment is to create enabling environment for the development student’s talents and abilities, the formation of competencies and cross-cutting skills in accordance with age and individual psychophysiological characteristics and needs, as well as determining the quality of education and finding ways to improve its effectiveness. The essence of formative assessment is revealed - a type of current assessment, which is aimed at clarifying individual problems in mastering the students’ program material and preventing difficulties in the subsequent stages of learning. The distinctive features of formative assessment in comparison with the current point assessment at the level of subject, object, forms, nature of assessment are determined. The algorithm of the teachers’ actions in the process of organizing formative assessment of primary school students is characterized (formulation of objective and understandable for students learning goals for a certain period; informing students about assessment criteria; providing students with feedback on their academic achievements in accordance with defined goals; creating conditions for reflection, adjustment of the educational process taking into account the results of assessment and students’ learning needs ). Techniques for organizing formative assessment of elementary school students are proposed: "Cards for clarifying the material", "Supplement statements", "False statements", "Find differences", "Two stars and one wish", "One minute essay", "Educational portfolio", etc.