In dissertation there is justified the theoretical basis of the students' achievements assessment problems in the studying process structure. There is clarified the sense of the following concepts: "students' achievements assessment" (complex and multicomponent determination process of students' achievements level, skills and know-how, creative work experience according to prescriptive norms and syllabus; permanent process: during the lesson, watching the pupil's learning activity, answers' evaluation, running different types of work by the pupil), "school grade" (representing in relative marks-grades, evaluation by teacher the level of students' achievements assessment). Considering some criteria (changes in regulatory documents regarding students' achievements assessment, changes in the structure of education and of the educational institutions types; problem formulation in the pedagogic theory, socio-political changes) there is established the rough periodization and determined the specifics of students' achievements assessment organization dynamic in the Ukrainian educational system of 80s of the 19th century - early 40s of the 20th century: I period (80s of 19th century - 1917) - intensification of students' achievements assessment system formation in the different types of state and private primary and secondary educational institutions in the imperial era; II period (1917-1931) - experiments and research in the students' achievements assessment considering foreign experience in the period of Ukrainian people liberation competitions and early soviet period; III period (1931-1944) - standardization of students' achievements assessment organizational and methodological aspects in the established unified state soviet school in the soviet era. There are determined and described in the historical periods such aspects, as content (part of studying process), functions (educational, developmental, motivating, corrective, disciplinary), types (current, thematic, semestrial, annual, transfer), forms (during the lesson, exam, test), criteria (knowledge quality (fullness, depth, consistency), creative approach to the tasks fulfillment), ways (grade and its characteristic), methods (oral and written answers, self-guided works and examinations, dictations, reports, compositions, exercises, theorem proving) of students' achievements assessment at primary and secondary schools. In the research there is established that students' knowledge assessment in the education institutions in the 80s of the 19th century - early 40s of the 20th century (in the imperial period and to the twenties of 20th century there had been functioning primary (lower and higher schools, zemstvo schools), secondary schools (real, commercial, exchange and theological schools, seminary (for boys), eparchial schools for girls, gymnasiums (both for girls and boys); in the twenties of 20th century in the USSR school education structure along with orphan asylum there existed a unified labor school; in the thirties-forties on the Ukrainian territory there was established unified state soviet school, that included: primary (1-4th form), modern secondary school (1-7th form) and secondary school (1-10th form), technical and career schools) was made at the lessons, during the writing tasks, tests (in twenties) and at the exams. In the comparative aspect it was found that for all the periods knowledge controlling function (motivating, corrective, prognostic, educational-testing, developmental, disciplinary) was stable. In different periods students' knowledge assessment methods were changing: in empire period - 5 and 12 grade scale, in grade judgements; recording into class "golden stand", certificate of merit, medal, student's report card; list of pupils in class journal according to the grades; in the 1917-1931 - 3 and 4 grade scale; in grade judgements; oral review; personalized color stamps; establishment of the diaries and characteristics for each pupil; 1931-1944 -5 grade word scale in the 30s of 20th century and digital - since 1944; in grade judgements; notebook record, class journal, social competition table, red flags. For the determined periods there were typical such methods of students' achievements assessment: in empire period - written creative works (compositions, dictogloss); exercises, theorem proving; in the twenties of 20th century - oral and written answers, self-guided works and tests, dictations, reports, handiworks, notebooks, drawings; 1931-1944 - reports, examination tasks etc. There is described the contribution of famous pedagogues and educationalists into the development of theoretical basis of the students' knowledge assessment in the investigation period. Great attention was paid to such aspects as content, functions, types, forms, criteria, ways and methods of students' achievements assessment. There was generalized a positive and negative experience of students' achievements assessment in practice of general educational institutions of the 80s of the 19th century - early 40s of the 20th century. Positive aspect of the students' achievements assessment in practice of general educational institutions of determined period meant that the grade performed educational, developmental, motivating, disciplinary functions; redounded to the implementation of different types and methods of assessment. All the while, negative aspect meant: grades not by the criteria, but by personal attitude of each teacher, that leaded to over- or under-estimation; not all educational institutions had used differentiated assessment methods, that could encourage good pupils results in studying.
