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in the keywords:  teaching and cognitive activities continuity of mathematical education
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The article deals with important didactic and methodological aspects of the process of teaching mathematics in modern school. Analysis, comparison, systematization and generalization of approaches to defining the general model of the teaching process and their adaptation to the modern social demands for the educational sector’s functioning, generalization of the teaching experience demonstrates the need for inclusion in its structure the phase of correction as it is, providing cyclical training, continuity of mathematical education, and thus increase of the students’ knowledge and skills quality level, their strength and consistency, broadening students’ understanding of the necessity of conscious attitude towards the program material mastering. Therefore, the following stages of the teaching process were considered by us to be the most important ones: the targeting one, the motivational one, the substantial one, the action-operating one, the controlling and evaluative one, and the correctional-regulative. At each stage among the defined the teacher’s activity (teaching) and the research and learning activities of students have their specific features, the essence of which is reflected in the article. The procedure of correcting is determined and characterized by the specific needs, motives, purposes, and terms for goals achievement, its planning and performance, the nature, the specific features and implementing of which are closely examined in this article. The presence of the featured ways of correcting the level of students’ achievements in mathematics allows considering correction a separate teaching and learning activity. All components and actions implemented in correction are individually oriented, and its efficiency and effectiveness is ensured only by the student’s hard work to remove the gaps in their own knowledge of mathematics. Thereby, the correction of students’ knowledge and skills has a significant impact on the entire educational process and an exclusive importance to ensure its effectiveness and continuity. Perspective directions for further research are related to the creation of modern methodological systems of correction (particularly self-correction) of the students’ learning outcomes, development of the appropriate methodological and didactic software, research for the opportunities in informational and communicational technologies fields as the effective means for the students’ mathematical knowledge correction.
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