In the work we define the theoretical and methodical basis of the complex organization of educational and cognitive activity of students of the basic school in teaching mathematics. The essence of the complex organization of the studied type of students’ activity is disclosed in the context of paradigm, activity of morphology, information discourse and characterized as a process unfolding in the main school during learning of mathematics on the use of various components of the poly-means basis, is carried out taking into account unequal forms of presentation of information of mathematical content, is built into various systems of interaction between the teacher and students in order to their knowledge of mathematical objects. To the poly-means basis of the integrated organization of educational and cognitive activity of students we include: the means of poly-activity basis (perceptual, problemoriented, search, variability, activity-observation, heuristic, research, educational and research, project work, graphic, practical activities and modeling activities); means of content basis (task, task) and means of constructing interaction with others (communication). The work characterizes the material, materialized, symbolic, mixed forms of information representation of mathematical content and the functioning of the systems of teacher-student interaction with students in the knowledge of mathematical objects, in particular. The essence of the notion "educational and cognitive activity" is disclosed in the context of system-oriented activities and interpreted as a kind of educational activity aimed at obtaining true and subjectively new knowledge about the object of knowledge and performed by the student independently and in interaction (direct and indirect) with others. The concepts which make up the terminological framework of the semantic field of the notion "educational and cognitive activity" are defined and documented. This work considers the organization of educational and cognitive activity of students as a process is deliberately realized with the use of appropriately selected means of polymeans basis and serves students to receive true and subjectively new knowledge about the object of cognition in the process of mental processing of perceived information during: the implementation of the mental effect of "goal-setting"; drafting an adapted version of the cognitive act of the action-components of the reference version of the cognitive act; self-monitoring on the basis of performing actions to verify the understanding of information entering the brain; reflection using the phrase-support, which drives the course of self-esteem considerations. We reveal the processes of sensory-perceptual display of mathematical content information in the images of objects of cognition and reproductive-creative use of images of objects of cognition in the process of formation of mathematical knowledge, expressed in representations and concepts. The components, criteria, indicators, characteristics of the readiness levels of the teacher of mathematics for the complex organization of educational and cognitive activity of the pupils of the basic school and students for the implementation of this type of activity during the lesson and the extra hours are determined. In the thesis, it is substantiated the necessity of introducing into the scientific circle the concept of "eco-inferential approach" to designations: 1) the scientific position regarding the organization of students' activity on the basis of purposeful harmonization of the effects of age and life crises; 2) the practical realization of ecologization as the teacher's orientation to minimize "life crises" experienced by students or individual learners as a result of special occasional circumstances that have become deployed on the personal, interpersonal or social levels, are revealed in a family circle or in a classroom; 3) flexible introduction of integration and differentiation in order to mitigate the course of age and life crises. During the pedagogical experiment, the effectiveness of the model of a comprehensive organization of educational and cognitive activity of students of the basic school in teaching mathematics and methodological support as a component. The determined criteria, indicators, characteristics of the level of readiness of the participants in the process served as the basis for formulating the conclusions about the effectiveness of the implementation of the experimental model in the educational process and the methodical support as its component.
