Data on the author of scientific research:

Surname, name, patronymic: Holodyuk Larysa Stepanivna.

Scientific degree: Doctor (habil.) of Science in Pedagogy.

Scientific supervisor, developer of electronic version of the project, executor of the project

e-mail: golodiuk_larysa@ukr.net

Title of scientific research: Theoretical and methodological foundations of a comprehensive organization of educational and cognitive activity of primary school pupils in mathematics education.

Year of defense: 2018.

Keywords of the dissertation: educational and cognitive activity, ecointedifferential approach, cognitive act in the student's educational and cognitive activity, poly-means basis, means of poly-activity basis, comprehensive organization of educational and cognitive students activity.

Key words of the monograph: perceptual activity, problem oriented activity, search activity, variation activity, observation, heuristic activity, research activity, educational activity, project activity, graphics activity, practical activity, and modeling activity.

Sources of coverage of scientific research results:

1. Golodiuk Larisa. On the Problem of Shaping Teaching and Research Skills of Mathematics Students [American Resource Library] // American Journal of Educational Research. 2014 2 (12B). do: 10.12691 / education-2-12B-8. – Access mode: http://www.sciepub.com/portal/search?q=Golodiuk Larisa

2. Golodiuk L.S. Research tasks in mathematics. Herald of Cherkasy University. Series: Pedagogical Sciences. Issue 20 (353). Cherkasy: red. type. from. ChNU after B. Khmelnytsky, 2015. pp. 88-96.

3. A conceptual framework for improving the mathematical training of young people: [monograph] / Eds. prof. N. Tarasenkova, & L. Kyba. – Budapest: SCASPEE, 2016. – 212 p. (4.3. Research Approach in the Current School Mathematical Practice / Golodiuk L., pp. 110–127).

4. Golodiuk L. S. Organization of educational and cognitive activity of the students of the main school in the study of mathematics during the lesson and extra-curricular time: the theoretical aspect: a monograph. Kropyvnytsky: Individual entrepreneur Alexandrova M.V., 2017. 404 p.

5. Golodiuk L. Functioning and Development of Different Systems of Arranging Students’ Educational-Cognitive Activity in Learning Mathematics / Current Status and Prospects of Mathematical Education : [monograph] / I. Akulenko, D. Bobyliev, O. Chashechnikova, Z. Chukhrai, L. Golodiuk, V. Kirman, T. Krylova, B. Lazarov, Yu. Leshchenko, I. Lovyanova, I. Sitak, N. Tarasenkova, M. Tretyak, I. Vasilenko, & K. Vlasenko; Eds. prof. N. Tarasenkova, & L. Kyba. – Budapest : SCASPEE, 2018. – P. 9-36.

6. Golodiuk L.S. Theoretical and methodological foundations of the complex organization of educational and cognitive activity of students of the main school in the study of mathematics: author's abstract. of Dis. for the Sciences Degree of Dr. Ped. Sciences: 13.00.02 – theory and methods of teaching (mathematics) / L.S. Golodyuk – Cherkasy, 2018. – 40 p.

7. Golodyuk L.S. Theoretical and methodological foundations of the complex organization of educational and cognitive activity of the students of the main school in the study of mathematics: diss. ... Dr. Ped. Sciences: 13.00.02 – theory and methods of teaching (mathematics) / L.S. Golodiuk – Cherkasy, 2018. – 652 p.

Terminology block:

1. The concept introduced into the scientific circle for the first time (with the indication of the source)

The concept of "ecointedifferential approach" was introduced into the scientific circle for the first time by the notation:

1) a scientific position on the organization of students' activity on the basis of purposeful harmonization of the influence of age and life crises;

2) the practical realization of ecologization as a teacher's orientation to minimize "life-threatening crises" experienced by students or a particular student due to special circumstances that have become deployed on the personal, interpersonal or social levels, are found in a family circle or in a classroom;

3) the flexible introduction of integration and differentiation in order to mitigate the course of age and life crises [6, p. 334]

For the first time, a poly-means basis was defined, which includes: means of a poly-activity basis (perceptual, problem-oriented, search, variation, activity-observation, heuristic, research, design, practical and modeling activities), means of content basis (task) and means of constructing interactions with others (communication (direct, indirect)) [6].

2. The interpretation of the concepts is specified (indicating the sources (a)):

The comprehensive organization of educational and cognitive activity of students of the main school in the study of mathematics is a process that unfolds from the use of the components of the poly-means basis of the organization of activities, is carried out taking into account the unequal forms of presentation of information of mathematical content, is built into various systems of interaction between teachers and students in order to know mathematical objects by them [6, p.400].

Educational and cognitive activity is a kind of educational activity, aimed at obtaining true and subjectively new knowledge about the object of knowledge and is performed by the student independently and in interaction (direct, indirect) with others [6, p.399].

The subject of educational and cognitive activity is a carrier of cognitive activity; used in relation to teacher and students; the activity of the subject is manifested at the level of interaction with other actors and at the level of knowledge of the object [6, p.399].

The object of educational and cognitive activity is what the subject interacts with; those on which his actions are directed; that fragment of objective reality (the object material, materialized, symbolic, mixed forms of presentation of information of mathematical content), which becomes a known [6, p.399].

The purpose of the general (specific) educational and cognitive activity are the prediction of the main expected result of both the activity of the teacher, and the activities of students in relation to the process as a whole (or in relation to a specific lesson) [6, p.399].

The goals of educational and cognitive activity are marks, which are imposed by the teacher and the students as a direction of movement towards the result, predetermined by the purpose [6, p.400].

The process of educational and cognitive activity is the definition and consistent implementation of actions in the composition of activities in accordance with its purpose [6, p.400].

Cognitive act in the teaching and learning of the student is a process which is a set of actions consistent implementation of which contributes to a true and subjective knowledge of the new object of knowledge according to the specific purpose of activity (tasks), achieved through mental processing of perceived information [4, p.323; 6, p.400].

The result of educational and cognitive activity is the desired changes in the subject of educational and cognitive activity; mental education (knowledge, skills) – the immediate results of the action to obtain true knowledge about the object of knowledge and the ability to carry out activities [6, p.400].

Annotation block:

1. Annotation on scientific research

The theoretical (goals, scientific approaches, didactic principles, preconditions, subjective factors, conditions, components of readiness of the process participants) and methodical (content, forms, methods, poly-means basis, system of interaction of process participants, stages of achievement of the goal) the basis of the complex organization of educational and cognitive activity of pupils of the basic school in mathematics teaching. Paradigm, activity morphology and informational discourse of this process are characterized. The essence of the concept of "educational and cognitive activity" is interpreted in the context of system-specific activities; concepts that constitute the terminology framework of its semantic field are defined and interpreted. The following are included in the policy-based basis: means of poly-activity basis (perceptual, problem-oriented, search, variable, activity-observation, heuristic, research, research, design, graphic, practical activity and modeling activities); means of content basis (task,); means of building interaction with others (communication (direct, indirect)). The essence of processes of sensory-perceptual display of information of mathematical content in 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, concepts, judgments and inferences) is disclosed. Components, criteria, indicators, characteristics of the readiness of the teacher of mathematics and students as process participants are determined. The expediency of introducing into the scientific circle the concept of "ecointedifferential approach" is substantiated. The effectiveness of the model of the complex organization of educational and cognitive activity of students of the main school in the teaching of mathematics and methodical support as its component is substantiated and experimentally proved.

2. Information about the components of the scientific work that can be implemented in the educational process in order to make modernization changes:

– disclosure of the essence of the perceptual [6, p.341], problem oriented [6, p.342-343], search [6, p.344-345], variational [6, p.346], observation activities [6 , p.349], heuristic [6, p.350-351], research [6, p.353-354], educational-research [6, p.359], design [6, p.360], graphic [ 6, p.361], practical activity [6, p.362] and modeling activities [6, p.363-364] as a poly-activity basis for the organization of educational and cognitive activity of students of the main school in the teaching of mathematics;

– definition of the characteristics of the three management cycles implemented by the teacher of mathematics (the subject of management) in relation to the object of management (the method of manifestation by students of different means of activity) during the educational and cognitive activity on the basis of the continuous circulation of information [4, p.297-308; 6, c. 285-293].