1 Introdução

Leonid Vladimirovich Zankov (1901-1977), Soviet psychologist and frequenter of the circle of L. S. Vygotsky, was responsible for relevant scientific research in the former Soviet Union, in which he questioned the traditional methodology of primary education, marked, according to him, by the simplification of school material, the limitation of theoretical knowledge, and the valorization of the formation of habits, multiple repetitions. In overcoming traditional teaching, L. V. Zankov proposed that the school should enhance the formation of theoretical knowledge as well as the integral formation of students.

According to Aquino (2013) and ^{Puentes and Aquino (2019}), L. V. Zankov is one of the precursors of a new didactics, created from the assumptions of L. S. Vygotsky. For this, he created a didactic system based on Vygotskian concepts such as the Zone of Near Development, the unity between teaching and development, and the unity between the affective and the cognitive. Its experimental system was applied longitudinally in the former Soviet Union, with recognized scientific success.

In the 1950s, L. V. Zankov carried out with his colleagues from the Russian Academy of Pedagogical Sciences his study in which they compared lectures with classes that made use of visual aids. 25 elementary schools were involved in the research, and the unexpected result of this study was that student development was surprisingly slow in both approaches. In the continuity of the study, they realized that the limited scope of the curriculum and the monotonous practice of repetition contributed to this result (^{GUSEVA, 2017}). Subsequently, a didactic system was implemented in stages. The first experiment was carried out through a pilot project in a single room in an elementary school in Moscow, where a pedagogical laboratory was created so that the researchers could follow the experimental room. By the early 1960s, it had reached more than 20 urban and rural schools, as L. V. Zankov and his group thought that the experiment should be carried out under varying conditions. A year later, that number had reached 100 rooms, with official support. In 1966-1967, there were more than 1200 rooms in different republics and territories of the former Soviet Union. The implementation involved the preparation of teachers, the production of experimental manuals, and consultation books for masters.

Considering the result of this implementation, L. V. Zankov's team developed school programs, materials, curricula, and textbooks based on Zankovian didactic principles. Thus, "many teaching techniques and methodologies for specific areas have been changed, and many new teaching methods have been developed." (ZANKOV,1984 apud^{GUSEVA, 2017}, p. 238).

This article presents a synthesis of the theoretical and methodological assumptions of the Zankovian didactic system, based on the reading of his works and the collaborations of national and foreign authors. The methodology has been a bibliographic review of the texts available in Brazil in Portuguese. Initially, the didactic systems implemented in the former USSR in the twentieth century, which originated in the Historical-Cultural Theory, in whose context the Zankovian system is inserted, are addressed. Next, a comparison of the philosophical and psychological assumptions of L. V. Zankov's didactic system is made in order to present later the didactic principles enunciated by the author as well as methodological principles for the organization of the proposed experimental system. Finally, the students' development process is exposed, which includes observation activities, mental activities, and practical activities. These are considered units, which allow us to know the concrete laws of the whole from the relations between them.

2 The Zankovian system in the context of other systems

The historical-cultural conception of psychology is developed in the context of Soviet psychology research, beginning with the Socialist Revolution of 1917 and the formation of the Union of Soviet Socialist Republics (USSR), with the goal of establishing philosophical bases based on dialectical materialism, led by L. S. Vygotsky and his collaborators, including A. R. Lria and A. N. Leontiev. Theoretical and methodological approaches to the school context evolve in the framework of discussions on the topic of development and learning, which may be defined as didactic systems. (^{NÚÑEZ; LEÓN; RAMALHO, 2020}).

These didactic systems, which developed from the Historical-Cultural Theory, were based on the Activity Theory and have the character of developmental teaching. Among the researchers who sought to continue the theses of L. S. Vygotsky in the 1940s, S. L. Rubinstein, A. N. Leontiev, P. Ya. Galperin, D. B. Elkonin, V. V. Davidov and V. V. Repkin; thus emerging, with the last three, the Theory of Study Activity and Developmental Learning.

E This is why it is possible to affirm that the Developmental Teaching of Activity still represents the most genuine pedagogical movement engendered within the historical-cultural approach of psychology and Marxist didactics, without, therefore, omitting the theoretical and methodological limitations associated with it, proper to a given historical moment and a certain level of development of science. (^{PUENTES; AQUINO, 2019}, p. 348).

Developmental Teaching was organized into different systems, among them the Zakhovian one. They can be classified as developmental systems, those that have the theoretical matrix in L. S. Vygotsky, Rubinstein and A. N. Leontiev, but each of them has its own particular interpretation of some of the main postulates of these authors, primarily the postulates of L. S. Vygotsky, producing diverse positions and theoretical divergences, which we will not deepen here, because our objective is the presentation of the system of L. V. Zankov and not the comparison between them.

Thus, the Zankovian didactic system was not the only one that originated from the Vygotskian theses from a developmental perspective, because parallel to it, others developed such as Galperin-Taliszina and Elkonin-Davidov-Repkin, according to Longarezi (2018), have a common theoretical matrix but present particularities in the conception and implementation.

The Elkonin-Davidov-Repkin and Galperin-Talizina systems had their main theoretical references in the field of psychology, in L. S. Vygotsky, being the representatives of the Moscow school, centered on the study of activity. L. V. Zankov's system, on the other hand, was mainly oriented by the works of L. S. Vygotsky and K. D. Ushinski, whose studies emphasized the learning and development of students' personalities. With this, L. V. Zankov and his collaborators were pioneers in conducting longitudinal pedagogical experiments to prove L. S. Vigostsky's thesis that the period of schooling as a whole is the ideal period for teaching operations that require awareness and deliberate control, boosting the higher psychological functions to the ideal level of their maturation.

The didactic system of L. V. Zankov is a little-known system in Brazil and aroused the interest of the authors of this chapter by their declared concern with affectivity in teaching-learning relations, among other aspects that will be treated in this text.

In the Zankovian system, the importance of the role played by the methods that trigger the spheres of emotion and will is revealed, meeting the needs classified by the author as "spiritual"⁵. Unlike other systems, it emphasizes the relationship between the formation of human thought and emotions in understanding the being who learns as a complete and integral being. "No other didactic system has expressed concern for studying the relationship between cognitive and emotional aspects in the process of integral child development. The focus has always been on the development of cognitive functions." (^{PUENTES; Aquino, 2019}, p. 361). Finally, the Zankovian system explicitly considers the aspects of the personality of the learner, understanding that emotions have a motivating force that can raise or reduce vital activity.

When analyzing the evolution of the developmental didactic system of L. V. Zankov against the systems of Galperin-Talizina and Elkonin-Davidov-Repkin, based on the assumptions of L. S. Vygotsky and S. L. Rubinstein, it is perceived that his attention was focused on the proposition of a didactic system that would allow to achieve the optimal result, that is, the integral development of the students, which considers together the affective and cognitive aspects of the learning process.

The author starts from the assumption that the relationship between teaching and development is determined by the specific methods used for the treatment of contents in the classroom, while the Elkonin-Davidov-Repkin system considers this relationship dependent on the content that integrates the school curriculum, from which the methods are only a derivation.

^{Davidov (1988}), accepting the Vygotskian assumptions and those of Activity Theory, dedicated his work to the investigation of the "studying activity" of schoolchildren. The author considers that "... entering school marks the beginning of a new stage of the child's life, in which much is changed both in the aspect of external and internal organization" (p. 76). Thus, according to Davidov's assumptions, studying activity is the dominant activity of school-age children.

^{Davidov (1988}) emphasizes in his studies the importance of knowing the characteristics of learning activities and how students perform their actions in the process of knowledge acquisition. Based on this understanding, students should be aware of their actions because, according to Davidov (1988, p. 178):

[...] the need for a study activity encourages students to assimilate the theoretical knowledge, that is, the motives that allow them to assimilate the procedures for the reproduction of this knowledge through the study actions directed to solve the study tasks (we recall that the task is the unit of the objective of the action and the conditions to achieve it)⁶. (our translation)

Thus, the author proposes a didactic model centered on the study activity that aims at the assimilation of theoretical knowledge based on a need and reasons stimulated by it and is accomplished through actions that materialize in study tasks. The Elkonin-Davidov-Repkin system emphasizes the formation of theoretical thought, even considering that this is the purpose of the school.

The other system, Galperin-Talizin, has as its precursor Pyotr Yakovlevich Galperin (1902-1988), an eminent scientist, physician, and psychologist of the former Russian Soviet Federative Socialist Republic and one of the collaborators of Vygotsky and Leontiev. P. YA. Galperin developed the Theory of the Planned Formation of Mental Actions and Concepts. This theory, according to ^{Núñez, León e Ramalho (2020}, p. 15), contributed to the understanding of the "phenomena and processes that occur during the formation of the mental plane and its dialectical interrelationship with the verbal and practical planes of the learning activity", as well as offered contributions to the orientation of teaching in the Near Development Zone (NDZ). With regard to the didactic system, the research and contributions of Nina Fiódorovna Talízina (1923-2018) play a fundamental role, applying Galperin's general propositions to the teaching-learning activity and seeking to demonstrate the close relationship between Vygotsky's Zone of Near Development and that of P. YA's Guiding Base of Action. Galperin (^{SOLOVIEVA; QUINTANAR, 2020}).

The focus of this system is placed on human action as a process, which occurs in stages: the material or materialized, the concrete perceptive, the schematic perceptual, and the verbal. Human action, according to Galperin, has three functional moments: guidance, execution, and control. The orientation phase concerns the anticipated representation of the task by the student and the conditions necessary to perform it. This plan for future action was called the guiding basis of the action (BOA). For P. YA. Galperin (1959/2009), mental action can be considered the ability to mentally perform a transformation of the object.

Hence, according to ^{Nunez, Leon, and Ramalho (2020}, p. 15):

The Galperin-Talízina System is a way of explaining the dialectical nature of teaching-learning processes, in which learning is conceived as a specific type of guiding activity, revealing a point of view of what learning is in the school context and the role of teaching in school.

L. V. Zankov, in his didactic system, defends the general "optimal" development of the student, considering that one of the main objectives of his education system is "to awaken the independent, restless thought of the student, linked to living emotions" (ZANKOV, 1984, p. 62). "Optimal" development refers to the relationship between teaching and development in which the proper organization of the teaching process leads the student to a lot of learning, which, in turn, promotes his integral development. Integral development is understood as one that transforms the individual internally and externally, changing his way of seeing and interacting with the world.

In this sense, the author points out that

The important thing is not to limit instruction to empirical or theoretical knowledge. The correlation and the interrelationships that must exist between one and the other depend on the didactic attitude and on the peculiarities of each subject of study (ZANKOV, 1984, p. 36, our translation).⁷

Not limiting instruction to empirical or theoretical knowledge is the only way for the necessary interrelations to occur through the didactic attitude and the peculiarities of each subject. Thus, the teaching process that leads to development becomes broader and more open to the needs and desires of each student, producing the necessary environment for the appropriation of an optimal general formation.

L. V. Zankov highlighted the importance of implementing its system in a compatible educational context: "Teaching will contribute to the process of the general development of students not through the application of disconnected didactic principles but only through the implementation of the complete didactic system" (ZANKOV apud^{GUSEVA 2017}, p.240).

This statement of L. V. Zankov is pertinent and coherent with the references on which it is based, in the sense of thinking of a didactic "system" and not sporadic, punctual didactic "actions" and "principles" that are unrelated. It is consistent with the principle of an organic relationship between part and whole, proper to the dialectical posture. To think of a didactic system is to think of the subjects it involves, the methods and processes of teaching and learning, the conditions as well as the contents, in an organic, grounded, and coherent way.

Despite the genuineness and its relevant aspects for didactic science, the systems derived from these theories still demand studies that will promote their dissemination, understanding, and application in the classrooms, making them capable of interfering in the process of school teaching and learning in the social, cultural, scientific, and educational context of the twenty-first century.

The philosophical presuppositions and psychological principles of L. V. Zankov's didactic system

Interpreting in his own way the main postulates of the authors, who established the bases of developmental teaching, primarily the postulates of L. S. Vygotsky, L. V. Zankov understands that the teaching that provides new psychological formations is developmental.

Questioning the teaching methods of his time, L. V. Zankov warns that they did not exploit to the maximum mental capacities, such as observation and thought, along with a positive attitude. Thus, it suggests other ways of approaching didactics that can lead the student to full development.

As ^{Puentes and Aquino (2019}, p. 458), state,

The Zankovian system believes that the relationship between teaching and development is determined by the specific methods used for the treatment of content in the classroom. His studies proved that the school did not use sufficiently effective methods and therefore did not exploit to the maximum the psychic reserves of the students for their development, especially the mental ones, such as the activities of observation, thought, and a positive attitude toward the process of obutchénie ⁸.

In presenting his object of study, the method, and the organization of the research he developed, La enseñanza y el desarrollo, L. V. Zankov indicates philosophical and psychological presuppositions. In relation to the object of the study, it states that "it consists in evidencing the objective pedagogical logic in the correspondence between teaching and development" (ZANKOV, 1984, p. 15). He was concerned with investigating the avenues of teaching that could lead to "optimal general development," while remaining faithful to the demands of Marxist-Leninist methodology and to the Vygotskian theses regarding teaching and development, in the sense that teaching must anticipate development.

In the search to evidence the objective pedagogical logic of the teaching-learning process, it is necessary to keep in mind that the action, or the task performed, does not evidence this logic; however, it guides the defined didactic work. Achieving a result or achieving a goal alone does not demonstrate the logic of the action taken. Objective logic is differentiated by expressing a certain order in the relations between phenomena and processes that interfere with objective reality. It is not a question of applying the results of the research in school practice but of investigating the logic of the teaching work that allows to achieve the expected results in the development of the students. Thus, Zankov (1984, p. 17) takes as a hypothesis of his investigation that "the structure of teaching is the cause of a certain process of general development in students".

Some questions have guided Zankov’s research, considering the experimental classes and those using traditional methodology:

Is there a limit to the development of students that is achieved through the traditional teaching methodology? If there is no limit, what should be the didactic system that leads to much better results in the development of students? What is the process of general student development through the traditional methodology and the experimental system of primary education?

Is it justifiable to suppose that, on the basis of substantial progress in the general development of schoolchildren, a really high-quality will be achieved in the assimilation of knowledge and in the mastery of habits?? (ZANKOV, 1984, p. 17, our translation⁹).

Hesse questions give the dimensions of your concerns and your research work. It is clear that he intended to compare the traditional methodology with another didactic system that would lead to superior results in the development of children.

Aquino (2013) makes a comparison of the assumptions that guided the Zankovian didactic system and presents them as the philosophical foundations of the system, from the perspective of materialist dialectics: The principle of "multilaterality" in the study of the object; the principle that all science must start from the facts given; the unity of the oppositions (reality-fantasy; object-representation); the principle that the law, which expresses a certain order of the necessary and stable relation between phenomena, is therefore narrow, incomplete, and approximate; the principle that the consequent activity of man is a form of objective process; These are the principles of a Marxist-Leninist methodology that must be observed, as L. V. Zankov (1984) affirms.

Regarding the principle of multilaterality, L. V. Zankov relies on Lenin when he considers that "in order to truly know the object, it is necessary to encompass and study all its aspects, all its links, and its "mediations." We will never achieve it completely, but the demand for multilaterality will prevent mistakes and stagnation.". (LENIN apud ZANKOV, 1984, p. 20). It affirms that the development of students should not be thought of in isolation but in the bonds of man with the outside world, in a movement of internal and external relations. In this sense, it uses the experiment because it is a general scientific method that allows to change the conditions of the observation of the phenomenon and its relations with other phenomena, seeking to find the causes and evidence of the laws of objective reality. It draws attention to the complexity of the pedagogical reality, which makes the experiment also complex, requiring the planning of the investigation in order to evidence the process of development of the students.

L.V. Zankov (1984), citing Engels, also considers, as one of his assumptions, that the approach to phenomena, the object of study, should not occur in an abstract way but start from the facts given, so that theoretical constructions must originate from them and not impose themselves on them.

Arguing that, in the study of thought, there is the unity of the reality-fantasy and object-representation contrasts, based on Lenin and Vygotsky, he indicates that in any generalization¹⁰, no matter how simple, "fantasy" is present. This assumption, in the understanding of the authors of this text, refers to the "rise from the abstract to the concrete", although this relationship is not explicit because the representation is an abstract moment. It is also contradictory and may not translate the concreteness of the phenomenon or object, hence the need to search for the essence translated into a concrete thought.

Defending the unity between fantasy and reality is perhaps a singularity of the Zankovian didactic system. Vygotsky, in his work La imaginación y el arte en la infancia, gives a different meaning to this pair, associating fantasy or imagination with the creative activity of the human brain.

To better understand the psychological mechanism of imagination and related creative activity, it is convenient to begin by explaining the link between fantasy and reality in human behavior. We have already noticed the incorrectness of the vulgar criterion that draws an impenetrable border between fantasy and reality (VIGOTSKY, 1998, p.5, our translation)¹¹.

L. V. Zankov believes that "objective logic, discovered through scientific investigation, expresses a certain order, a causal, necessary, and stable relationship between the phenomena and processes of objective reality." Thus, when referring to the investigation of the objective relationship between the structure of teaching and the development of students, he states: "In our investigation, it means that the structure of teaching is the cause of a certain process of the general development of students" (ZANKOV, 1984, p. 17). This necessary and stable relationship is expressed by means of a law; however, according to Hegel, cited by L. V. Zankov (1984, p. 21), the law is always "narrow, incomplete, and approximate", because it translates the fixed elements.

Regarding the psychological aspects, according to Aquino (2013), L. V. Zankov relied on representatives of historical-cultural psychology, L. S. Vygotsky, S. L. Rubinstein, and A. N. Leontiev, in addition to contributions from other Russian psychologists such as I. Pávlov. It highlights the following assumptions present in Zakhovian research: "the development of the child's psyche is of a social nature, and that the source of development is cooperation and teaching" (p. 241); "the unity between consciousness and activity" (p. 242); "the principle of age-related steps" (p. 241); and "The Zone of Near Development (ZDP)" (p. 243), a construct by L. S. Vygotsky. To these principles cited by Aquino (2013), one more can be added, presented by L. V. Zankov (1984, p. 22), which is that of the "integrity of development".

L. V. Zankov (1984), in situating his research problem, expresses these principles. He maintains that, for L. S. Vygotsky, the investigation of human psychology has as its source the social environment to which man belongs and not his interior. In relation to the principle of age-related stages, it states that the basis for the characteristics of each stage lies in the "change of the functional structure of consciousness". "The general law of development," writes L. Vygotsky, "is that consciousness and mastery correspond only to a higher rung in the development of any function”.¹² (ZANKOV, 1984, p. 8, our translation). In early childhood, perception is dominant in the system of interfunctional relationships; at preschool age, memory is dominant; at school age, voluntary attention and memory are dominant.

Continuing Vygotsky's postulate of unity between consciousness and activity and A. N. Leontiev's conceptualization of main activity, S. Rubinstein characterizes the game as the dominant activity in preschool; at school age, systematic study.

Dealing with the Near Development Zone (NDZ), L. V. Zankov (1984) recalls that teaching should act not on already mature functions (the current development zone), but on those still in the process of maturation (the potential development zone), thus creating a development zone resulting from the distance between the current and the potential (the proximal development zone). In the NDZ, internal and external processes occur, both relevant to child development, as described by Vygotsky:

The importance of teaching comes from the fact that it creates the zone of proximal development; that is, it stimulates the child's interest in the environment, which in turn awakens the processes of internal development. Once awakened, development will advance only through interaction with the environment and through interpersonal relationships. And despite the need for external stimulation, intellectual maturation or growth will be an internal and individual achievement for each child. (VYGOTSKY, 1991 apud^{GUSEVA, 2017}, p. 228).

This quote helps to understand that between teaching and development there is no direct causal relationship; that is, the processes of teaching and the processes of development do not coincide in their trajectories, a fact already verified by L. S. Vygotsky, with which L. V. Zankov agreed. Development presupposes interpersonal relationships and requires external stimulation, but it also depends on the individual internal processes of each student. For this reason, it cannot be guaranteed that an optimal organization of teaching will cause the optimal development of all students.

Based on the integrity of development, L. V. Zankov considers that, when taking as an object of study the general development of school-age children, it would be an irregular way to think of this general development as the sum of psychic processes: sensation, perception, memory, etc. The author considers that integrality is not a sum of isolated parts but that it constitutes an indivisible whole. By this means, it is necessary to analyze the psychic development of the child from his interactions with the world in an upward movement that leads to the essence of the phenomena.

Regarding teaching and child development, L. V. Zankov, based on L. S. Vygotsky, considers that teaching should not only aim at cognitive development but also at emotional development. According to ^{Guseva (2017}, p. 227), "the Zankovian system defends that early childhood education should stimulate the cognitive (mind), volitional (motivation), and affective (emotions) development of the student", thus involving elements capable of stimulating the optimal development of the individual.

This intentionality was verified by ^{Ferola (2019}), when interviewing the Russian professor Natalia Nechaeva, a researcher in the laboratory of the Academy of Pedagogical Sciences, led by L. V. Zankov, who explained it beautifully through the metaphor "mind, heart, and hands", referencing the uniqueness of these three lines of development in its system and attributing to it the reason for the recognition of the Zankovian system around the world.

For L. V. Zankov, there is no teaching or learning if there is no transformation of the human being. For this transformation to occur, it is necessary that the student feels and that he perceives the emotions associated with knowledge, a fact that can help positively when the related emotions are good or negatively when these emotions are not good, generating a possible aversion to the content and an increase in the difficulty of his learning.

In his experiment, from the first stage and throughout his development, he sought to find, through the process of mediation by the teacher, the various aspects of the personality and feelings of the student. Thus, the movement of the experimental system could reveal, with great transparency, the passage from one stage to another, the active role that the methodology has regarding the emotional sphere, in addition to the will of the students and their spiritual needs. It is worth considering that in the general and emotional characteristics that are present in psychological science, emotion is characterized as an attitude of man towards the world, of what he experiences, experiences, and performs in the form of feeling.

According to L. V. Zankov (1984, p. 63),

Emotion is characterized as man's attitude toward the world, even that which he experiences and accomplishes in the form of direct feeling. Emotions express the state of the subject and his attitude towards the object. [...] Emotions have a motivating force. They can increase or reduce vital activity; therein lies its dynamic importance. (our translation)¹³

Emotions, in general, are characterized by a positive and a negative sense, such as satisfaction and dissatisfaction, joy and sadness. With positive emotions come spiritual elevation, sympathy, and admiration; within negative emotions are anger, revulsion, and frustration. The emotions mentioned, as well as others, operate in different ways and are distinguished by different qualities and nuances. In general, the types of emotions stand out due to the spheres and psychic activities of man and the various faces of his activities before the world: intellectual, moral, and ethical. These would be, then, for L. V. Zankov, the various facets of a man's attitude.

Emotions have a motivational force and can raise or reduce vital activity. Quoting Lenin, he writes: "Without human emotions, there has not been, there is not, and there will not be a human search for truth" (ZANKOV, 1984, p. 63). For an active and creative work of thought, it is of paramount importance that a man, when faced with something incomprehensible, raises questions that surprise him and that stimulate his emotions. The incomprehensible generates astonishment because the doubt generated in the face of the lack of evidence forces man to perform the work to the end to achieve full thought, even with all the difficulties that may arise along the way. Passion and joy influence the accomplishment of work and studies, leading the student to have more strength and energy for practice. On the other hand, boredom and frustration hold him back. In this sense, it can be understood that emphasizing the role of emotions in the mobilization of the student for learning potentiates the sense of "need" in the Activity Theory

Didactic principles of L. V. Zankov

L. V. Zankov found that traditional teaching methodologies emphasized the development of knowledge, skills, and practices, which led him to broaden these objectives to encompass integral cognitive development, beginning with the adjustment of the role of the teacher, who would no longer assume the position of instructor, passing to that of guide of the learning process.

In this new conception, the teacher remains with the functions previously assigned to him, such as that of performing the organization of the content and that of didactic mediation, but absorbs the characteristic of the one who points out ways through the organization of the learning process, guided by clear principles, that promote the evolution of the student in function of the content.

To direct in his system the action of the teacher and the whole teaching-learning process, L. V. Zankov was based on five didactic principles in order to promote the general development of the student and a greater effectiveness of teaching. These principles were structured during the stages of the experiment. They are:

The last principle, according to L. V. Zankov (1984), defines the field of action of others because the organization of teaching is a condition for others to be affected. It also highlights that these principles are linked to each other but act on different planes and are distinguished by their functions.

First principle: The role of the rector of theoretical knowledge

The formation of theoretical concepts or theoretical thought is a concern of L. S. Vygotsky and his followers. They emphasize that the role of teaching is to promote the formation of theoretical thinking and not empirical thinking. ^{Resende (2019}) draws a parallel between them, based on Davidov.

Source: ^{RESENDE, 2019}, p. 307. Elaborated on the basis of ^{DAVIDOV (1988}, p. 154-155) and DAVÝDOV (1982).

Table 01 - Parallel between empirical thought and theoretical thought from Davidov's perspective. 

It is clear that empirical thinking is based on external, apparent aspects of the object, is in the sphere of appearance, and has the purpose of cataloging, of classifying, while theoretical thinking aims at internal connections, arises from the mental transformation of objects, and is in search of the essence within a whole, of an integral system.

Although L. V. Zankov was concerned with the formation of scientific concepts, giving them the role of "rector" in the proposed didactic system, he also stressed the importance of considering the sphere of emotion and will of the students in order to obtain the integral development of the student.

L. V. Zankov (1984) associates this principle with the next, stating that the high degree of difficulty implies arriving at knowledge of the interdependence of phenomena and their substantial internal relation, which allows us to say to the essence, going beyond the empirical level of thought.

In the Zankovian system, students are encouraged to verbalize their observations on the subject studied, while the teacher directs attention to the patterns and connections evidenced by them, leading them to deduction and explanation of the nature of relationships. The emphasis should be on concepts and not on the manipulation skills of mathematical or linguistic signs, although L. V. Zankov values the formation of habits and skills that become more developed when they are linked to a deeper understanding of concepts.

In the example presented by ^{Guseva (2017}), in a geometry class, what is observed is that the teacher presents a geometric element in a figure—the diagonal—and goes instigating and questioning until the student reaches a more complete concept, containing all the necessary elements, which go beyond the immediately observable.

This type of approach to knowledge guides the teaching-learning process that has the student as the protagonist of the appropriation of his knowledge, but not alone. There is a collective construction, guided by the teacher, that will lead the students to the concept, but at different moments of the process, thus respecting each individual, their limitations, and their abilities.

In Conclusion

In the context of Brazilian education, especially in the second decade of the twenty-first century, it is faced with teaching proposals, present in the legal provisions (National Common Curriculum Base/NCCB - BNCC in Portuguese - Law 13.415/2017 that changes the organization of High School, among others), whose centrality is the development of skills, the "know-how", the valorization of what is applicable in the day to day, specialization, and early options, which impoverish the role of teaching and school. In this context, studying, presenting, proposing, and testing didactic systems that are based on other assumptions is urgent and necessary. We are not advocating the transposition of models adopted in other countries, in historical and cultural contexts different from ours, but discussing theories, assumptions, and experiences that can illuminate paths for an education that goes beyond neoliberal and capitalist interests, to educate for the market, for consumerism, for competition. .

The Zankovian didactic system, as it is treated here, has elements that can greatly contribute to the integral development of children and young people in school education, having clear and grounded relations between teaching and human development. Although it considers the guiding role of theoretical knowledge, its purpose is the integral development of the student, including cognitive, emotional, and volitional aspects.

In the treatise, some aspects that may be present in research, in the organization of didactic systems, and in the organization of teaching in all spaces and levels are highlighted: interdisciplinarity, the gradual presentation of themes, the promotion of curiosity, the inclusion of all those involved in the process, the appreciation of feelings and imagination, and the recognition that, in the development of the student, units of a whole are the activities of observation, mental or theoretical activity, and practical activity.

Every system has limitations because reality is dynamic and flows. However, the system presented has assumptions that have a proven scientific basis and that can support articulated, long-lasting, more organic, and less punctual proposals. Proposals that seek the optimal integral development of the human being of the twenty-first century.

The main limitation of the present study is the fact that we worked only with texts available in Brazil, in Portuguese or Spanish. Future research on the subject could: a) search for scientific articles from the last five years in international databases, such as Scopus and Scielo, in Russian, English, and Spanish; b) expand the team of researchers with mastery of these languages; c) make a systematic literature review according to the PRISMA methodology (2020).