INTRODUCTION

This article aims at continuous training of teachers who teach Mathematics in the first years of elementary teaching. We reported results obtained by original data from doctoral research focused on the content-form relationship present in the actions of the organization of teachers' education in training activities, not within the scope of a training movement.

To go beyond the verification and understanding that the changes of two subjects do not occur in activity, we developed, as an empirical field of research, a continuous training movement with teachers and coordinators in a full-time municipal school from the Brazilian education system.

The participation of teachers and coordinators of the 1st or 5th grade in the continuous training movement includes moments of discussion of questions related to their mathematical knowledge, analysis of their teaching practices, and spontaneous moments of socialization of their experiences. By formative and research actions, we sought to investigate and understand how changes in content and form can be produced through the modes of organization of teachers' continuing education and their teaching organization.

The theoretical-methodological principles of the historical-cultural theory, with specificities in the Vygotsky method and the theory of activity, according to the contributions of Leontiev, will base the formative actions, the structure, development, and analysis of the research.

The research results show that when scientific knowledge is taken as the content of the activity in the teacher education, contributing to the development of theoretical thinking, in search of the appropriation of new meanings about the organization of Mathematics teaching and also its objects of teaching, the actions taken from the collective work in the school evidence changes that occur in the content of the teaching activity and its pedagogical action.

We observed that these changes do not occur in a linear and/or isolated way, but are related to the forms of school organization. In this case, changes both in the content and in the form of teaching activity depend on breaking with the ties of a context that has capitalist relations as a source that generates the concrete working conditions of the teacher.

TEACHING ACTIVITY, TEACHER'S PLACE, AND THE EDUCATION OF THEORETICAL THINKING

The principles of cultural-historical theory and assumptions of activity theory make important contributions to rethinking the role of education in human development, with special attention to school education and teacher training. When looking at the teaching work from these assumptions, we identified the teaching activity as the main activity of the teacher, since, in it, the teacher seeks to respond to his need to intentionally organize teaching.

As the teaching activity is the essence of teaching work, the performance of its function

demands ways of organizing this teaching. Their actions depend on such an organization so that student learning can be systematically and intentionally established (^{MOURA et al., 2010}).

According to ^{Eidt (2009}, p.106, author's emphasis),

[...] the end of each teacher's action (preparing classes, teaching classes, answering questions, preparing tests and exercises, correcting them, etc.) is also indirectly related to the object of the educational activity, to the socialization of knowledge objective in its highest forms, all other motives being subordinate to it. The teaching activity must therefore be composed of a series of intentionally planned actions, such as studying the content to be taught, developing teaching strategies or actions through which this content will be taught, teaching the content, analyzing the actions and operations employed by students during the process of appropriation of that content, etc. Although each of these actions is partial, they are related to a totality that has the action of teaching as its final objective.

In this way, the teacher's actions are carried out intentionally to organize teaching, when they aim at student learning, make up their teaching activity. As explained by ^{Moretti (2007}, p.100), “[...] the teaching activity is a process, not a product. The teacher, moved by his need, is in teaching activity before, during and after his/her meeting with the students in the classroom”. In the school classroom, through his/her intentional work, the teacher can enable students to appropriate elaborated knowledge.

Reflecting on the role of the school in his studies on the relationship between school education and development, ^{Davídov (1988}) states that the task of the contemporary school consists in teaching students to think from teaching that drives or develops, based on scientific knowledge.

Still in this sense, ^{Martins (2011}, p. 55-56, emphasis by the author) reinforces that it is up to the school “[...] to teach what a large part of the population will not learn outside it: knowledge historically systematized by humanity.”

Thus, we highlight one of the founding assumptions in Vygotsky's studies (2010), in which learning promotes development. Consequently, it is up to the school, as an institution, to provide conditions for developmental education.

As pointed out by ^{Bernardes (2012}), in the current school context, it is usual for neither teachers nor students to carry out actions that promote the movement of humanization through the appropriation of historically elaborated knowledge, that is, the way of organizing current teaching is has not enabled the development of maximum human potential. The concern that permeates the school, most of the time, is just the preparation of students to meet the demands of the job market, an objective defended by neoliberal ideas present in public policies of current Brazilian education.

The ideas of developmental teaching (^{DAVIDOV, 1988}), in general, are still distant from the current Brazilian educational proposals. According to ^{Duarte (2010}) and ^{Mello (2010}), from Vygotsky's studies disseminated in the Brazilian educational field, in a broad sense, few known ideas have become a fad, lacking in-depth knowledge of his work.

Some concepts of Vygotsky's theory, despite being part of the vocabulary of teachers, such as “mediation” and “zone of close development”, do not interfere in the way of organizing current teaching, nor do they contribute to rethinking the ideas of innatist and environmentalist theories that still support the teaching and learning conceptions of most teachers since they were appropriated in a fragmented way, without knowledge of the totality of their work.

Therefore, it is important to consider proposals for teacher training that understand school education as a driver of human development, in which the teacher's work acquires another meaning, gaining centrality in the educational process, since “[...] educational work is an act of producing, directly and intentionally, in every single individual, the humanity that is historically and collectively produced by all men.” (^{SAVIANI, 2008}, p.13).

By valuing the knowledge developed and defining ways of organizing teaching that allows their students to take ownership of it, the teacher enables the maximum development of their abilities, without this depending solely on innate abilities or favorable external conditions.

Along with the active role of students and teachers, school contents acquire great relevance. However, it is not about teaching any content, but specifically teaching scientific concepts, which contribute to the development of theoretical thinking, as defended by Davídov (1982, 1988).

There is a dialectical relationship between the processes of the creation of spontaneous and scientific concepts. Spontaneous concepts are the basis for scientific concepts; however, when appropriate, they allow the creation of other spontaneous concepts. According to ^{Vygotsky (1983}), spontaneous concepts are formed in everyday life through concrete experience, in direct communication with people. On the other hand, scientific concepts are formed intentionally through school education, due to a guided, organized, and systematic process, involving the performance of mental actions of abstraction and generalization.

It is also important to consider that the appropriation of scientific concepts does not only mean the acquisition of new information, it is, in fact, the possibility of forming an organized thought system, which directs thought to the mental activity (^{SFORNI, 2004}).

In this sense, ^{Davídov (1982}, ¹⁹⁸⁸) analyzes the development of two types of thinking: empirical and theoretical. Empirical thinking “[...] is a transformed and verbally expressed form of the activity of the sense organs, linked to real-life; is derived directly from the object-sensory activity of people.” (^{DAVIDOV, 1988}, p. 123).

Theoretical thought has, like its content, the mediated, reflected, essential existence and consists of “[...] a process of idealization of one of the aspects of object-practical activity, reproduction, which represents the universal forms of objects.” (^{DAVIDOV, 1988}, p. 125).

In the analysis of the traditional teaching methods of Russian schools, Davídov (1982, 1988) identifies that this type of teaching only provides the development of empirical thinking. This is because is based on formal logic and points out the need to “reorient the entire school system to form in children not discursive-empirical thinking, but to develop in them contemporary scientific-theoretical thinking.” (^{DAVIDOV, 1982}, p. 442, author's emphasis, free translation).

Thus, for school education to contribute to the development of maximum human potential, it is essential that both the teaching activity and the study activity - developed by the student - provide the appropriation of theoretical thinking. The teacher's education activity must generate and promote student activity.

DIALECTIC CONTENT/FORM IN THE EDUCATION ACTIVITIES OF THE TEACHER IN THE FORMATIVE ACTIVITIES

The discussions presented in this topic about the dialectic between content and form in the teacher's activity guided the empirical investigation presented here and also the process of analyzing the data obtained during the formative movement carried out. We need to highlight the determining role of content for the form and the complexity of this relationship.

Marking the theoretical basis that structures the speeches about the understanding of the content-form relationship explained here is essential for the understanding that there is no commonplace when looking at Brazilian research in the area of Education. Questions that may seem simple such as what content and form mean or what relationships can be established between content, form, and the teacher's activity, demand treatment appropriate to the level of complexity that they encompass, when viewed through the lens of content-form dialectics.

The categories and the scientific knowledge are products of certain conditions that arise from the historical development of man's practical and cognitive activity. Thus, they are products of consciousness that were formed in the process of knowledge development, having their content borrowed from objective reality. According to ^{Kopnin (1978}), objective reality and human practice are the basis for the emergence and development of all categories.

^{Kopnin (1978}, p.34) states that the categories of dialectical materialism are based on the generalization of the entire experience of knowledge and the practical reconstruction of the world, because “[…] in them, the synthesis (and not a simple sum) of the knowledge derived from the most diverse fields of science is carried out. This synthesis generates new ideas, in which a new approach to the phenomena of reality emerges”. In the case of our research, the content-form category is used as a support point for the knowledge and apprehension of the researched reality, aiming at the perception of changes in the teaching activity in the process of continuing education.

Researching the content and form of the teacher's activity means investigating how this relationship is established in the movement of the teacher's action in activity. Dialectically engendered both in the teaching activity, the essence of teaching work and in the training activity, which aims to subsidize teachers' access to the knowledge of the educational space, content, and form are composed in unity, in the teaching activity, and the formative activity, in line with the knowledge that guides the organization of teaching and the implementation of an educational project proposed by the school collective (^{MOURA, 1996}).

But what do the content and form categories reflect? ^{Rosental and Straks (1960}) explain that content and form occur in all things and processes of reality, with the content being its internal aspect and form its expression.

^{Cheptulin (1982}, p.263) states that

content is not the simple set of elements or aspects that make up the thing, it is a process in which all these elements and aspects are constantly in interaction, in movement, change in one another, and sometimes manifest one, and sometimes another of its properties.

The form is the organization, the structuring of the content. According to ^{Fischer (1976}, p.143), “the form is the manifestation of a state of equilibrium reached a given moment”. Movement and transformation are characteristics of the content while the form presents more stably.

According to ^{Rosental and Straks (1960}), the content of objects and phenomena is constantly developing. The form also develops but more slowly than the content because it has greater stability than it. “Although this is undoubtedly a simplification, we can define the form as conservative and the content as revolutionary.” (^{FISCHER, 1976}, p. 143).

Also according to ^{Rosental and Straks (1960}, p. 199, free translation) “there is no content whose development does not cause certain changes in its form, as there is no form that does not influence the development of the content”. The content is in constant movement and transformation, but the form offers resistance, which generates a sharp conflict between the new content and the old form. This conflict will culminate in the destruction of the old form, giving rise to a new form for the new content.

In this way, form and content act in the development process as dialectical opposites, which mutually condition each other, as follows:

Initially, the new form corresponds to its content, it gives it every possibility to expand, so the content begins to develop impetuously. But, during its development, it reaches a stage that the form begins again to compress it, to restrain its development, when the appearance of discordance between form and content which, as a result of development, leads to the rejection of the old form, inserting into this new form which, as a result of development, knows the same fate. And so on until infinity. (^{CHEPTULIN, 1982}, p. 269)

In the relationship between content and form, the role of content is decisive. The content, unlike what idealist doctrines defend, operates as a guiding principle, as it represents a set of elements and processes that constitute the foundation of the existence and development of objects and phenomena (^{ROSENTAL, STRAKS, 1960}).

Based on studies by ^{Davídov (1988}), Davídov and Márkova (1987), and Bernardes (2006), the content of the teaching activity is the theoretical knowledge about the theoretical-methodological foundations of the teaching organization. Its form is how the teaching is organized by the teacher.

In the existing unity between the teacher's activity and the students' activity, the content of the teaching activity is also theoretical knowledge. However, it is not considered only the theoretical knowledge about the teaching object (in this case, the mathematical knowledge), but the theoretical-methodological foundation of the teaching organization, which involves knowledge related to child development, pedagogical practices, and social and philosophical relationships that mediate the teacher's performance in the school context, as defended by Bernardes (2006).

Also according to this researcher, when thinking about the content of the teaching activity, we need to consider “[...] the need for the appropriation of specific knowledge by the educator that relates teaching, learning and human development in a historical dimension” (BERRNARDES, 2006, p. 305), since a teaching activity is aimed at the education of theoretical thinking.

When thinking about the content-form relationship in the teacher's activity, we need to consider that changes in the form of teaching organization will be conditionally caused by continuous changes in the content of the teaching activity, since “as a result of the accumulation of quantitative changes in the content, there will, sooner or later, be a change of form, which is accompanied by the passage from material education to a new qualitative state.” (^{CHEPTULIN, 1982}, p. 348).

The field of Brazilian teacher education, since the beginning of the 1990s, has gone through periods of transition that, in their marks, bring the role of the teacher to the center of discussions, in which it is not uncommon for them to end up deprived of the teaching activity when the essential content, represented by access to theoretical knowledge, is supplanted by empirical knowledge about the organization of teaching. In general, it is a type of training that contributes little to the process of humanization of the teacher, as it does not allow advances beyond common sense, that is, it does not allow the development of his/her theoretical thinking.

Even with the appearance of so-called revolutionary proposals for teacher education, many of the current processes of teacher education hide their real content. Instead of enabling the “[...] construction of the meaning of being a teacher by expanding the meanings attributed to teaching work [...]” (^{MARTINS, 2012}, p. 465, author's emphasis), these proposals have been an adaptation of teachers to ongoing educational reforms, increasingly focused on market requirements, identifying education as a commodity and the school as a company (^{MAUÉS, 2003}).

Therefore, despite the discourse of valuing education, we observe the emptying, fragmentation, and lightening of the teacher training process, a consequence of the introduction of neoliberal policies in the educational field, which meet the interests of a certain social group.

The form hides its content. As ^{Fischer (1976}, p.148) defends, regarding the organization of society, “[...] every ruling class that feels threatened seeks to hide the class content of its domination and seeks to present its struggle as destined to maintain not a determined social, historical form, but something 'eternal', concerning all human values.”

Therefore, changing this framework will require changes in the content of the teacher's activity, especially in the teacher training processes, since only “[...] the new content breaks the limits established by the old forms, creating new forms.” (^{FISCHER, 1976}, p. 144). However, this is a process that takes time, as the form offers resistance to the new, that is, this movement of change is quite complex.

Another aspect to be considered in this context is the current way of school organization, a product of a capitalist society, which aims at the education of adaptable individuals to the job market. This educational model privileges individual competence, hindering question and reflections that lead to political projects and non-alienating pedagogical practices (^{MORETTI, MOURA, 2010}). Thus, the school form needs to be understood as an obstacle that offers resistance to changing the content and form of the teacher's education activity.

It is not possible to deal with the relationships between content and form in the teacher's activity, disregarding their specific working conditions because that would be quite naive. The dialectical movement between content and form depends on the historical and social conditions. It is not something that happens naturally and without interference.

In this way, when investigating the relationship between content and form in the teaching activity in a process of continuous education, it is necessary to consider the concrete working conditions of the teacher, that is, the school organization, the duration of work, their remuneration, the possibility or not of collective work within the school, among other aspects.

An effectively transforming action in school education depends on education processes that configure as an activity for the teacher and on changing the current concrete working conditions, an aspect that is related to appropriate changes in the current form of school organization for this to occur. Expressed in other terms, the contradictions that involve the current school form and the teacher's activity must be overcome.

THEORETICAL-METHODOLOGICAL PRINCIPLES OF HISTORICAL-CULTURAL THEORY, ACTIVITY THEORY, AND THE METHOD IN VYGOTSKY

Considering the assumptions of the historical-cultural theory, in the method of apprehending the phenomenon of education, the principles of historical-dialectical materialism are established from the actions developed in the formative movement to the apprehension and analysis of the data collected in the process of research since the method is linked to the phenomenon in the same way that the phenomenon is revealed by the method.

As shown by ^{Vygotsky (1995}), the method is configured as a prerequisite and product, instrument, and result of the study. Thus, the need to study the phenomenon in motion is a requirement of the dialectical method, that is,

When an investigation encompasses the process of development of some phenomenon in all its phases and changes, from the moment it appears until it disappears, this implies manifesting its nature, knowing its essence, since only in movement, it demonstrates the body that exists. (^{VYGOTSKY, 1995}, p. 67-68)

It is also understood that the phenomenon is not given and that it must be sought through procedures to be adopted. In the actions of the teacher in education activities, evidenced in this article, the focus on the content-form dialectic implies “[...] apprehending the movement that takes the professional teacher from one quality to another”, through the effort of “[. ..] to identify qualities that may be indicative of the training phenomenon and that allow us to understand the way to train a teacher” (^{MOURA, 2000}, p. 48).

Therefore, from the studies carried out on the cultural-historical theory, more specifically the activity theory, the properties of the formative movement stand out as a possibility, and throughout the process, attention is directed to the actions developed by the teachers to apprehend possible changes in the form and content of their teaching activity along the path established by the group information.

The option for the formative experiment for such a path was based on principles, whose roots are found “in the investigation processes originating from the psychology of the 20th century, [and] has its genesis in the genetic-experimental method developed by LS Vygotsky (1896- 1934) for the study of psychic development.” (^{LONGAREZI, 2019}, p.162).

The bases of the generic-causal method explained in the works of Vygotsky are, according to Davídov and Márkova, “multilaterally expanded in the works of A. Leontiev, A. Luria, P. Galperin, A. Zaporózhets, D. Elkonin and their collaborators” (^{LONGAREZI), 2019}, p.176) and endorse the constitution of investigative systems in unity with educational systems, so that

[...] in the context of the formative experiment, the educational activity constitutes the “heart” of the investigative activity, in the same way, that the research activity is configured at the heart of the Study Activity. According to VV Davídov and VI Slobódchikov (1991, p.122, author's translation), “[...] the experimental investigations, the design (construction) of new didactic-pedagogical systems and the elaboration of means of performance and verification of their effectiveness are organically united.” (^{LONGAREZI, 2019}, p.200, author's emphasis)

The adoption of such principles as a basis for the continuing education of teachers enabled the researchers involved to be identified as allies in the search for possible solutions to problems faced by teachers in their school work. The actions were forwarded to contribute, via mediation instruments, to the researcher-knowledge-teachers dialectic relationship, towards the development of the teacher's theoretical thinking and in search of school education modes that promote human development.

For the apprehension of empirical data, attention was directed to the actions developed by the teachers throughout the formative movement carried out. Empirical data were obtained through recordings of all meetings held with the teachers, the records produced by them throughout the training process, and the organization of a researcher's field diary to record the actions developed in each meeting and also the observations made, to enable the reconstitution of the investigated phenomenon.

In this way, the dialogues produced during the meetings, the observations recorded in the researcher's field diary, and the written records produced by the teachers made up the data set to apprehend the movement of the training process, to analyze the relationship between content and form in the teaching actions of the teacher in formative activities.

This set of data was organized by episodes, divided into scenes. According to ^{Nascimento (2010}, p.133), “[...] they allow the data to act as triggers or illustrators of theoretical reflections”, constituting as “a way of organizing the research exhibition process, that is, of directing the reader to the movement of our analyses”, without losing sight of the totality of the investigated phenomenon.

The episodes can be written or spoken phrases, gestures, and actions that constitute scenes that can reveal interdependence between the elements of a formative action. Thus, episodes are not defined from a set of linear actions. It may be that a statement made by a participant in an activity does not have an immediate impact on the other individuals of the collectivity. This impact may be revealed at another time when the individual is asked to use some knowledge to participate in an action in the collective. The researcher, like the film producer, is the one who reads these various actions, which seem isolated, looking for the revealing interdependencies of the way of training. (^{MOURA, 2004}, p. 276, author's emphasis)

Excerpts from the episode 'Development and evaluation of collective teaching actions', which expose representative moments of the formative movement carried out, will be presented below, highlighting the results of the research.

THE DEVELOPMENT AND EVALUATION OF COLLECTIVE TEACHING ACTIONS THROUGHOUT THE FORMATIVE MOVEMENT

By understanding teaching as the main object of the teacher's activity, we recognize, as defended by ^{Moura (1996}), that the teaching activity can enable both the education of the student and the education of the teacher.

Some scenes extracted from the formative movement carried out show how the movement of planning, developing, and evaluating collective teaching actions can trigger changes in the content and form of the teaching activity, when conditions are provided for teachers to appropriate new meanings about the teaching object and the modes of teaching organization, since:

The collective elaboration of teaching activities is what will allow the use of theory appropriately, as it is at the service of a collective project to seek improvement of learning conditions. Actions and operations are part of this movement of seeking to implement the activity. It is the definition of instruments that will enable to enhance the educational action carried out consciously. The choice of teaching strategy is the operation of the activity and the material is the tool that will allow the optimization of actions. Hence the need for intentionality: to choose instruments in a way that is adequate for the necessary action. (^{MOURA, 2000}, p. 42)

Through this collective elaboration of teaching activities, according to ^{Moura (2000}), the process of continuing education can be configured as a training activity. The search for the activity, which involves the choice of teaching strategies and the definition of instruments, generates, in the teacher, the need to appropriate theoretical knowledge, which can cause changes in the content and form of their teaching activity.

SOME CONSIDERATIONS

Discussing teacher training also means discussing the role of the school in today's society. Based on the assumptions of the cultural-historical theory, we argued that the school should enable students to appropriate elaborated knowledge, scientific concepts. Reinforcing the thesis of Vygotskian studies that teaching should promote development, it is up to the school to teach the knowledge historically elaborated by humanity to enable students to develop their theoretical thinking.

Therefore, in this context, the need to change the modes of organization of current teaching stands out, which implies rethinking the proposals for teacher training. The research developed sought to contribute to this process, by analyzing how changes in the content and form of teaching activity can be produced through the modes of organization of teachers' continuing education and their teaching organization.

Through actions of planning, development, and evaluation of teaching situations, carried out collectively, understanding the school as a learning space for the teacher, possibilities for changes in the content and form of the teaching activity were evidenced.

By taking the teaching activity as a training object, the teacher can reflect on their actions and, through the appropriation of new knowledge, modify them. Also, planning, developing, and evaluating teaching activities, in partnership with other teachers, as observed during the formative movement, can lead to the creation of new needs and the appropriation of new knowledge, which can lead teachers to produce other meanings in the developed actions.

Another aspect highlighted in the process of carrying out teaching activities, carried out throughout the training movement, was its contribution to the development of the collective work at school, going against the individualization and fragmentation of teaching work, characteristic of the current form of school education in a capitalist society.

However, changes in the form of teaching organization, as already stated in the content-form dialectic, depend on changes in the content of the teaching activity, since the content operates as a guiding principle of the form (^{ROSENTAL, STRAKS, 1960}). This is a complex relationship, because, as explained by the same authors and observed in the formative movement developed in this research, the content causes changes in its form, but the form also influences the development of the content.

In this way, the process of changing the form as a result of the content takes time, since, despite the content being in constant movement and transformation, the form offers resistance. Only when there is a sharp conflict between the new content and the old form does a new form arise. Form and content, therefore, act in the process of development as dialectical opposites, which mutually condition each other. (^{CHEPTULIN, 1982}; ^{FISCHER, 1976}; ^{ROSENTAL, STRAKS, 1960}).

We also need to emphasize that, in the analysis of the relationship between content and form in the teacher's activity, it is also necessary to consider the concrete conditions of their reality, since the dialectical movement between content and form does not happen naturally and without interference but it is conditioned to historical and social conditions.

When discussing the relationship between content and form in the teacher's activity, it is also necessary to consider their working conditions - salary, working hours, material conditions of the school, time for study, among other factors -, since the processes of teacher training are not defined in isolation.

An effectively transforming action in school education depends on training processes that configure as an activity for the teacher and also as ways of overcoming the contradictions generated by the current concrete working conditions, an aspect that is related to changes in the current form of school organization. Expressed in other terms, the contradictions that involve the current school form and the teacher's activity must be overcome.

The change in the content of the teaching activity depends on the activity developed by the teacher, both in the training processes and in their performance at school. It is only in the process of appropriation of theoretical knowledge about the teaching object, the subject of learning, and the relationships established between the two in the teaching and learning processes that the teacher will be able to develop his theoretical thinking and, from there, change the content of the teaching activity, enabling changes in its form.

Thus, the transformations in the way of teaching organization, observed in our research, reveal that only when it is constituted as an activity and acts at the level of theoretical thinking can the process of continuous training, supported by the organization of teaching as a training activity, be able to contribute to changes in the content and, consequently, in the form of the teaching activity.