Introduction

The training of teachers has been, in recent decades, the subject of studies of several researchers. In the works, particularly, that demarcate the construction of knowledge and the investigative tendency in Mathematical Education seems to exist the consensus that we live a historical problem in the constitution of practices that promote the acquisition of knowledge, knowledge and/or skills necessary for teaching and that when the subject involves the first years of schooling, the difficulties of the teachers are aggravated, especially. According to ^{Valente (2019}, p. 52, author's highlights):

The debate on the training of teachers who teach mathematics leads us to reflections on the knowledge that should be present in the training of teachers. Which mathematics should the future teacher train? Or, to put it another way: which mathematics represents the specific knowledge of this teaching professional? Or, further: what mathematics should be appropriate for a professional teaching knowledge in basic school? Such questions are on the agenda, it seems, a long time ago.

Taking the author's questions as a problem that has affected us directly and indirectly, either by the formative action that refers to the degree course in Pedagogy of which we are members (as an academic and as a teacher trainer), or by the experience of approaching research in Mathematics Education, which materializes in the research project "Who teaches Mathematics in Pedagogy Courses? The profile of the teacher trainer of public institutions in the State of São Paulo", under financing from Fundação de Amparo à Pesquisa do Estado de São Paulo - FAPESP (Process: 2019/ 10135-7) in force since August/2019.

We frequently observe in the results of studies already carried out in this field (^{GOMES, 2002}; ^{CURI, 2004}; ^{ORTEGA, 2011}), that there are "harsh" criticisms to the Pedagogy course and to the professionals’ egresses of this degree when they enter the career and start teaching different subjects, among which is Mathematics. However, there still seems to be little production of knowledge when the subject refers to the profile of the teacher responsible for this discipline, as well as the characteristics of their education, the constitution of their professionalism, for example.

The foundations that support the structuring of the study in check are based on the belief that there are other aspects that can also compose the scenario of challenges that the teaching and teaching of Mathematics in the first years of schooling announce, one of them highlighted in the article is the profile of the trainer of teachers who will teach mathematical content in Basic Education. This theme we intend to raise in this paper, initially, with the characterization of the production of scientific knowledge of the area from the mapping of theses and dissertations, which we had the possibility to explore from the realization of the first stage of field research that will be presented in the next sections.

The Research Problem

With the end of investigations already carried out previously, in the scope of the actions of the "Study and Research Group on the Beginning of Teaching and Teaching of Mathematics¹" - GEPIDEM/CNPq - it is possible to affirm the existence of indications that demarcate the possible influence of the formative practices that the degree presents to the future teacher, This is because, in thesis, this teacher of Higher Education is responsible for giving future teachers the opportunity to have access to basic knowledge and knowledge of teaching in the initial years.

Works such as ^{Soares (2014}), ^{Zortêa (2015}), ^{Muniz (2016}), ^{Mariano (2016}), ^{Cremoneze (2017}), ^{Almeida (2018}), ^{Neves (2018}) and ^{Santos (2018}) are examples of research that strengthen the belief that we need to look at the profile of those who work on aspects of Mathematics teaching in the training of teachers in the initial years, Since in the final results of these studies, it was recurrent the observation that the practices of Higher Education can distance and/or bring the pedagogue closer to the area of Exact Sciences depending on his expectations and experiences with the discipline in the graduation.

Therefore, in the FAPESP research scenario, we take as a research question: What is the formative trajectory of the professionals who teach the subjects related to Mathematical Education in the Pedagogy courses of public universities of the State of São Paulo?

To this end, we aim to operationalize a field work that involves identifying and knowing, in more detail, the profiles of teachers who teach "Foundations and Methodologies of Mathematics Teaching", respectively the processes of teaching and learning in the early school years.

The formation of teachers is a rich and promising field to be explored, this is not a new data, since there are more and more aspects that touch directly on processes of reformulation of the curricular grids of the graduations what moves, without a doubt, in the conception of a teacher who wants to graduate or, as in this study, in the ideology of formative practices related to Mathematics that concern "what" a pedagogue needs to know/understand to teach in the first years.

^{Lima (2007}), when studying the polyvalent teacher² and the teaching knowledge to the exercise in the public school, highlights the existence of an amalgam of factors that interfere in the identity of this professional. For the author, he "[...] is an essential professional of the Brazilian educational system, since he works daily and directly at the base of the pyramid with children in public schools" (^{LIMA, 2007}, p. 5). In this understanding, the figure of the pedagogue in the school environment becomes of fundamental importance to citizenship, this requires the valorization of his career, better working conditions, as well as a formation that contemplates the current requirements of doing pedagogic in the educational system. This, without a doubt, goes through the conception of formation present in the graduation courses and, in the specific case of this proposal, from the formation to the teaching of Mathematics to teach in the schools.

Thus, we understand, in agreement with both the specialized literature on the subject and the current curricula, which is the object of discussion and, therefore, teaching in the initial years the knowledge of "Numbers and operations", "Quantities and measures", "Space and form", "Statistics and Probability" and, since 2017 with the Common National Curriculum Base - BNCC - (BRAZIL, 2017), the inclusion of elements of "Algebra", of algebraic thinking in particular.

The development of these needs to be linked, beyond the specific knowledge of the mathematical properties implicit/explicit in the exploration, systematization and materialization of concepts, to pedagogical knowledge and curricular knowledge (^{SHULMAN, 1986}), because it will not help the teacher to understand the content if he doesn't know how to teach, the possibilities of organization of pedagogical work, as well as the specificities of its teaching in classes of the initial years, which will require the teacher of higher education not only knowledge of the area, but also professional experience of acting in these school levels, because the experience will presuppose, in the defense that we have, knowledge of the cause-effect relationships when the theoretical-methodological approach with Mathematics Education in childhood. Therefore, being a teacher trainer in Pedagogy courses, within this component of the curriculum, we think it is necessary to have knowledge of the reality that permeates the school and the classroom, which it has exercised to teaching and, based on this, can redirect to practices and try to break through the barriers constituted by students who often come to graduation for fear of Mathematics, with negative marks of the process experienced as students of basic education.

The challenge is to break the negative view of this area. Evidently, to achieve this formative objective, the theoretical and practical directions exercised by the teacher trainer will have a "weight" of great value that can, depending on the teacher, contribute to overcoming difficulties or enhance the feeling of "powerlessness" in the process of teaching and learning concepts by future teachers.

^{Gatti and Nunes (2008}, p. 22), in an analysis of the Pedagogy courses in Brazil, specifically those that address the group "Knowledge related to specific professional training" conclude that.

The subjects of this group bring menus that register concern with the justifications on why to teach, which, in a certain way, would contribute to prevent these subjects from becoming mere prescriptions. However, only in a very incipient way do they register what and how to teach. A large number of menus register generic phrases that do not allow specific contents to be identified. There are institutions that propose the study of the teaching contents associated to the methodologies but, even so, in a panoramic and not very deep way. So, even in this set of 28% of subjects that can be classified as focused on specific professional training, what the menus suggest is that this is still done in a very insufficient way.

The picture highlighted by ^{Gatti and Nunes (2008}), although already has more than a decade, still presents itself contemporary in the scenario of the elaboration of the Pedagogical Projects of Courses (PPC's) of the graduations in Pedagogy. In this way, it becomes necessary, when one wants to analyze this aspect, to observe situations beyond what is on paper, considering that in practice, as the authors highlight, there will be much more or so little of what is stated on the menus. Therefore, to look at what the teacher's action is based on, both for the elaboration of menus, teaching plans and classroom actions, is information pertinent to the configuration of a study proposal that aims at characterizing the profile of who is "behind the documents", that is, the teacher of Higher Education.

For this reason, we are also looking here: Who are the trainers? What kind of practices do they declare to constitute with their students? What conceptions permeate the teaching and learning of Mathematics foreseen in their teaching plans? What knowledge and contents are needed for the approach in the initial years in your visions? Finally, what formative trajectories have these teachers had with Mathematics Education and how can they interfere in the way they see the formation in Pedagogy courses?

Higher education in Brazil has grown considerably, with an increase in the number of places available for this segment of education in both the public and private sectors in recent years. The education/training model in public universities, in particular, is based on a paradigm that aims at the indissociability of teaching, research and extension and, in this context, ^{Cunha (1996}), invites us to reflect on how difficult it is for teachers to move through these three dimensions in order to guarantee the necessary quality within institutions. Another issue raised as a problem by the author is the fact that Brazilian legislation does not provide for a university teaching degree, but only states that this degree should be in the form of postgraduate scricto senso, however, it does not explain how this degree should be, highlighting that it generates a mistaken interpretation that research knowledge is automatically transformed into teaching knowledge. Although research knowledge is fundamental, given that in this field of teaching there is no disengagement from research, there is a whole range of knowledge for teaching that are different, leading many to choose a career in universities as the place where research is done, forgetting to reflect that it is among their duties to be a teacher (^{CUNHA, 2009}).

Regarding the teaching of Mathematics in Pedagogy courses, we find a problem that also bumps into the performance of Basic Education teachers, the real "dread" that pedagogues have of it, as well as the negative feelings generated during their schooling process. ^{Xavier (2015}), in his master's thesis, brings in an explicit way this issue, placing in his reflection that the role of the teacher of Mathematics in Higher Education, especially in the courses of Pedagogy, is to break this barrier, minimizing the fears of students and focusing on pedagogical practices that can form and facilitate the future teaching action of their students. For us, this situation is also directly linked to the formation of the teacher who teaches Mathematics in the initial formation of teachers.

After these reflections, we believe it is indispensable to take a more careful look at the degree courses in Pedagogy, specifically observing the formation of the professional who teaches the subjects in the field of Mathematics Education, evidencing their formative trajectory, which conceptions they have elected to be primordial in the menus and teaching plans, thus trying to understand and discuss ways that can lead to the improvement of this field so essential, but still feared by future teachers.

Staking - Methodological Design

The production of scientific knowledge, in Human Sciences, requires an approach that allows it to make considerations that go beyond the obvious, the consequence, the observable in a practical way, the findings evident to the eye. It is necessary to try to understand what is in the "between the lines" of the data. Therefore, qualitative research in education (^{LÜDKE; ANDRÉ, 1986}), of a descriptive-analytical nature, is an approach that allows us to weave more detailed considerations of certain subjects.

Qualitative research in the field of education has a significant importance, since it is based on this view that it is possible to make an in-depth reflection on the context of the reality to be studied, its specificities, its variables and the external influences that permeate each and every environment, thus being able to, make an analysis that enables discussions that lead to the diagnosis of problems, that is, qualitative research in education aims to understand the process of quality of the situation and not only the final results, but the reasons why they were reached, thus facilitating interventions to improve the practices to be developed (^{ZANETTE, 2017}).

In this work, we chose as an instrument of data production the mapping in which the "State of the Art" perspective was used, since such an approach implies "[...] the challenge of mapping and discussing a certain academic production in different fields of knowledge, trying to answer that aspects and dimensions have been highlighted and privileged in different times and places [...]" (^{FERREIRA, 2002}, p. 257), which we aim to do by making contact with studies, their production conditions, as well as their central results.

Seeking to respond to the objectives of the mapping, we elected three research descriptors [keywords], being them: "Formation of Trainers", "Teaching in Higher Education" and "Professional Identity". The option for these descriptors refers to the correlation between the terms "formation", "teaching" and "identity" of the teacher, since the research work that we are carrying out is located in this triad of studies precisely because it focuses the teacher trajectory in the formation of the teaching in Higher Education. Therefore, these keywords made it possible to filter investigations that helped us to expand the theoretical-methodological reference.

The survey was conducted at the Biblioteca Digital Brasileira de Teses e Dissertações - BDTD - (http://bdtd.ibict.br/vufind/), Brazilian Digital Library of Theses and Dissertations and at the Catalogue of Theses and Dissertations of the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES - (https://catalogodeteses.capes.gov.br/catalogo-teses/#!/) - Coordination of Improvement of Higher Level Personnel. In this process, we have adopted the "Human Sciences" filter and researched programs in the areas of "Teaching", "Education" and "Teaching of Sciences and Mathematics".

Table 1 illustrates the results found, in quantitative terms, at the time of insertion of each descriptor in their respective bases, as well as the centrality of production, in the sense of the collection indexed in these platforms.

As verified, in the mapping carried out, when searching for works of the three descriptors, in the two databases, we reached the number of 14,200 searches defended in the decade from 2009 to 2019. Of this total, 33.042% (4,692) correspond to the descriptor "Formation of Trainers"; 34.564% (4,908) to "Teaching in Higher Education"; and 32.394% (4,600) refers to the percentage number of theses and dissertations on "Professional Identity".

An important factor to be observed is that a large part of the research is concentrated in the South and Southeast regions, more predominantly in the Southern region of the country, specifically works defended in graduate programs of Universities of the State of Rio Grande do Sul, such as the Federal University of Rio Grande do Sul (UFGRS), Federal University of Santa Maria (UFSM) and State University of Rio Grande do Sul (UERGS).

Despite the significant number of researches found when searching based on the descriptors, we have in this work a specific questioning about who is the professor who teaches Mathematics in the Pedagogy courses and, for that, from the direct contact and the previous reading of the localized texts, when tuning, few works help us to think about this research problem, since a significant part of the production of knowledge in the area is focused on Basic Education in general, this falls, without a doubt, on the need of more indepth investments for studies in the field of Higher Education.

Thus, in synthesis, from the general quantity of studies (14,200), in the filter from the reading, initially of the summaries of theses and dissertations, and, later, of the works in their entirety, we find five directly linked to the theme that we are working on in the project in question, being these, therefore, the ones that will be presented in the next items.

Thesis and Dissertation Mapping: What Does the Production of the Last Decade (2009-2019) Say?

Final Considerations: Where Do The Studies Guide Us?

The researchers analyzed and listed in this work give us ways to think and analyze some inferences regarding the teaching of Mathematics in the initial years of elementary school, as well as the initial formation of teachers who work in this stage of teaching. In addition, the experience of mapping the production of knowledge in the area in the last decade has given us the opportunity to know and detail theses and dissertations that highlight the work of the teacher trainer in the field of Mathematics Education, his knowledge, knowledge and experiences, since, without a doubt, it has contributed greatly to problematize the object of study and also to identify characteristics of the profile of those who teach Mathematics in the degree in Pedagogy, based on the literature of the subject.

As we have seen, throughout this article we have sought to characterize aspects of the work of the trainer. We have mobilized a theoretical-methodological reference that was constituted from mapping the production of knowledge, through theses and dissertations, located from 2009 to 2019 in the perspective of understanding the studies on "" Education for Trainers", "Teaching in Higher Education" and "Professional Identity". Regarding the descriptor "Formation of teachers," we find the works of ^{Manfredo (2013}), ^{Reis (2014}), ^{Utsumi (2016}) and ^{Castro (2018}), which have delineated themselves more for general studies of the field, with low correlation with the education of the trainer who teaches Mathematics. About "Teaching in Higher Education", ^{Crahim (2013}) was the only text related to the focus of our study. This, no doubt, seems to signal the fact that they become relevant production in this area, given the low proportionality of the research. The research on "Professional Identity" did not allow connections with the work we are doing.

In the theses and dissertations presented here, it is possible to notice that the results of these investigations demonstrate that the courses of Pedagogy, in what concerns the mathematical formation and the formation for teaching, the central focus of the formative actions falls with emphasis on teaching methodologies, that is, they focus on "how to teach" and not "what", in specific terms of the elementary mathematical contents to be introduced with the child of the initial years, which corroborates, even if more than a decade has passed, with the data of the doctorate research of Edda ^{Curi (2004}).

Another important factor is that, according to Resolution CNE/CP No. 1 of May 15, 2006, which institutes the National Curricular Guidelines for the Graduation Course in Pedagogy, the initial formation of the pedagogue must contemplate aspects, in the different dimensions, of the field of Early Childhood Education and the first four years of Elementary School, which is not observed, when the subject is Mathematics Education, at least in the theses and dissertations highlighted here. In other words, what we mean is that the menus of the subjects responsible for the pedagogues' mathematical formation seem to have no spacetime to discuss the aspects of mathematical language in acting with the small child (nursery, maternal and kindergarten). By way of problematization, although this is not the focus of our research, we investigate: Where is the Mathematics of Early Childhood Education in the initial formation of the pedagogue?

To what the data of the research presented shows, most of the teachers acting in the pedagogical license were not pedagogues, perhaps this justifies, in thesis, the non-appearance of the discussions "of" and "about" Mathematical Education in childhood. The formative trajectory of the teacher educators indicates, due to the work we brought to the dialogue, that they are not related to the process of teaching and learning mathematics in childhood.

Referring to the study we are developing, the differential lies in the fact that we are concerned with looking at the formation of the trainer, as he constituted his trajectory to be in this place, so that we can contribute to the theoretical field of Mathematical Education in the initial formation of teachers, we understand that what we have built up to now helps us to develop the future stages of the research project in course, which originated this production.

In summary, studying processes that involve the formation, performance and conception of trainers to characterize "those who teach Mathematics in the degree of Pedagogy" represents, to the scientific initiation scholar, a first contact with the field of academic research, which can be a path to new ventures such as master's and/or doctorate. Studying a theme directly linked to the formation in Pedagogy, in the case of this study of Mathematics, allows one to have a vision on how this field of knowledge relates to the initial years, as well as the access to specialized literature that may help in the future teaching practice of the first author (academic of Pedagogy at UFSCar), to understand that, many times, the trainers do their best with the workload they have in the disciplines and also how challenging it is to LearnMathematics in formative processes of the teacher/pedagogue.