The review that first highlighted the importance and potential of the study of professional identity to investigate the teacher

Beijaard, Meijer, and Verloop (2004) conducted a literature review in the area of Education, covering research undertaken on the teacher’s professional identity published between 1988 and 2000. The authors searched for the term “Professional identity” in the title or as the most prominent descriptor in the databases linked to the “Web of Science” website and the ERIC⁵ database. Twenty-two articles, which were the outcome of this search (all written in English), were analyzed under the following aspects: objectives of the study, definition of assumed professional identity, concepts related to this definition, the methodology developed by the study, and its main results.

These articles were divided into the three categories, considering the focus of the investigated study: formation of the teacher’s professional identity, identification of characteristics of the teacher’s professional identity, and professional identity evidenced by/in the stories told and written by the teachers.

The authors conclude that most studies have distinct conceptualizations of identity or do not conceptualize it. Additionally, they state studies that confuse concepts close to identity are frequent and use them as if they were identical, whereas literature regards them as distinct. That is the case of some reviewed studies that use the terms “I” and “identity” interchangeably without clarifying how these terms are conceptually related.

Beijaard, Meijer, and Verloop (2004) finalize the review by suggesting that researchers seek, in their articles, greater conceptual clarity for professional identity. Furthermore, they point to the potential of studying the relationship between the individual stories told by teachers and their identities as a fruitful pathway to theoretically and methodologically support future research on the teacher’s professional identity. They also highlighted that in studies in which identity and individual narratives are present, the social context is relevant in the constitution of teachers’ identity. The authors, therefore, acknowledge the narrative as a fundamental resource for the analysis and discernment of identity.

When elaborating an interpretative synthesis of the narrative perspective on the identity of this review, we can affirm that, for Beijaard, Meijer, and Verloop (2004), the teacher’s professional identity is conceived as having a central nucleus, more or less coherent, constituted by sub-identities that harmonize to some extent. Regarding the relationships established by the sub-identities, the authors emphasize that,

Some of these sub-identities may be broadly linked and can be seen as the core of teachers’ professional identity, while others may be more peripheral. It seems essential for a teacher that these sub-identities do not conflict, i.e., that they are well-balanced. (BEIJAARD; MEIJER; VERLOOP, 2004, p. 122).

The path to harmonizing those sub-identities is considered convenient. In addition, this core would be woven from the lived experiences and practical knowledge personally built by the teacher in different times and professional spaces they have been part of throughout life.

The researcher who assumes such a perspective understands that, by exploring the plots an investigated teacher constructs to compose their narratives, they can access this central core of the teacher’s professional identity, likewise their most peripheral aspects. Thus, by retelling and reliving their professional histories, such a teacher reflects on them and reconstructs, in time and space, their professional practical knowledge, renovating their identity through the integration of what, individually and collectively, is considered good teaching (BEIJAARD; MEIJER; VERLOOP, 2004). From these narratives, perceptions can emerge about the manners a teacher explains and justifies their relationships with themselves and with various characters (parents, students, principals, teacher trainers) present in different professional scenarios they participate, such as schools; continuing education groups, among others. On the other hand, when assuming this perspective, the analyzes are based on the stories the teacher tells, leaving in the background data that do not constitute narratives, such as discussions and conversations with their students, colleagues, or teacher trainers. In this direction, it is necessary to consider that such episodes may be absent from the narratives reported by the teacher or reconstructed in order to hide aspects of their professional identity, in case they do not identify themselves or do not want to be identified, with the ways of being a teacher evidenced in the episodes of professional performance.

The literature review that jointly addresses the identity of students and teachers who teach mathematics

Focusing on mathematics education, ^{Darragh (2016)} reviewed studies published in English from 1997 to 2014, which dealt with the identity of students and teachers who teach mathematics. The author researched five education databases: Education Sage Full Text Journal Collection, Education Research Complete (EBSCO host), ERIC, JSTOR, and ProQuest Education Journals. She used the terms “Mathematics”, “Education”, and “Identity” in the search performed in each of the five databases. After reading the title and abstract, she selected 188 articles to compose the analytical corpus of the review.

^{Darragh (2016)} analyzed the definition of identity present in each study and its theoretical foundations. The author found five categories that characterize the ways of defining identity in the studies she reviewed, but without distinguishing between student and teacher identity: participatory, narrative, discursive, psychoanalytic, and performative. She noted that some articles did not assume or clearly adopt a definition of identity, although they had revised the definitions of other authors.

Among those who have assumed a conceptualization for identity, it was predominant the use of theoretical perspectives from fields outside mathematics education and education, particularly ^{Lave and Wenger (1991)} and ^{Wenger (1998)}, followed by ^{Holland et al. (1998)} and ^{Gee (2000)}. In the field of mathematics education, ^{Sfard and Prusak (2005)} have been the most cited in the studies reviewed. Furthermore, the author found theoretical-methodological inaccuracies and inconsistencies in this research, such as the existence of articles that assumed a conceptualization of identity within a sociological framework but deployed analytical procedures linked to a psychological perspective of identity.

In her review, ^{Darragh (2016)} advocated a sociological and performative conceptualization of identity. For her, identity is not something inside us but something we do (identity as action). When we tell stories, gather in groups, act in a particular way at a given time, or position ourselves and others through discourse, we enact our identities for specific audiences, which may or may not recognize us as we wish to be. Thus, identities are the result of processes of self-identification or identification by others. Recognizing identity as a performance that may or not be recognized as desired is also pointed out by ^{Darragh (2016)} as an effective and promising direction for future studies.

Making an interpretative synthesis of ^{Darragh’s (2016)} sociological and performative conception of identity and how to investigate it, we can say this perspective moves away from the idea of identity existence, with a central or essential core constituted throughout the professional life of a teacher, to assume the existence of multiple identities evidenced at specific moments when the teacher acts professionally in the different educational and training contexts he participates. From this perspective, it is possible to interpret the enactments of their various “I – teacher” focusing on the moment they are acting in their classes, negotiating with their students and managers, and with other participants in the school context, without necessarily telling us these stories.

In this sense, it is crucial that the researcher, when investigating the teacher’s identity, make audio and video records of the teacher’s professional practice and select dialogues and performances in class or with the professional community they participate, prioritizing moments of negotiation. Such a procedure allows the researcher to access the different “staged” identities when acting as a teacher. From a sociological perspective, the researcher can identify, analyze and understand the relations of power that permeate the different moments of action and how the teacher welcomes, incorporates, or rejects the way they are acknowledged and positioned in their school or group (professional or investigative) they participate, endorsing their professional identity assumed in a performative perspective.

A literature review centered on the identities of mathematics teachers

The study developed by ^{Lutovac and Kaasila (2018)} focuses on the field of mathematics education and has the mathematics teachers’ identities as the seat of attention. To select the articles, these researchers analyzed studies published in academic journals in the realms of mathematics and teacher education. Furthermore, they conducted searches in the Education and Social Sciences and ERIC (ProQuest) databases, using the keywords Identity, Mathematics, and Teacher. Eventually, forty peer-reviewed articles were chosen — written in English and published between 2000 and 2015.

^{Lutovac and Kaasila (2018)} recognized six central themes about teacher identity: theoretical models and what constitutes identity; contextual factors in identity and its development; the development of identity at the beginning or continuing education; affective relationships with mathematics and changes in the teacher’s identity; post-structural studies and issues of power, social justice, gender and race in identity discourses; and the link between identity and teaching practice.

The authors found multiple definitions of identity that vary according to the adopted theoretical frameworks. However, they observed that all these studies presented at least an operational conceptualization (SFARD, PRUSAK, 2005) for identity. In addition, they found that most of these conceptualizations were borrowed from other fields of research and based on established theories. For example, Lave and Wenger’s Situated Learning (1991); Wenger’s Communities of Practice (1998); or Foucault’s works on discourse, knowledge, and power. They also found studies that portrayed individuals as storytellers with their identities constituted by these stories or defined by them. In the conclusions, ^{Lutovac and Kaasila (2018)} suggest that researchers in mathematics education incorporate, more frequently, theories from the realm of Education in their research, thus avoiding the isolation of this field of study.

Although ^{Lutovac and Kaasila (2018)} admit that social context molds teachers’ identities, they emphasize the importance of affection and emotions related to mathematics in the constitution of the teacher’s identity. These researchers argue that sociocultural and post-structuralist perspectives focus on social structures, leaving the participant’s inner world in the background. Thus, they recommend taking a more balanced psychosocial theoretical perspective on the conceptualization of identity — an aspect found in many of their studies. For example, Kaasila, Hannula and Laine (2012) argue that the way people position themselves socially (or are positioned) influences how they express their emotions or not. ^{Lutovac and Kaasila (2018)} argue that research relating affection and cognition to identity can provide a broader understanding of identity, linking it to learning and teaching.

In an interpretative synthesis of the identity perspective of a mathematics teacher assumed by ^{Lutovac and Kaasila (2018)} and how to investigate it, we can highlight that the researcher needs to gather narratives of multiple professional experiences of that teacher in order to evidence and understand their different identities constituted in their stories, considering the context and the interlocutors present in each narrated plot. From a story about a teacher’s conflicting relationship with formal mathematics, told in a narrative interview with a researcher, a mathematical identity can emerge (^{KAASILA, 2007}) associated with overcoming actions and positive emotions. However, the same story told to teachers participating in their training group may reveal another identity connected to negative emotions and actions of distancing from mathematics. In this perspective, different identities can arise from different situations, and the same teacher may have many narrative identities connected to other contexts or social relationships (KAASILA; HANNULA; LAINE, 2012). Identities are understood as means of argumentation and modes of positioning (KAASILA; HANNULA; LAINE, 2012) being, therefore, something the teacher uses and not something they have inside.

Current trends in international research on the identities of mathematics students and teachers in literature reviews

In the field of mathematics education, ^{Graven and Heyd-Metzuyanim (2019)} conducted a review of the literature reviews on identity published in the last three years (2016-2018). The analytical corpus of this study consists of reviews⁶ that deal with the mathematics teachers’ and students’ identity. The common findings and criticisms revealed by the reviews were summarized and compared to the results of 47 recent studies (2014-2018), aiming to establish the current research trend in this field. The articles, written in English, dealt with the identity of mathematics learners or teachers. To select them, the word identi* was used in several fields in a search performed in the twenty most prominent peer-reviewed journals in the Academic Search Premier and ERIC databases.

^{Graven and Heyd-Metzuyanim (2019)} analyzed the articles considering two dimensions: quantitative (statistical) and qualitative. Descriptive statistics on the regional location of studies, the object of study (teachers’ or students’ identity), methods, and sample sizes, were performed and compared with those of the other reviews discussed. They used a qualitative approach to group the articles, analyze, and discuss them in terms of the following: the theoretical reference used, the definitions of identity and the ways to operationalize them, the presence/absence of mathematical objects in the studies, the “Ontological Collapses”⁷ and the goals and functions for using the concept of identity.

^{Graven and Heyd-Metzuyanim (2019)} also identified a predominance of socio-cultural frameworks to study the identity of both students and teachers, in addition to the prevalence of empirical studies over theoretical studies. They found that ^{Holland et al. (1998)}, ^{Sfard and Prusak (2005)}, ^{Lave and Wenger (1991)}, and ^{Wenger (1998)} theoretically supported most of the reviewed studies. Furthermore, they found that conceptual inaccuracy and inconsistency were still present in research on students’ and teachers’ identity, despite obtaining some advances. They verified that articles published in the last five years already contained explicit definitions of identity. Such an advance paves the way for a new challenge — how to operationalize such definitions. In this direction, ^{Graven and Heyd-Metzuyanim (2019)} argue that the researcher must, in addition to stating what identity means to them, explain how this conception of identity will be studied and treated analytically and empirically.

^{Graven and Heyd-Metzuyanim (2019)} are closer to studies that use narrative conceptualizations where identity is acknowledged as a discursive action, along the lines of ^{Sfard and Prusak (2005)}, whose coherence of the results is related to an analysis focused on the narrative itself and its structure.

By making an interpretative synthesis of the narrative perspective of identity evidenced by ^{Graven and Heyd-Metzuyanim (2019)} and how to investigate the teacher’s identity, we understand that the discourse of this teacher about their experiences in different contexts and told to different audiences express their identities. Story Collections of their lives as beginning math learners or teachers experimenting with new investigative practices in classes or training groups can convey aspects of their multiple identities. When grouped and given meaning by the researcher, they can tell about their way of being a math learner, investigative, or teacher-researcher. Understanding the structures of stories in different contexts — an interview or a video-recorded discussion of a collaborative group meeting — is a possible way to highlight identities. In this perspective, it is fundamental to analyze what, about whom, and to whom this teacher speaks, besides why they express themselves in a certain way in each context. Identity is considered a discursive action (^{SFARD; PRUSAK, 2005}). Therefore, observed linguistic and discursive resources can be beneficial to help understand it. On the other hand, the researcher’s interpretations of interactions observed and not spoken by the teacher or others involved remain in the background.

The review of Brazilian research on the professional identity of teachers who teach mathematics

^{De Paula and Cyrino (2018)} aimed to analyze the theoretical and epistemological⁸ poles underlying the Brazilian theses and dissertations that proposed to investigate the PEM’s professional identity, published between 2006 and 2016.

There were two stages to conducting the corpus definition of the analysis. The first occurred when the authors examined 858 dissertations and theses involving PEM. After that, there was a selection of 15 studies published from 2006 to 2012, chosen through their abstract readings. In the second stage, the time frame was extended to 2016, when a new survey was performed with the Capes Theses Bank, using “identity professional” as a search descriptor between 2013 and 2016. Eventually, nine further studies were found, totaling 24, all written in Portuguese, and became the corpus of the review study analysis.

Initially, the studies were organized into the following seven categories: the PEM’s working conditions, public policies, programs or development projects, different contexts of teaching training and development, the community of practice or study groups; initial PEM’s training and pedagogical practices, the PEM’s training in distance learning; and PEM as a secondary approach. In a second analysis, the studies were grouped according to the authors’ theoretical choices. Most of the research was based on Claude Dubar’s research, followed by Selma Pimenta’s and Stuart Hall’s (^{DE PAULA; CYRINO, 2018}). The authors found four epistemological perspectives for the PEM’s professional identity: sociological, cultural, psychological/psychoanalytic, and generalist, not being mutually exclusive.

As for the theoretical references used, they observed that most were external to the field of mathematics education, and it was up to each researcher to make the necessary approximations to discuss the identity of these teachers. They detected that few studies published in a foreign language were used as theoretical support in Brazilian research. The authors concluded that there is a scarcity of national studies that specifically discuss the PEM’s identity and suggest the expansion of theoretical discussions aimed at the specific characterization of this professional identity. In addition, they highlighted that, in general, when the analyzed studies present their theoretical foundation regarding the teacher’s professional identity, different perspectives of this identity are mentioned without the researcher taking a position or indicating the choice/adoption of a specific reference.

^{De Paula and Cyrino (2018)} understand the PEM’s professional identity as “a movement that takes place in view of a set of beliefs and conceptions interconnected with self-knowledge and knowledge about their profession, associated with autonomy (vulnerability and sense of agency) and political commitment” (^{DE PAULA; CYRINO, 2019}, p. 637). As a result, they admit complexity, dynamicity, temporality, and experientiality as qualifying aspects of the movements that constitute such a professional identity (^{DE PAULA; CYRINO, 2019}).

Making an interpretative synthesis of the identity perspective assumed by ^{De Paula and Cyrino (2019)} and how to investigate it, we can say that the teacher’s identity can be seen as mutable in a movement of a permanent constitution and associated with their ways of dealing with the possibilities (and impossibilities) they experience in their profession. Their understandings — constructed from beliefs and conceptions, as well as what they know about themselves and others — about what it means to be a “good math teacher”, are highlighted. These can change depending on the context (educational group, school, and society) and the moment they live their experiences of being a teacher and participating in different professional communities. Their understanding of possible ways of being a mathematics teacher (such as a mediator, teacher-researcher, communicator of knowledge, promoter of social equity, and others) in a given context may constitute indications of the constitution movement of their identity, for example, teacher-investigative, teacher-trainer, teacher-militant, or teacher-traditional. The modes of participation in the different groups and the political and social positions gain evidence.