The construction of mathematical identities among early adolescents

Abstract Many children experience challenges with school mathematics during the transition from primary to secondary education, with several studies documenting a decline of performance, motivation, and self-efficacy. In order to understand how early adolescents construct their mathematical identities during this transition, this study explores, along the lines of grounded theory, the ways that identity manifestations are expressed by children in Oslo, Norway. Participants were 21 early adolescents between the ages 12–13, during their last months of primary education (year 7), and right before their transition into lower-secondary education (year 8). Data collection involved focus-group interviews with all children, as well as individual interviews with six of them. Thematic data analyses yielded three themes around which participants construct their mathematical identities: popularity, effort, and achievement. Aiming at further unpacking the complex relations between the three themes, we focus on the case of Tina. We conclude with suggestions for further research and implications for practice.


Introduction
Transitioning from primary to secondary school can be challenging for many children. Specific to mathematics education, many pupils appear to have negative predetermined ideas about the challenges and difficulties of mathematics at the next school level (Attard, 2010). Consequently, several studies investigating children's experiences during such transitions have documented a general decline of engagement with the subject (Martin et al., 2015), a decline of self-efficacy, motivation, and performance (Rončević Zubković et al., 2021), and a reinforcement of stereotypes regarding gender and mathematical performance (Denner et al., 2018). It is often suggested that these findings can partly be attributed to teachers' self-efficacy (Midgley et al., 1989), teachers' and parents' emphases on goals (Friedel et al., 2010;Madjar & Chohat, 2017) across the two school levels, as well as differences in the ways primary and secondary teachers use instructional materials, such as textbooks (Fan et al., 2013), in the mathematics classroom. While these issues concern the role of adults (teachers and parents), to the best of our knowledge little is known about how pupils position themselves in relation to mathematics and construct their identities as learners of the subject, during the transition from primary to secondary education. In this respect, some related studies have placed specific emphasis on gender (e.g. Darragh, 2013;Jackson & Warin, 2000;Rončević Zubković et al., 2021). Yet, in this paper we "zoom out" from variables such as gender (often approached from a binarised perspective), and aim at examining patterns in mathematics identity construction by children at early adolescence. Drawing on data from a smallscale project in Oslo, Norway, we seek to provide answers to the following research question: In what ways do adolescents construct their mathematics-related identities during the transition from primary to secondary school? In doing so, we are fully aware that specific characteristics such as gender, social class, ethnicity and immigrant background, disability, religion and so on influence identity construction in mathematics (Gutiérrez, 2002;Radovic et al., 2018). However, these are not considered here, as we are more interested in identifying ways of mathematics identity construction beyond individual differences. In other words, while acknowledging that individual characteristics are highly significant in identity construction, here we aim at pinpointing characteristics that appear to be common, not least within the context of this study, across individual people.

Theoretical considerations
To frame our work, we draw on literature about adolescents and mathematics learning in general, and on the role of identity in learning mathematics, more specifically.

Adolescents and mathematics
According to the World Health Organization, 1 adolescence is a transitional phase of growth and development between childhood and adulthood, covering the age range between 10 and 19. It is typically divided in three stages: early (ages approx. 10-13), middle (ages approx. 14-17), and late adolescence (ages approx. 18-19). During the whole age range, adolescents experience physical growth and change, as well as emotional, psychological, social, and mental change and growth (Salmela-Aro, 2011). Regarding mathematics learning, several studies highlight that, despite the cognitive/intellectual developments that take place during early adolescence (Rowan-kenyon et al., 2012;Veenman et al., 2005), there is a general decline of children's interest in the subject during this period (Frenzel et al., 2012), with many children arguing that they do not see the relevance of mathematics to their lives (Matthews, 2018). This decline typically begins with the progression from primary to secondary education (Rončević Zubković et al., 2021) and continues to the last years of secondary education, with late adolescents expressing, at best, utilitarian beliefs about mathematics (e.g., seeing it as a tool in support of everyday shopping, future employment, and management of personal finances) rather than appreciating mathematics for qualities like logical thinking, problem-solving, and esthetics (Nosrati & Andrews, 2022). Perhaps unsurprisingly, negative emotions and attitudes towards mathematics are more likely to be expressed by adolescents who face mathematics learning difficulties or those who score low in conventional performance assessment, than by pupils who perform relatively well (Holm et al., 2017). To help adolescents develop greater appreciation for mathematics, various interventions are reported, such as approaching mathematics lessons through fiction (Usnick & McCarthy, 1998), linking the teaching of the subject to physical activity (Anderson, 2015;Lubans et al., 2018), and supporting parents to appreciate mathematics so that they can later convey its importance to their high school children (Harackiewicz et al., 2012). However, while early adolescence is identified as the period where children begin to lose interest in the subject, mathematics identity construction during this period is generally unexplored by research. We aim to contribute to filling in this gap by turning our attention in this direction.

Identity and (mathematics) learning
Conceptualising identity in mathematics education research is not a straightforward endeavour, as different epistemological and ontological traditions perplexed the situation (Graven & Heyd-Metzuyamin, 2019;Westaway et al., 2020). For instance, while Holland et al. (2001) define identity as an internal process of understanding oneself, Bucholtz and Hall (2005) see it as the social positioning of the self and others. In acknowledging the definitional variations in the relevant literature, we align with Sfard and Prusak (2005), who conceptualise identity as collections of stories people tell about themselves. These stories, argue Sfard and Prusak, need to be (a) reifying (i.e. they are associated with verbs like be, have or can rather than do, and with the adverbs always, never, usually, and so forth, to stress repetitiveness of actions), (b) endorsable (i.e. when asked, the storyteller ought to be able to say that the story faithfully reflects the state of affairs in the world), and (c) significant (i.e. implying one's membership in, or exclusion from, various communities, while any change in the narrative is likely to affect the storyteller's feelings). Additionally, Sfard and Prusak propose two further subcategories of identity. The first is actual identity and has to do with how one sees themselves in the present, typically expressed using the present tense, and constitutes a result of past experiences, capital, and habitus. The second is designated identity, or as Black et al. (2010) call it, leading identity. Designated, or leading, identity describes one's thoughts about who they expect to be in the future. Even though the reifying quality of stories one tells about oneself alludes to a sense of stability, identity is not something that is fixed or static. Quite the opposite, it is a lifelong dynamic process (Boaler et al., 2000), and as such, it can change when the stories people accept and tell about themselves as mathematics learners do so, often as a result of interactions between the storyteller and their social environment (Andersson, 2011).

Adolescents, schooling, and identity construction
Adolescence is critical to many aspects of developing self and identity (Pfeifer & Berkman, 2018). In fact, [b]y constructing a sense of identity in the form of autobiographical stories, adolescents recognize that they are the same person across time and different contexts. Importantly, these life narratives are based on real experiences but are also highly subjective, as adolescents form them according to their own understanding of what was important for who they have become, and are also subject to change, as what adolescents find important for their identity may change over time (Branje et al., 2021, p. 908).
In a recent review about the role of schools in early adolescents' identity construction, Verhoeven et al. (2019) analysed 111 studies from different sub-disciplines of educational research. Their findings are summarised as follows: At school, messages may unintentionally be communicated to adolescents concerning who they should or can be through differentiation and selection, teaching strategies, teacher expectations, and peer norms. Teachers who intentionally wish to support the fostering of positive identities could organise explorative learning experiences, which need to be meaningful and situated in a supportive classroom climate.
In relation to school mathematics, and especially during the transition from primary to secondary education (Mkhize, 2017), learners' participation in the subject often decreases, not due to any cognitive "deficiency", but mainly because of a lack of motivation on behalf of children (Rončević Zubković et al., 2021). As a result, many lower secondary pupils often share negative stories about their experiences with school mathematics (McCulloch et al., 2013;Usher, 2009). To develop positive mathematical identities for adolescents, research suggests that teachers ought to consider enhancing their sensitivity to pupils' psychological needs, quality of feedback, and instructional learning supports in their daily interaction with pupils (Darragh, 2013;Lim, 2008;Miller & Wang, 2019). Nevertheless, to do so, the voices of pupils themselves (McIntyre et al., 2005), especially regarding identity construction (Bragg, 2007;Czerniawski, 2012) need to be taken into consideration.

The Norwegian context
In Norway, where this study was conducted, compulsory schooling is for 10 years, between the ages of 6 and 16. These years form what is called "grunnskole" in Norwegian, which is further divided into primary (barneskole, years 1-7, ages 6-12 approx.) and lower-secondary school (ungdomsskole, years 8-10, ages 13-16 approx.). In fact, many primary and lower-secondary schools are on the same premises, like the school this study was conducted. After year 10, children can choose not to continue schooling or can attend three or four more years of upper-secondary education, following either an academic or a vocational path respectively. In the academic path (three years), pupils start on a general study programme in the first year, choosing between two mathematics subjects: the theoretical and the practical. All pupils are required to take at least two years of upper-secondary mathematics. For those pupils who choose to have mathematics for all three years, there are two separate mathematics tracks: mathematics for social sciences and mathematics for natural sciences (Borge et al., 2022). Pupils in the vocational path (four years) typically follow a 2 + 2 model, that entails two years in upper-secondary schools followed by two years of apprenticeship training and productive work in a training enterprise or public institution. During the first two years, pupils take, among other classes, mathematics as a core subject (Utdanningsdirektoratet, 2020).

Participants
In this study, there were 21 participants/pupils in the last months of year 7 (roughly speaking, ages 12-13), right before they officially began lower-secondary education. We are aware that educational systems around the world are structured differently, meaning that in other contexts children of the same age would already be considered attending lower-secondary education. The pupils, who voluntarily expressed interest in taking part in this project, attended the same school in urban Oslo and were from three different classes of the same year group, sharing the same mathematics teacher. They all knew each other well and formed friendships across classes. Author 1 was familiar with the school and pupils, as she had previously completed her school placement (as part of her own teacher education) there.

Data collection and analysis
Pupils were divided in five groups and participated in focus group interviews. This method is based on conversations in which participants can gather around specific issues, to discuss how knowledge and strategies are constructed within certain communities (Postholm & Jacobsen, 2018). Focus group interviews can facilitate exploratory research by "allowing opinions to bounce back and forth and be modified by the group, rather than being the definitive statement of a single respondent" (Frey & Fontana, 1991, p. 178). This method has been used by other colleagues for examining children's mathematics-related experiences (e.g. Berry et al., 2011;Nosrati & Andrews, 2021;Seah & Wong, 2012). Prior to the interviews, we discussed group allocation both with the children and their teacher, and formed the groups based on who felt more comfortable being with whom. Even though gender was not a factor examined here, we are aware that it can be a source of influence in identity construction among adolescents (Darragh, 2013;Lim, 2008). For this reason, we considered the gender pupils identified with when forming the groups. Specifically, groups 1 and 2 included four girls each; groups 3 and 4 included five and four boys, respectively; and group 5 included two girls and two boys. To elicit ways adolescents constructed their mathematical identities, each group participated in several activities, in the form of clinical interviews (Zazkis & Hazzan, 1998). For example, pupils were asked to choose as many adjectives as they wanted from a given list (or add any other adjectives they wanted) to describe school mathematics, put school subjects in an order based on how interesting and how important they were to them, and choose from a list of statements those best describing themselves, and mathematics. Each of the activities provided opportunities for Author 1 (who conducted the interviews) to ask more questions about the importance of mathematics, how pupils positioned themselves as learners in the present, where they would like to be in the future, and how their claims linked to their own stories. Each focus group interview lasted from 60 to 90 minutes and was transcribed soon after its completion.
Due to the exploratory nature of the study, no predetermined coding scheme was utilised. On the contrary, a reflexive thematic analysis was employed, aiming at identifying patterns in our data (Braun & Clarke, 2021), across all focus groups. Our analysis was data-driven (Brinkmann & Kvale, 2015), moving from open to axial coding (Scott & Medaugh, 2017), similar to the ways described by grounded theorists (Glaser & Strauss, 1967/2017Strauss & Corbin, 1998). During the analysis process, the authors had regular communication. The fact that Author 1 is Norwegian while Author 2 is not, allowed us to bring insider and outsider perspectives respectively to a data analysis and interpretation. In undertaking our analyses, and drawing on Bjuland et al. (2012), we have tried to privilege the words pupils used, as it is from these words that their identities can be inferred. Finally, by employing a data-driven thematic analysis and elements of grounded theory, we were fully aware that the themes identified might not correspond to our prior readings of the literature, and that we might need to revisit the academic literature to draw on new resources (Lambert, 2019).
Through the process described above, we identified three themes around which the 21 participants constructed their mathematical identities. These are presented and discussed below. Nonetheless, while we found each of them interesting and important in their own right, we felt that approaching the themes individually would not suffice to tell a complete story about the ways early adolescents construct their mathematical identities. Furthermore, as we can see in the pupils' quotes as presented below, the themes were often in communication with one another. For this reason, we decided to conduct further individual interviews, to explore how the themes were possibly connected and how they can be used to inform us about pupils' mathematical identities. Revisiting the field and collecting further data as part of an iterative cycle is common for studies located within the grounded theory tradition (see for example, Bonner & Adams, 2012;Gasson & Waters, 2013;Hachtmann, 2012;Karpouza & Emvalotis, 2019). Therefore, the 21 participants were invited to a follow-up individual interview. Six of them responded positively and participated in an individual semi-structured interview with Author 1, with the aim of further unpacking pupils' stories around these three themes. Later on, we will demonstrate the case of Tina, not necessarily because it is particularly extreme or unique. Instead, Tina was chosen randomly among the six participants and serves as a suitable example of how the three themes identified are interlinked.

Ethical considerations
This study was conducted in accordance with the ethical standards of the Norwegian Centre for Research Data (NSD). Before collecting any data, we received the approval required by the NSD. For the pupils participating, information-and-consent forms were signed both by the children themselves and their parents/legal guardians. All measures have been taken so that the anonymity of the participants is maintained. Also, different criteria of trustworthiness, as outlined by Lincoln and Guba (1985), were applied through different stages, to ensure the rigour and quality of our analyses. For instance, the data collection method (focus group interviews) entailed triangulation, as we employed both conventional interview techniques and various activities, common in clinical interview approaches. In addition, our insider-outsider perspectives allow us to raise the credibility of our analyses, findings, and interpretations. Finally, for transferability purposes, we acknowledge that our findings are framed by the Norwegian sociocultural context, and so we refrain from making generalisations or claims about universality and applicability in other contexts. Nonetheless, what can be taken as transferable from our work is the methodological approach, which we would like to encourage colleagues to apply in other contexts, to investigate how early adolescents construct their mathematical identities elsewhere.

Findings and discussion
Our analysis yielded three themes around which participants construct their mathematical identities. These are concerned with popularity, effort, and achievement. We unpack them below, with the use of representative quotes from the pupils. In doing so, we do not present the themes separately, as they often intertwined in pupils' responses. Also, in line with the principles of grounded theory (Lambert, 2019), we explore new resources from the academic literature, to help us interpret the themes.
During the focus-group interviews, the concept of popularity (a.k.a. high social status) was brought to the table by all groups. As several studies point out, popularity is often desired by early adolescents to a greater extent than the desire for high academic achievement (Chase & Dummer, 1992;Ferguson & Ryan, 2018). Let's see an example from Group 2. Mathilde: Yes, and Nathaniel is a geek.
Othilie: Yes, he's a bit of a geek.
In this example, the girls used "geek" to describe a fellow pupil who finds enjoyment in mathematics. Interestingly, the term "geek" was used by all groups to refer to what pupils understood as the opposite of being popular, the same way the Cambridge Dictionary 2 defines the term as "someone who is intelligent but not fashionable or popular". This echoes Latterell and Wilson (2004), who express concerns about the fact that people who enjoy mathematics are often depicted as "geeks" and "abnormal" in popular culture. Ådne from Group 3 argued that the most popular children in the class are those "who are not geeks". His comment led to a discussion about the connotations attributed to the word "geek", with Ulrik arguing that "[i]t's another word for smart, I guess. But that kind of smart that comes with lots of effort. It's not always used positively. Also, a geek is usually a little shy".
As the discussions developed around popular vs geek, some children reached to realisations about the links between geek and mathematical effort. While actual effort in mathematics is typically associated with high levels of motivation (Liu, 2021;Morano et al., 2021), adolescents do not appear to self-report high effort (Pinxten et al., 2014), as they are often concerned that it might compromise their popularity (Kurtz-Costes et al., 2008). Here, the boys of Group 4 drew some interesting parallels between mathematics and football.
Isak: The word "geek" is perhaps mostly used when people talk about studying. You don't call Ronaldo and Messi geeks.
Isak: What are they, then?
Edvard: Ronaldo is a football genius and has talent, and . . .

Isak: And works hard
Edward: Yes. Hard working.
Later, Group 4 expressed objections about the relationship between popularity and mathematical effort. The statements stood out from the conversations that took place in the other groups, as the boys here challenged their own understandings of "geek", especially when seen as the opposite of being "popular".
Isak: Some people don't quite know what "geek" means. Just because someone wants to work hard for . . . Let's say someone wants to do well on a maths test and is very focused, then you're not a geek even if you want to be focused so you . . .Someone who is geeky like that thinks that they are judged a bit like that and that they are not that cool because they only focus on that, so they try to be slightly different, but it's really a bit of a jerk because then they change their minds, as it's actually nice to work hard for things.
Edvard: Think about Messi, for example. He's like, he was probably a geek who didn't want to. . . He probably didn't go to parties, he was probably out practicing his football techniques hard instead, and now it's paying off.
Isak: Well, I don't quite know what "geek" means but I think of it as someone who cares a lot about something.
I: How much effort should one put into maths to become popular, then?
Edvard: Popular, I don't think that working with maths makes you popular.
I: Does working a little on maths make you more popular?

Isaac: Yes
Edvard: Yes, I actually think so.
Isak: Yes, I think so too, but it's really stupid because then people work worse with things, and suddenly such cleverness and economy just go down.
I: Yes, do you think about those who take over society. . .?
Isak: Yes, because then you work a little worse for it, and it can be a bit silly. Because, you don't have to judge people for being like that, since it's not a bad thing.
A third theme, concerned with mathematical achievement, came to the fore from the discussions of all groups. While several studies highlight positive relationships between effort and achievement (Hemmings & Kay, 2010;Marsh et al., 2016;Pinxten et al., 2014;Xu, 2018), pupils in our study appear to add popularity into the equation to talk about the desire of high achievement with minimal effort. Below we see Group 2 talking about this.
I: How does it feel when the teacher gives you challenging mathematical tasks and you answer correctly?
Tina: It feels great! Mia: Very good! Othilie: Yes, it's a good feeling.
I: How would you describe someone who manages to finish the task first and present a very interesting, unique solution?
Mia: Then that person is cool.
I: Hmm. Earlier you were discussing geeks and effort, right?
Tina: Yes, but if you manage to be smart without putting too much effort into it, then you're not a geek. You're cool.
To better understand how the three themes (popularity, effort, achievement) might be related, we turn our attention to the case of Tina, one of the six pupils who voluntarily participated in individual interviews. Tina's participation in a one-to-one interview with Author 1 provided a space for her to feel more comfortable and discuss how the three themes relate to her actual and designated identities.

The case of Tina
Tina's case sheds light on the tensions she experiences between popularity, effort, and achievement. To illustrate the complexities and interconnections between the three themes, we draw on both her participation in the focus-group interview and her individual interview, to sketch her mathematical identity profile. Tina describes herself as someone who has always performed well and with little effort in mathematics. As she states, mathematics "has always been too easy, really. (. . .) I don't think it's that difficult, and nothing motivates me to want to work harder in anything". She clarifies that she does not consider herself a geek because "geeks put in a lot of effort to perform high, while I don't". As she argues, the combination of excessive effort and high achievement, a typical characteristic of geeks, does not necessarily relate to popularity. In fact, as she comments, "[y]ou don't have to be good at maths to be popular. The reverse is actually true". At some point during the group interview, the discussion between Tina and the other three girls is on whether popular pupils in their class are also good at mathematics. Tina responds immediately: Tina does not believe that popular pupils in the class are necessarily good at mathematics. Through her statement, she distances herself from the status of being popular. Mia's response, however, informs us that Tina is perceived as both a high achiever in mathematics and popular by her peers. Yet, in her individual interview, Tina confesses that she does not see herself as highly popular since "popular girls are usually the pretty ones and popular boys are good at football. How shall I put it? Not smart". On the contrary, she describes herself as "a good pupil, especially in mathematics", but one who is "naturally smart".
She also expresses a wish that her peers saw her as "popular". She says, "I don't think it helps that I'm so shy. Well, my best friends would say I'm funny but to others I am more of a shy person". Tina's views about her own identity contradicts Mia's statement that Tina is, in fact, perceived as a very popular pupil, in line with Sfard and Prusak (2005) who argue that the stories one tells about oneself are not necessarily aligned with the stories told by other people about that person.
During the focus group interview, Tina highlights an interesting idea, saying that "if you manage to be good at maths without putting much effort into it, then you are at least cool!". The overall impression we have of her is that she wants to maintain and promote an image of a high achiever in mathematics, yet with little effort. In relation to her desire to be more popular, she aims at achieving this by demonstrating how effortlessly and well she can perform in mathematics because "often, popular people do not put much effort in mathematics". For this reason, in her individual interview she describes an incident from a mathematics lesson that, in her own view, put her in "an embarrassing situation" and "could ruin my image". According to this story, the teacher gave the class a mathematical task, which for Tina was so easy. I had solved much more difficult tasks than that. But I made some stupid mistakes. I forgot to add some numbers. The right answer was 85. I got 35. And who got the same answer as me? The most beautiful, popular girl of the class. Who, by the way, is not very good at maths. She and I got the same answer, 35. That was a bit annoying. She is popular because she is pretty. I can't be doing stupid mistakes like this! Everyone expects me to get it right.
Overall, Tina's responses indicate that the relationships between the three themes (popularity, effort, achievement) are complex. In her case, effort and achievement are inversely related; with little effort she performs well in school mathematics. Things become more complicated when popularity is also considered. On the one hand, Tina thinks that popularity and high achievement in mathematics do not co-exist, not least in the way she sees herself and her peers. On the other, she wants to raise her image as a popular student; yet not in the "conventional" way of being "a pretty girl", but by demonstrating how effortlessly she can be a high achiever in mathematics. For this reason, "stupid mistakes" like rushing to solve a mathematical task, can "ruin", in her view, her attempts to become more popular.

Bringing the three themes together-a proposed model
Effort, popularity, and achievement are identified as the main themes around which early adolescents in this study construct their mathematical identities. Furthermore, as we see in the case of Tina, the links between these themes are complex and cannot be described in terms of cause-andeffect. To make sense of these, we revisit an activity from the individual interviews with Tina and the other five pupils. Each was given scales, as shown in Figure 1, and was asked to locate themselves in relation to where they felt they were at present and where they would like to be in the future, corresponding to what Sfard and Prusak (2005) call actual and designated identities. To clarify, this activity was not designed to quantify pupils' responses in any way. Rather, it was introduced as a warm-up activity to enable pupils to share their stories in relation to the three themes.
In retrospect, we propose the model presented in Figure 2, as an operationalisation tool of Sfard and Prusak's (2005) concepts of actual and designated identities. In this tool, the themes of effort, popularity, and achievement serve as axes of a Cartesian coordinate system. We also demonstrate how the tool illustrates the actual and designated identities of Tina ( Figure 3) and Nicolai (Figure 4), based on their responses to the aforementioned task during their individual interviews. The tool can be used for facilitating discussions with pupils. Nonetheless, we envision its use in future studies for the purpose of uncovering whether the desire for popularity in the classroom can act as a possible obstacle in early adolescents' effort in learning mathematics, and whether popularity and effort can compromise achievement. The visual element could enable easy comparisons between cases of different pupils or the same pupil at different times. Figures 3 and 4, for example, show that both Tina and Nicolai (the case of whom we do not present in detail) would like to raise their achievement and popularity, but also reduce their effort in learning mathematics. This alludes, in a way, to their underlying values about mathematics and its learning (Bishop, 2001), which, however, is not examined here and could be the topic of future investigations.

Concluding thoughts
The work presented here identifies popularity, achievement, and effort as important elements of early adolescents' mathematical identities. Furthermore, the relationships between these three elements are found to be complex and often work in inversely proportional ways, for example, the perception that increased effort in learning mathematics will decrease popularity. In other words, pupils' participation and positioning in the mathematics classroom, as well as the effort they put in learning mathematics, may be affected by their perceptions of their social status. While all participants here argue about the importance of mathematics for their futures, many appear willing to "sacrifice" effort for popularity in the present time, while others wish for a high achievement that comes effortlessly. Such perceptions, we believe, are not independent of popular stereotypical images of mathematics and mathematicians (Jensen & Sjaastad, 2013;Picker & Berry, 2000), especially when films and other media contribute to the maintenance of these images (Latterell & Wilson, 2004). Despite older and more recent attempts to raise public awareness of mathematics, how the field is depicted in popular culture, and the impact of these depictions on educational discourse (see for example Appelbaum, 1995;Behrends et al., 2012), there is still much to be done towards this direction.
This study has theoretical, methodological, and pedagogical implications. Theoretical implications involve the extension and refinement of our understanding of identities as narratives constructed by individuals about themselves (Sfard & Prusak, 2005). As extensively discussed earlier, our study suggests that the mathematical identities of early adolescents who participated here were organised around three primary dimensions: popularity, achievement, and effort. Our research also holds methodological implications, with the creation of a threedimensional model that enables both quantification and qualitative exploration of students' mathematical identities. This model may have pedagogical implications, as it can be utilised by teachers and teacher educators, to prompt discussions about what it means to be a "mathematical" person and to challenge stereotypical images that portray mathematicians and other mathematics users as unpopular or as individuals who have no interests beyond mathematics.
In closing this paper, we would like to point out some limitations of our work, which could also be seen as opportunities for future research. As mentioned at the beginning, in this project we do not address issues such as gender, ethnicity and immigrant background, disability, social class, and religion, even though we are fully aware that these may have a significant role in identity construction (both in relation to school mathematics and in general). Future research could explicitly take these into consideration and examine how each of these issues may impact identity construction during early adolescence. Furthermore, while our findings present three interesting themes around which early adolescents construct their mathematical identities, we refrain from making generalisations outside the context of our work. For this reason, we would like to encourage other researchers, both within Norway and in other countries, to carry out similar investigations, to confirm the transferability of our themes, or refute/adapt them by considering other culturally situated conditions that might have been unnoticed here. Finally, our work is concerned with children at early adolescence, and especially at the threshold of transitioning from primary to secondary school. Future research could examine mathematics identity construction by employing longitudinal research design, to shed more light on these three themes developed diachronically, as well as how their interrelations might change as children progress to middle and late adolescence, and later to adulthood.