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This section deals with students’ negative mathematical identity, which in this study was characterised as Oppositional identity. The key feature of this identity type was the students’ negative mathematical self-perceptions linked with their unwillingness (or oppositional tendencies) to take part in mathematical activi- ties. Specifically, negative self-perceptions of mathematical competence that characterised all students in this identity category was associated with unwill- ingness (even resistance) to take part in assigned mathematical tasks (e.g., home work) and to interact with others in pairs organised by the teacher. They dis- played low or non-existent ambition and commitment to learning mathematics. This finding suggests that while the role of the current teacher is important in the development of students’ Oppositional identity, this identity is also linked to the students’ previous encounters and self-evaluations related to mathematics (Allen & Schnell, 2016; Bishop, 2012). Based on consistently weak mathematical per- formances despite effort expenditure, students in the present study judged them- selves as having low capacity for succeeding in mathematical activities. As a result of these judgments, they gave up learning mathematics mostly in the third grade of their secondary school. Before giving up, these students had set achievement goals and strived to realise them in specific mathematical tasks. But when their strivings were associated with frequent failure despite increased ef- fort expenditure, students began to doubt their capabilities in executing the tasks and ultimately gave up. For these students, failure to succeed in mathematical activities and doubting their mathematical competence had begun several years prior to the third grade.

Students’ negative mathematical self-perceptions and associated unwillingness to engage in mathematical activities were further related to the way they per- ceived mathematics. Students had come to view mathematics as a subject that was irrelevant to their imagined future studies and careers. Mathematics had thus been ‘mentally’ excluded from the list of subjects that were perceived as rele- vant to their lives. Consistent with this, Anderson (2007) argues:

Students who do not see themselves as needing or using mathematics outside of the immediate context of the mathematics classroom may de- velop an identity as one who is not a mathematics learner. (p. 9)

However, despite the students’ negating previous experiences and the perceived irrelevance of mathematics to their present and future lives, they were coerced into attending mathematics classes where their pattern of inactivity was strengthened with no actual learning (cf. Lerman, 2001). The link between nega- tive mathematical self-perceptions and a tendency to be oppositional to such classes was evident in the classroom (cf. McGee, 2015; Martin, 2000). Students, while perceiving themselves as belonging to the Arts group, tended to sit in the back of the classroom and were often preoccupied with non-mathematical activi- ties as opposed to students with positive identities who preferred front seats and being near the teacher.

Furthermore, for students with Oppositional identity, the link between mathematical self-perceptions and emotion was unique compared to students with positive identities. While students did not set achievement goals and did not strive to succeed in mathematics tests, they reacted to their extremely low scores with indifference. That is, they did not show interest or concern for their scores. Positive emotions associated with high scores or negative emotions associated with failure in a test were only experienced in the Arts to which students were committed. In rare cases in which the students had scored unexpectedly high in mathematics (though still low compared to students with positive identities), the emotional reaction was surprise.

Even though this emotional aspect of Oppositional identity is seemingly not evident in existing literature on students’ mathematical identities, it can specula- tively be explained in three ways. First, the emotional reaction suggests a sig- nificant disconnection between students and mathematics; students did not feel belonging to the community of mathematics learners (Anderson, 2007; Cobb et al., 2009; Wenger, 1998). Second, the reaction suggests that, due to previous negative experiences with mathematics, they had no hope in the subject even after an increased effort. Finally, it also suggests that since mathematics could not be mastered even with increased effort (as perceived by the students), it was useless for the students’ present and future lives.

Lastly, Oppositional identity, like positive identities, was characterised by stu- dents’ tendency to endorse their negative mathematical self-perceptions by justi- fying these self-perceptions based on previous mathematical experiences. How- ever, the endorsement associated with Oppositional identity was different from one characteristic of positive identities. While students with positive identities cited their previous positive experiences to explain their positive self- perceptions, students with Oppositional identity cited previous negating experi- ences. Essentially, Oppositional identity was characterised by citations of fre- quent failure in previous mathematics tests in primary and secondary schools and of the associated fruitless effort they had spent on mathematics. The role of endorsement through justification seemed to be impeding. That is, justifying an oppositional (and negative) mathematical identity served to sustain it, thus hold- ing students back from striving for success in mathematics.

In short, the features of Oppositional identity—students’ negative mathe- matical self-perceptions, perceptions of mathematics as useless, indifference to failure in mathematics tests, and endorsement (through justification) of the nega- tive mathematical self-perceptions—all characterised Oppositional identity as constituting an impediment to mathematics learning.