5.2 Features of negative mathematical identity
5.2.1 Characteristics of Oppositional identity
Students with Oppositional identity, to some extent, varied among themselves in their mathematical backgrounds. For example, whereas Zuberi, Daudi, and Mapunda had occasionally been taught arithmetic or counting by their parents before primary school, Edwin, Ema, and Mary had not learned such skills (see
Appendix D for more detail). Also, in primary and secondary school, their effort at learning mathematics resulted in little or no success, and ultimately they gave up learning mathematics in the secondary school third grade after specialising in arts. Although they were opposed to learning mathematics at this stage, they nonetheless attended classes because such classes were compulsory. Other fea- tures associated with these students’ Oppositional identity are outlined in Table 9 and elaborated in the following subsections. The quotations presented in this section are drawn from the 6 (of 9) most representative students with Opposi- tional identity.
Table 9. Characteristics of mathematical Oppositional identity
-Negative perceptions of mathematical competence
-Limited interactions and rare or no personal involvement in mathematical tasks
-Lack of ambition to succeed in mathematics -Lack of commitment to learning mathematics
Self-perceptions of mathematical competence
Self-perceptions of mathematical competence among students with Oppositional identity were negative. That is, these students perceived themselves as having low mathematical competence and, more specifically, as lacking a gift in mathematics. Mapunda, for example, illustrates these perceptions:
I know you can’t be smart in maths in this school if you don’t have a special thing in your head. You must have it. Its’ not for everyone… People everywhere say maths is so difficult. I agree. I’ve seen it, but life is possible without maths. (Mapunda)[“you” refers to ‘I’]
The students’ perception of their low mathematical competence due to lacking a gift in mathematics was supported by their parents. They had observed their children’s’ consistently low test scores, and they had explicitly concluded that their children lacked a mathematical gift. This applied, for example, to Mary. She was convinced that she consistently got poor test scores because she had no gift in mathematics as described below:
My parents, especially my father, saw my poor score in every report… But it is only in maths and maybe chemistry sometimes. They saw me trying to work hard in mathematics in holidays…and they looked at my exercise books and saw that I was not doing well. My father said that I have no gift in maths….in other subjects it was different… and he said that I should work hard in subjects I could do well… And, yes, I feel my father was saying the right thing because I feel the same way and I do very well in other subjects. (Mary)
In addition, these students had frequently compared their mathematics test scores with those gained by other students in their class. They had found that their scores were much lower compared to the other students’ scores. This fur- ther confirmed their perceptions of lack of innate qualities for succeeding in mathematics as Zuberi narrated:
I’ve no gift...Of course, each time I was feeling uncomfortable because my friends always got very high scores even if they did not really work hard like me (Zuberi)
These students’ consistent failures in previous mathematics tests despite their effort had led to their negative self-perceptions of mathematical competence. As a result of these experiences and perceptions, the students had given up mathe- matics and concentrated in arts subjects, perceiving themselves as being in school only for gaining knowledge in arts.
Self-perceptions of mathematical participation
Students with Oppositional identity perceived themselves as individuals who did not willingly take part in mathematical activities or interactions related to learn- ing mathematics. Even though these students attended mathematics lessons as required by the school policy, they perceived themselves as individuals who only pretended to participate in mathematical activities when the teacher was close to them, for example, when he monitored their pair discussions. In prac- tice, this involvement was not genuine but it resulted from students’ fear of their teacher. Daudi illustrates such behaviour:
The teacher wants everyone to do his exercises. If you don’t do it you get punished. So you pretend you’re doing but in fact you’re not doing it… When the teacher collects the exercise books for marking he sees nothing is done so he just writes a big zero in the exercise book and writes words like POOR or LAZY. But it’s ok for me (Daudi)
Observations of the mathematics class again revealed that often the teacher stood in front of the room when teaching. These were the moments when stu- dents’ behaviour in relation to mathematics was expressed. As Ema stated, stu- dents with Oppositional identity used the time to engage in non-mathematical activities, whispered to one another, or remained quiet but without listening:
It’s always good when he is far. I mean if he is teaching in front of us, we do anything to push time. We talk silently or do homework, or maybe just think about something. (Ema)
Similarly, these students perceived themselves as individuals who did not really participate in teacher-organised pair discussions. They viewed themselves as persons who always took this time to discuss non-mathematical matters of inter- est as evidenced below:
We talk about anything we like, even if we look like we talk about a teacher’s questions or exercises… We can talk about it if he walks near us, but if he’s away we talk other things… We have to talk because the teacher wants everyone to talk at that time… So, you can’t just keep quiet (Zuberi)
The key reason why students did not genuinely engage in mathematical activi- ties was the students’ self-perception of mathematical incompetence, of not be- ing part of those who can learn mathematics, and of the uselessness of mathe- matics to their personal lives. These perceptions are reflected in Edwin’s re- marks, for example:
I don’t learn maths because I can’t do it. But I know that I don’t need it because I have Arts, not Science, and I will not choose subjects that have maths in them..I will study Arts like languages.(Edwin)
In short, self-perceptions in relation to mathematical participation and interac- tions were negative among students with Oppositional identity. They viewed themselves as not individually engaged in mathematical tasks or in interactions related to learning mathematics although they perceived themselves as students who regularly attended classes as required by the school. These students had given up mathematics, and this explains their oppositional behaviour in the mathematics classroom.
Self-perceptions of commitment to learning mathematics An important feature of Oppositional identity was the students’ perceptions of themselves as not committed to learning mathematics. In the past (in the first grade), students in this category had experienced mathematical commitment and had perceived themselves as committed. However, with time, the commitment had faded away and their self-perceptions of commitment became negative as Edwin illustrated:
When the teacher teaches, I feel like nothing important is going on. I liked maths in form one and I thought of working hard to become good in maths or to be a maths person like Pius [Edwin’s friend], but I failed.(Edwin)
Instead, these students viewed themselves as often experiencing a feeling of resistance or an impulsive desire to refrain from mathematics classes. Daudi experienced this impulse but was required by the school policy to attend classes and remain in class until the classes ended.
I have to be in class. It’s a must. So, I just sit there with the feeling that I want to go away from maths lessons. But, I must be there till the end of a lesson…I don’t like being in maths class because I don’t want to learn anything about it, but if you go out they punish you. (Daudi)[“you” re- fers to ‘I’]
Some students displayed unwillingness to think about mathematics or even to hear other people talk about it in or out of the classroom. Instead, these students turned their minds to subjects for which they had a stronger sense of commit- ment. Mary, for instance, often focused on English and History to avoid bore- dom due to the need to attend a mathematics class and to “learning nothing”, as she narrated below:
I don’t like those lessons or to have math in my head. But it is boring to be in class and learn nothing. What should I do? - I start doing things that make me feel good and not bored…I do English homework or maybe history. These are the significant subjects to me. (Mary)
Generally, these students perceived themselves as not only lacking mathematical commitment, but also reported resistance toward being exposed to mathematics.
Self-perceptions of ambition in learning mathematics
Oppositional identity was also associated with students’ perceived low or lack of ambition in learning mathematics. Clearly, these students viewed themselves as individuals who neither set goals for accomplishing certain mathematical tasks nor thought much about learning goals in mathematics. For example, Mary per- ceived herself as not one who set mathematics achievement goals or thought about those goals as shown below.
Since I became an Arts student I haven’t thought like how high I should score in maths. I only thought of it in the past… Now, I only spend my effort in whatever I can do in the examinations. Sometimes I only write my name on the paper and take it back to the teacher. (Mary)
Instead, students with Oppositional identity perceived themselves as individuals who set ambitious goals in other school subjects (Arts) in which they all wanted to excel.
Another feature of self-perceptions of mathematical ambition was the stu- dents’ view of themselves as individuals who reacted to their low mathematics test scores with indifference (i.e., the “I don’t care” reaction), as illustrated, for example, by Ema:
No, I don’t do maths at all so if I get F it’s just ok for me...I don’t com- plain or feel bad...It’s because I know I can’t pass any math exam. After a maths test I just go out of the exam room and don’t think about it.(Ema)
Among these students, negative self-perceptions of mathematical ambition were accompanied by expectations of failure in mathematics tests and indifference about these expectations as Mapunda remarked in the following quotation:
I know I’ll fail. Even if you give me a test now I’ll get F. So, why should I worry about it? Maths is too tough and I’ve no gift for it…I don’t even need it in my life. So, I don’t worry about it. (Mapunda)
In general, Oppositional identity was characterised by students’ self-perceptions of being individuals who lacked ambition for learning mathematics, that is, as individuals who did not set mathematics learning goals for themselves. Their
scores they gained during the third grade. The scores were the lowest compared to students with all other identity types. Table 10 presents average mathematics test scores for the 10 students with Oppositional identity.
Table 10. Mathematics test scores for students with Oppositional identity
Type of test Average score (in %)
Mid-term test 11.6
Terminal test 9.2
Annual (final) test 5
Average score (annually) 8.5
Note: The number of students in this category was 10 (assessment scale ranged from 0%
to 100%). Data source: school files of mathematics test scores.
Conclusion
In the secondary school third grade, the students with Oppositional identity per- ceived themselves as individuals who had low mathematical competence. They confirmed or justified these negative self-perceptions by citing their consistently low scores in previous mathematics tests, which they had gained despite their effort. The students had given up learning mathematics and perceived them- selves as not participating in mathematical activities, uncommitted to mathemat- ics, and as students without mathematical ambition.