Challenges in the study process

To enter the field for research purposes, particularly if the field is a formal insti- tution, permission has to be sought from persons who hold positions of author- ity. Because these persons control access to sources of information, they are often labelled “gate-keepers” (Garfinkel, 1967). When seeking permission from gate-keepers to enter the field, a sense of uncertainty about whether the permis- sion will be given or not is inevitable. I experienced this uncertainty while wait- ing for permission from the Commission for Science and Technology (COSTECH) in Tanzania to do fieldwork in Northern Tanzania. The delay of the

after the permission was granted. The second gate-keeper, the deputy head of school, did not cause such uncertainty as the permission was granted immedi- ately.

The disruption of my fieldwork plans throughout the fieldwork period was particularly challenging. This disruption occurred after classes were unexpect- edly suspended. Decisions to suspend classes were made due to students’ misbe- haviour. While the students were outside their classrooms, they were given man- ual work such as cleaning or gardening. They were sometimes ordered to assem- ble outside their classrooms to hear an announcement from a teacher-on-duty or listen to a short speech given by an important visitor. There were a few cases in which students who had not paid school fees were ordered to go home and col- lect the fees. Although disruptions were not regular, they were frustrating when they occurred and resulted in rescheduling my plans from time to time.

Challenges appeared also in relation to the data collection and analysis. One challenge consisted of complications related to the sources and nature of data to be collected. The data were collected in a school with authoritarian characteris- tics; as a result, students’ concern about their personal security initially seemed to inhibit them from giving honest views about the school and themselves in relation to mathematics. While considering this inhibition and its implications, I was not certain about the trustworthiness of the responses they would later nar- rate to me. But two events occurred that increased the possibility of obtaining valid data from students. First, the deputy head of school, also a mathematics teacher, announced the permission she had given me to all the teachers and stu- dents in the school. Second, the third grade mathematics teacher showed interest in my fieldwork by encouraging his students to provide me with the needed in- formation.

However, this was not enough to gain students’ trust. I was at the school as a stranger seeming to be accepted by the school authority and the mathematics teachers. I thought there was likelihood that students would not trust me but would think that I might provide their data to the mathematics teachers and school authority. I dealt with this challenge by familiarising myself with the students and interacting with them during the preliminary observations of the school and classroom. While interacting, I behaved in a friendly manner and showed willingness to learn from them. Trust was gradually built in the first few weeks of the fieldwork. But even after the trust was ultimately gained and stu- dents were willing to openly respond to my questions by writing their responses in notebooks, they still wanted their names to be hidden using numbers as secret codes and to be accessed only by me. This gave the students a sense of personal security and they could write ‘sensitive’ information without fear of punishment. Another challenge with the data collection was related to language transla- tion. Some third grade students wrote their diaries in Swahili and thus required translation of the data into English before analysis. Despite my fluency in Swa-

hili, I needed a longer than expected time to translate the data and verify the translation while retaining the meaning of the original data. The first drafts of my translation were verified through repeatedly asking the students to clarify the data. Apart from this translation challenge, there were additional problems with the data. For example, some of the data given by students were not relevant to the diary questions. Also, a few students did not respond to some of the ques- tions, particularly questions on their pre-school Mathematical experiencing. During interactions with the students, I learned that this problem occurred be- cause the diary questions were not clear to students or were not specific enough to limit the students to the specific kinds of information that I needed. Three of the students seemed unable to recall well their childhood mathematical experi- ences. In response to these observations, I asked these questions again in a dif- ferent and simpler manner and excluded the data from three students who failed to clearly recall their childhood mathematical experiences.

Even after students understood my diary questions and responded to the questions in detail, some of their texts had parts that were not legible. I asked the few students with illegible handwriting to spare time for diary writing in order to write their texts slowly and more carefully. The data that were illegible or gener- ated through unclear diary questions were not analysed. A further difficulty with the data related to its size, being too large to handle easily. I faced this challenge despite my attempt to conform to the saturation principle (Corbin & Strauss, 1998) during data collection and analysis (i.e., ending data collection when new data leads to no new insights on a phenomenon being investigated). In the proc- ess of data collection and analysis, judging whether saturation was reached or not was sometimes difficult because the number of students in each of the four identity types was too large and resulted in the large amount of data. As a result, a large amount of repeating (and thus redundant) data characterised my initial drafts. I reduced the data and its sources (i.e., the students) for each identity category so that the remaining data and its sources clearly addressed the main research questions and were representative of students in each of the four iden- tity categories.

Moreover, the emergence of Image-maintenance identity was unexpected during the fieldwork because it had not been documented or theorised in the literature on mathematical identity that I had reviewed. To gain a theoretical understanding of it, I reviewed the literature on identity outside mathematics education, mostly in sociology. After beginning to understand it, there was still a puzzle not addressed in the theory: the association of Image-maintenance iden- tity with a decline in mathematics test scores as evidenced in this study. The data suggest that the reason was the students’ specialisation in Arts and increased study time in these subjects. But the question is whether this identity type would always accompany a decline in mathematics test scores when students specialise

maintenance identity who specialise in Arts may provide a satisfactory explana- tion.

Furthermore, interpretation of data was based on the meanings the data sug- gested as well as my understanding of theories and concepts of identity that I had reviewed in literature. It is possible that the influence of theories and con- cepts may have led to inconsistency between data and my interpretation because of the theoretical bias (Brewer, 2000). In an attempt to minimise this possible inconsistency, a critical approach was applied by raising awareness of my pre- conceptions through reflexivity and being self-critical of them, by asking ques- tions relevant to the broader aims of the study when these aims had fully evolved, by constantly comparing questions with the data and the data with the theory to ensure consistency between them, and by maintaining trust between myself and research participants. Similarly, the labelling of the four mathemati- cal identity types was based on my interpretation of the data and my understand- ing of theoretical ideas on identity. This labelling was not done at once. Labels changed as the study progressed and final decisions on the labels were made when the study was nearing its completion. The aim was to ensure that these labels clearly reflected features of each mathematical identity type. The ultimate labels and categories are still subjective. Another researcher might have labelled the identity types differently.

Finally, the findings may not be completely representative of students beyond the school and classroom where the study was conducted. From the post- positivist perspective, this is a major weakness (Brewer, 2000). However, gener- alisation was not the purpose of this study. Being exploratory, its mission was to identify important features of students’ mathematical identity and its develop- ment in a Tanzanian mathematics classroom. The overall value of the findings of this study is its revelation of the complexity of Mathematical experiencing and its role in mathematical identity development among students in that classroom. Moreover, the development of different mathematical identities as a result of variations in the way students had experienced mathematics may characterise other mathematics classrooms in Tanzanian secondary schools. This likelihood derives from the understanding that mass failure in secondary school mathemat- ics examinations in Tanzania has a long history (Appendix C) and that mathe- matics classrooms are typically overcrowded with students and have insufficient mathematics teachers and teaching materials (Kisakali & Kuznetsov, 2015). It also derives from the fact that students from wealthier homes and those whose parents have formal education have a better chance to succeed in mathematics learning compared to children whose parents are materially poor or have no formal education (Uwezo, 2010, 2011).