Posibilidades para la persona trabajadora

An important distinguishing characteristic of ethnographic studies is the incor- poration of contextual information related to participants being investigated (Eisenhart, 2001; Silverman, 2005). Two kinds of data were sought based on this characteristic. The first kind of data focused on students’ mathematical identity and experiences. The second kind of data related to the context (i.e., system of education, school, and mathematics classroom) in which students learned mathematics. While data on student’s identity and experiences was collected using the diary method, data on the school and classroom context derived from general documentary information, questionnaires administered to mathematics teachers and school administrators, and direct observations of the mathematics classroom and school.

The diary method and procedure applied

The diary method was used for gathering data on how individual students per- ceived themselves in relation to mathematics and how they had experienced mathematics. In acknowledging that there are different kinds of diaries, an ap- propriate choice of diary method was needed. Memoirs are diaries that are often written with the intention of publishing them (Allport, 1943) whereas intimate journals as personal records are intended to be kept as private documents (All- port, 1943; Lida, Shrout, Laurenceau, & Bolger, 2012). Logs also represent private records consisting of a list of events without detailed commentary (cf. Allport, 1943; Lida et al. 2012). The diary method used in this study is in the category of intimate journals. It was useful in gathering detailed data about stu- dents’ mathematical identity (cf. Robson, 1993) since it was considered as a “powerful way for individuals to give their accounts of their experiences” and thoughts about their experiences and themselves (Clandinin & Connelly, 1994, p. 421). Open-ended questions were designed to guide students’ writing of their diaries.

The diary method is useful particularly when data cannot be accessed through other methods such as interviews (Clandinin & Connelly, 1994). For this study, the diary method was considered the most appropriate one. In a school where teachers had immense power and authority over their students, students did not accept being tape-recorded. They were highly concerned about preserving their anonymity and security during and after the research process. This fear of being tape-recorded meant that the interview method would not succeed. In conse- quence, the diary method was chosen as an alternative method and was also

However, like many other methods of data collection in social research, the di- ary method has weaknesses. For example, a great deal of responsibility is placed on the student, who has to record information according to the researcher’s in- struction (Robson, 1993). Also, there are possibilities of misreporting for various reasons, such as trying to please the researcher (Robson, 1993). To address the first problem, participants were asked to write diaries when they had free time. Many of them chose to write their diaries after classes and during weekends. The possibility of misreporting was difficult to detect. However, students did not need to please the researcher who was an outsider and not one of their teachers or other school staff. Also, students’ willingness to reveal ‘risky’ information about their ‘difficult’ mathematics teacher reflected their trust in the researcher.

The diary procedure was based on a common pattern of interaction between students and the teacher using notebooks as a medium of communication. In the school, notebooks were sometimes used as tools for more individualised teacher- student communication related to mathematics learning. First, teachers provided assignments and asked students to do the assignments in their notebooks. The notebooks were then brought to the teachers after the assignments were com- pleted. The teachers marked the assignments and wrote comments or provided other forms of feedback in the notebooks, including asking students to come to their offices for extra tutorials. The teachers then brought the notebooks back to students so that each could read the teachers’ feedback.

I applied a similar approach during the fieldwork of the study. I wrote open- ended questions (one question at a time) in the notebooks that I had bought and issued to students only for research purposes. Students responded to the ques- tions by writing in the notebooks. In response to what they had written, they were asked more specific questions to let them elaborate on what they had pre- viously written. This procedure was maintained during the entire period of the fieldwork until the stages at which further questioning yielded no new informa- tion (Corbin & Strauss, 2008).

Other methods of data collection

In order to gain understanding of the context in which students learned mathe- matics, methods other than the diary method were applied. Documentary sources and their analysis represented such data. The value of this method in research is summarised by Mason (2004):

“The analysis of documentary sources is a major method of social re- search, and one which many qualitative researchers see as meaningful and appropriate in the context of their research strategy. The idea of documentary research used to conjure up a mental image of a researcher digging around in a dusty archive among historical documents, but in

fact there are many different ways of generating data through docu- ments” (p. 103)

Documents for this study consisted of records of the Tanzanian mathematics curriculum for secondary schools and students’ mathematics test scores. With the consent of students and the school’s academic officer, the scores from school’s official records were obtained. They were useful in understanding the possible implications of students’ mathematical identity for their academic per- formance. Media texts related to education in Tanzania and ministerial docu- ments (e.g., circulars, school inspectorate reports, Tanzania education policy, and educational programmes) also were an important source of contextual in- formation and helped in contextualizing students’ thoughts about themselves in relation to mathematics (cf. Mason, 2004; Pink, 2001; Platt, 1981). The docu- ments provided information about the broader social, political and economic aspects related to mathematics education in a Tanzanian classroom. They spe- cifically provided data on both the macro (i.e., broader, systemic and cultural setting) and micro (i.e., the classroom/school) context in which students learned mathematics. Some of these documents were available at the school and some were in the main libraries of Tumaini University Makumira and University of

Dar es Salaam.

Additional data were gathered through open-ended, self-made questionnaires constructed by the researcher on the basis of preliminary observations (see Ap- pendices C and D). The questionnaires sought to explore teachers’ and adminis- trators’ views and feelings about the school students and their progress in mathematics learning. Two mathematics teachers—a third grade teacher whose class was the main focus of the study, and a second and fourth grade teacher— filled these questionnaires. In addition, two school administrators (i.e., deputy principal and academic officer) filled another questionnaire. While their views provided valuable contextual insights for the study, the most important data de- rived from the conversations with the grade three mathematics teacher when observing his class, teaching activities and behaviour. Relevant parts of these conversations were hand recorded immediately after each conversation and later typed.

The researcher’s observations of the mathematics classroom provided infor- mation on events and practices in the classroom of the study. The classroom was observed eleven times in total and field notes were written each time. The time interval between the observations ranged from three days to two weeks. Each observation took about 40 minutes (i.e., the whole lesson) and the class was observed once for each topic being taught during the period in which observa- tions were done. The observations focused on students’ attendance and charac- teristics of the physical environment of the classroom. Other observations tar-

tions, when asking questions to students, assigning tasks to students, and when students responded to this teacher behaviour. In addition, observations were made of student-student interactions while participating in the class (e.g., in “pair discussions”) and of students’ free talk, particularly in the absence of the teacher. Furthermore, group discussions with the third grade students were con- ducted during the first two weeks of classroom observations. These took place outside the classroom (in the school library building) and were selectively re- corded by hand and later typed. The data were used in identifying and character- ising students’ mathematical identity and experiences.