CHAPTER 3: RESEARCH DESIGN
3.3 POPULATION AND SAMPLING
The population from which the sample was drawn comprises learners from primary schools in and around Zomba City. In this study, learners from standard 1, mathematics teachers for standard 1 and head teachers (principals) from five primary schools in Zomba Cityconstituted the sample. Zomba City was purposefully sampled. Educationally, Zomba City is divided into two districts – Zomba urban and Zomba rural. There are 18 primary schools in Zomba Urban and 193 primary schools in Zomba rural. One primary school from Zomba Urban and four primary schools from Zomba rural were purposefully sampled. Purposeful sampling means that the criterion for sampling is the purpose for which the sample is required. Considering that this study is an in-depth look at daily life, I had to focus on schools that were typical for their context (Merriam 2009).
3.4 DATA COLLECTION INSTRUMENTS, SOURCES AND
PROCEDURE
The data was mainly collected using lesson observations. Learners in standard 1 classes from the five primary schools in Zomba were observed as they were learning numeracy.
78
Further, a video camera was used to record all the lessons which I observed. The utterances in the videos were consequently transcribed. This was done to make sure that a close to accurate flow of the lessons was recorded, since the human instrument (the researcher) may leave out some very important elements of the lesson if only taking some fieldnotes.
The main data collection instrument in this study was the researcher - myself. Since observation constituted the major form of data collection, I made fieldnotes to accompany the recordings. Madden (2010:75) points out that an ethnographer is a form of recording device that must always be ‘on’. My role in this study changed. This is so because I am a researcher at a Malawi national curriculum development centre and I frequently visit the schools to monitor curriculum implementation and carry out different studies. I did not enter the schools as an officer from a national curriculum development centre. I entered as a student. This was reflected in the way I presented myself in the schools through the way I negotiated entry to the schools, talked to the participants and the way I dressed. This assisted in making sure that I did not look like an official. Further, a semi-structured interview schedule was in some cases used to interview teachers after the lessons. The semi-structured interview schedule allowed for probing the teachers’ responses as the interview was going on.
The other data collection instrument that was used in the study was a focus group discussion guide (see appendix 5). The guide was to elicit the mathematics culture from the learners’ perspective. The items in the guide were developed in such a way that learners’ voices about mathematics learning would be captured. Before using the focus group guide, the instrument was subjected to validation by ‘critical friends’. Revision of the instrument was made based on the comments that were made.
Furthermore a questionnaire on teachers’ mathematical beliefs (see appendix 6) was used in the study. Section A was crafted so that teachers’ biographic data was collected, section B was aimed at collecting teachers’ beliefs about mathematics, section C, to collect teachers’ beliefs about learning mathematics while section D was aimed at collecting teachers’ beliefs about teaching mathematics. For sections B to D, statements used in a study by Raymond (1997) to represent the teachers’ beliefs were adopted. The statements were put in a table form and provided for
79
columns for teachers to either strongly disagree, disagree, agree or strongly agree. The questionnaire was then validated by ‘critical friends’ before using them in schools.
The data were collected in three phases over an academic year. Data collection visits were done every term7. The number of days spent in the field and at each
school is shown in Table 3.1.
Table 3.1: Data collection phases
Phase Specific activities Duration of the field work
Phase 1 1. Setting the scene 2. General observation
5 days (1 day per school)
Phase 2 1. Lesson observation 2. General observation
10 days (2 days per school)
Phase 3 1. Lesson observation 2. Focus group discussion
3. Teacher questionnaire administration 4. General observation
20 days (4 days per school)
Table 3.1 shows the three phases in which data was collected, the actual activities that took place during each of the three phases and the duration of the phase. At each of the five primary schools, head teachers, standard 1 teachers and standard 1 learners were asked to participate in the study. Head teachers provided data through unstructured in-depth interview aimed at getting the general picture about the school. Standard 1 learners were observed as they were engaging in mathematics8. Careful
attention was given to what they were doing and speaking during the lessons. Pictures (still) were captured to aid description of the activities. In addition to being observed as they were learning, 6 learners (3 male and 3 female) were asked to participate in a focus group discussion (see appendix 5 for the instrument that was used). The six learners from each of the four schools where focus group discussion were held were purposefully selected. Two learners were below average, two were
7In Malawi, there are three terms in an academic year. The first term starts in September and ends in
December, the second from January to March and the last term starts in April and ends in July.
8 The subject that anchors number concept in standards 1 to 4 in called Numeracy and mathematics but from
80
average while the remaining two learners were above average. Teacher’s knowledge about the learners was instrumental in the selection.
The teachers were observed as they were teaching. A post-observation interview was, in some cases, conducted with the teachers to clear up some issues that were not clear during the lesson or to find out why the teacher did what she did during the presentation of the lesson. Teachers participating in the study were also asked to complete a questionnaire. The questionnaire was aimed at finding out their beliefs about the nature of mathematics, the nature of mathematics teaching and the nature of mathematics learning (see appendix 6). Three out of the five teachers that participated in the study completed the questionnaire. One teacher returned uncompleted questionnaire and expressed unwillingness to complete it despite her not expressing it when I was giving it to her. The other teacher that failed to complete the questionnaire was not available at a time she was required to complete the data collection tool. She was out of school on official duties for the whole week. This is the same teacher whose two lessons were not observed (note that I was supposed to observe 30 lessons but I ended up observing 28).
Several artefacts (items visually displayed at the school) were collected from the five schools to provide a better understanding of the schools. Examples of artefacts that were collected (or their copies or pictures) include: the school timetable, trophies, classroom rules, work by either teachers or learners pasted on the classroom walls, and displays in the head teachers’ office.
Since short forms (some sentences were not written in full during the observations) were used in collecting notes from the field, the notes were translated so that they were in the form they could easily be understood. This was done the same day because according to Fetterman (2010), the notes should then be translated immediately after either the interview or the observation while the memory is fresh. This ensured that as much information as possible was remembered from the notes.
Analytical memos were also written on a daily basis. According to Mills and Morton (2013:121 - 122), an analytical memo is a short note or piece of writing that seeks to précis and distil one’s emerging thinking and findings about a situation, event, person, or concept. In this case it was on what were observed during the school visits and included ‘scenes’ that were particularly striking and noteworthy. When
81
writing these memos, “some would rather keep these reflections and developments integrated within one’s fieldnotes, but others prefer to separate out memo’s and label them accordingly” (Mills & Morton 2013:122). In this study, the memos were separate and well filed both electronically and using hard copies.
Of particular importance in any inquiry is the security of the data that is collected. One’s efforts can be useless if the collected information either gets destroyed, lost or stolen. To avoid this phenomenon, every bit of record was digitised and stored securely using multiple sources including Google drive, a cloud-based storage system that helps to keep files secure and one can access the data anywhere as long as there is internet.