DATA ANALYSIS

I started data analysis and coding during the first phase of data collection. That is, when I finished observing the first school, I started transcribing the lessons and analysed them

58 immediately. This procedure allowed me to make necessary adjustment and improvement on the instruments and on the data collection procedures. However, the adjustment on the instruments improved the reliability of the data collection procedures. In the meantime, I proceeded with data collection for the remaining schools. Moreover, by improving my data collection procedures, the data collected towards the end (especially the last school) were richer with information than the first data, therefore, the improvement was worthwhile.

3.6.1 Video transcripts

First, I transcribed the video-taped lessons verbatim. Then I read and re-read the transcribed lessons several times in order to make sense of the raw data. I formulated categories for specific themes as they emerged from the lessons, see Table 3.5 below. In order to check for consistency or reliability, I revisited the analysis categories after some weeks or months and verified whether the coding was still consistent with the initial coding system. Where adjustments were made, it was done by going through all the documents once more.

Reliability refers to “the extent to which any particular method of data collection is replicable” (Hitchcock and Hughes, 1995, p.107). It is also defined to mean “dependability or consistency” (Neuman, 2003, p.178). In qualitative research, reliability can be described as a match between what the researcher records as data and what actually happens in the natural setting that is being researched (Bogdan and Biklen, 1992 cited in Cohen et al., 2000, p.119). Yet, some researchers believe that replication of qualitative studies is difficult if not impossible because naturalistic studies include

59 situations that are unique and idiosyncratic (LeCompte and Preissle, 1993 cited in Cohen et al., 2000, p.119).

Neuman (2003, p.184) cautions that it is difficult and uncommon to have perfect reliability in one’s study, especially qualitative study processes that are unstable over a period of time. Hence, Neuman has proposed four ways to increase the reliability of measure: (1) clearly conceptualize constructs, (2) use a precise level of measurement, (3) use multiple indicators, and (4) use pilot tests. I addressed the issue of reliability by conducting a pilot study and by revisiting the coding schemes several times (after some weeks and months) and by checking the consistency of the coding.

For this research, I addressed the issue of validity by using descriptive and interpretive validity in Chapters 4-5. That means, for descriptive validity I used the extracts from the raw data to describe the analysis procedures and for interpretive validity I used evidence from the video transcripts and the verbatim transcribed interviews to interpret and give meanings of the events as stated by the participants themselves. The evidence was further used to catch the meaning and interpretations of events in the Mathematics classrooms and to construct descriptive categories or themes.

Maxwell (1992) cited in Cohen et al. (2000, p.107) describe descriptive and interpretive validity in qualitative methods as follows:

60 • Descriptive validity is the factual accuracy of the account that is not made up, selective, or distorted. It is the notion of ‘truth’ in research – the notion of what actually happened;

• Interpretive validity is the ability of the research to catch the meaning, interpretations, terms, intentions that situations and events or data have for the participants/subjects themselves in their terms.

The term validity means “trustworthiness of inferences drawn from data” (Eisenhart and Howe, 1992, p.644). Neuman (2003, p.185) describes it as “the bridge between a construct and the data.” According to Bless and Higson-Smith (1995, p.129) the term validity is “concerned with just how accurately the observable measures actually represent the concept in question or whether, in fact, they represent something else.”

Recently, the term validity has been defined more broadly than the earlier versions that described validity as a demonstration that a particular instrument is valid if it measures what it purports to measure (Cohen et al., 2000, p.105). They explain that validity in qualitative research can be addressed through the truthfulness, depth, richness and capacity of the data achieved, the participants approached, the extent of triangulation, and the disinterestedness or objectivity of the researcher (p.105).

3.6.2 Interview transcripts

I transcribed the audio-tapes for interviews verbatim. I read the scripts over and over in order to identify incidences that matched the discovered categories from the observed

61 lessons. I was reflexive because I conducted verification of initial findings and maintained a self-critique during data analysis procedures.

According to McMillan and Schumacher (2001), reflexivity is defined broadly as a concept that

includes rigorous examination of one’s personal and theoretical commitments to see how they serve as resources for selecting one of several qualitative approaches, framing the research problems, generating particular data, ways of relating to participants, and for developing specific interpretations (p.411).

Cohen et al. (2000, p.141) explain that because reflexivity recognizes that researchers are part and parcel of the social world that they research, they bring their own life history to the research situation and participants are likely to behave atypically in their presence. Cohen et al. (ibid) also caution that highly reflexive researchers should be acutely aware of the ways in which their selectivity, perceptions, background, and inductive processes and paradigms shape the research (p.141). During data presentation and data analysis I addressed reflexivity as much as possible by recording data procedures, decisions and actions that I made in terms of data presentation and discussions before making concluding remarks.

3.6.3 Triangulation

The term triangulation is a borrowed concept from surveyors and sailors to describe a process of looking at something from different viewpoints (Neuman, 2003, p.137). Cohen et al. (2000, p.112) defines triangulation “as the use of two or more methods of data collection in the study of some human behaviour.” That means the term is frequently used to express the way researchers view their methods and methodologies in more than one way. Neuman (2003, p.137) for example, describes different types of triangulation:

62 Triangulation of observers: Multiple observers add alternative perspectives, backgrounds, and social characteristics and tend to reduce the limitations of one observer bias. In this study, although I used a video camera during classroom observations, I was the sole observer. Therefore, this study has the shortcoming of not using multiple observers during data collection.

Triangulation of method: Could mean to combine qualitative and quantitative styles of research and data. This study did not use mixed qualitative and quantitative methods but instead it used multiple data-collection procedures that include observation, videotaping, interviews and other supporting documents. Figure 3.1 below summarizes the triangulation process in this study.

Figure 3.1: Data triangulation

Summary

This chapter described the research methodology and design used in this study. A video camera was used to record a total number of 22 Mathematics lessons at Grade 11. The

Video lessons Interviews

Observations Field notes

63 video transcripts formed the main source of data in this study and were transcribed verbatim. Transcribed interview scripts were also used to support data findings. Issues of validity and reliability were addressed through a pilot study. The chapter also discussed ethical issues related to data collection and procedures. The next chapter presents detailed results of the study.

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Chapter 4

STUDY RESULTS