DEALING WITH DATA

The trustworthiness of a research study is important to evaluating its worth (Lincoln & Guba, 1985). To ensure trustworthiness in this study, the following criteria were established: credibility (confidence in the truth of the findings); transferability (showing that the findings have applicability in other contexts); dependability (showing that the findings are consistent and could be repeated); and confirmability (a degree of neutrality or the extent to which the findings of a study are shaped by the respondents and not researcher bias, motivation or interest) (Lincoln & Guba, 1985).

3.10.1 Credibility

Credibility refers to the “adequate representation of the constructions of the social world under study” (Bradley, 1993: 436). The following activities recommended by Lincoln and Guba (1985) helped improve the credibility of the research results in this

study: prolonged engagement in the field; persistent observation; triangulation; peer debriefing; negative case analysis; referential adequacy; and member checks.

3.10.1.1 Prolonged engagement

The researcher spent a day at each school and a day at each university. The time was considered adequate to talk to both teachers and lecturers to learn how mathematics and science was taught. This helped the researcher to become oriented to the situation so that the contexts could: be appreciated and understood; be able to detect and account for distortions that might have been in the data; be able to rise above his own preconceptions; and to build trust.

3.10.1.2 Persistent observation

The characteristics and elements of mathematics and science education that are most relevant to the problem were identified and a detailed focus was placed on them. Persistent observation, therefore, provided depth (Lincoln & Guba, 1985).

3.10.1.3 Triangulation

This involved using multiple data sources in this investigation to produce understanding and to ensure that the account was rich, robust, comprehensive and well developed. Four basic types of triangulation as identified by Denzin (1970; 1978) and Patton (1999) were used to enhance the credibility and trustworthiness of the results of this study. They are: data triangulation; investigator triangulation; theory triangulation; and methodological triangulation.

Data triangulation depicts the use of multiple data sources in the same study for validation purposes. According to Denzin (1978), there are three types of data triangulation, namely: time; space; and person. These types of data triangulation come as the result of the idea that the robustness of data can vary, based on the time that data were collected; the people involved in the data collection process; and the setting from which the data were collected. A variety of data sources, such as teachers of mathematics and science, lecturers of mathematics and science education and policy documents were used in this study.

Investigator triangulation can be defined as the use of more than two researchers in any of the research stages in the same study. It involves the use of multiple observers, interviewers, or data analysts in the same study for confirmation purposes (Denzin cited in Thurmond, 2001). However, in the case of this research, one researcher was involved in all the stages of the research.

Theory triangulation is defined as the use of multiple theories in the same study for the purpose of supporting or refuting findings, since different theories help researchers to see problems at hand, using multiple lenses (Denzin cited in Thurmond, 2001). Both related and/or competing theories can be used in formulating hypotheses for the purpose of providing a broader and deeper understanding of the research problem at hand (Banik, 1993). Multiple perspectives from realism (social and critical), rationality and constructivism were considered in this study.

Methodological triangulation is defined as the use of more than two methods in studying the same phenomenon under investigation (Mitchell, 1986). However, only the qualitative research method was used in this study.

3.10.1.4 Peer debriefing

This process involved exposing the researcher to a disinterested peer in a manner paralleling an analytical session for the purpose of exploring aspects of mathematics and science teaching that might otherwise remain only implicit within the researcher’s mind (Lincoln & Guba, 1985). An example of such aspects was the language of teaching mathematics and science. The researcher expected teachers to use English in their teaching, since English is the official language of teaching and learning and questions in examination papers are asked in English. This was not the case; rather, teachers of mathematics and science were more inclined towards teaching in indigenous languages.

3.10.1.5 Negative or deviant case analysis

Elements of the data that did not support or appear to contradict patterns or explanations that emerged from data analysis, such as how teachers deal with the lack of computational skills of learners were discussed. Another element that did not appear to support or contradict patterns concerned measures that were used to

ascertain maximum class attendance, such as where students were made to sign logbooks and attendance registers.

3.10.1.6 Member checks

Data, analytic categories, interpretations, and conclusions were tested with members of those groups from whom the data were originally obtained. These included the researcher’s colleagues who participated in the study. This was done informally during the normal course of observation or conversation. For instance, the researcher established what informants knew about different types of knowledge.

3.10.2 Transferability

This refers to the degree to which the findings of a study can transfer beyond the project (Lincoln & Guba, 1985; Bradley, 1993). One technique that was used to establish transferability is ‘thick description’. This refers to the detailed account of field experiences in which the researcher made explicit the patterns of cultural and social relationships and put them in context (Holloway, 1997).

Teacher knowledge of mathematics and science was described with sufficient detail to help the researcher to evaluate the extent to which the conclusions drawn were transferable to other times, settings, situations and people.

3.10.3 Dependability

Dependability is an assessment of the quality of the integrated processes of data collection, data analysis, and theory generation (Lincoln & Guba, 1985; Creswell, 1998; Miles & Huberman, 1994). One technique to establish dependability is through external audits. External audits provide an opportunity for an outsider to challenge the process and findings of this research study, as discussed by Lincoln and Guba (1985) and Bradley (1993). In this study, the external audit involved having a researcher not involved in the process examine both the process and product of the research study. The purpose was to evaluate the accuracy and evaluate whether or not the findings, interpretations, and conclusions were supported by the data.

3.10.4 Confirmability

Confirmability is a measure of how well the inquiry’s findings are supported by the data (Lincoln & Guba, 1985). The techniques used in this study for establishing confirmability were: confirmability audit; audit trail; triangulation; and reflexivity (an attitude of attending systematically to the context of knowledge construction, especially to the effect of the researcher, at every step of the research process).

3.11 CONCLUSION

This chapter outlined and described the research design of the study. Aspects of the research design discussed were firstly, the description of a paradigm. Secondly, a discussion on the assumptions underlying interpretive paradigm as the adopted paradigm of this study followed. Justification of the choice of the interpretive paradigm was also done. Thirdly, the methods and approaches used in this study were described. Fourthly, the research questions and propositions for this study were outlined. Lastly, sampling strategies and procedures for trustworthiness were discussed. This research design helped the researcher to address the meaning that lecturers and teachers ascribed to the different types of knowledge required to teach mathematics and science. In the fourth chapter which follows, the results of the study are reported.

CHAPTER FOUR