Measures of Trustworthiness

The notion of ‘trustworthiness’ is a demonstration of “the soundness and adequacy” of the quality of the research methods opted for in the study (Holloway & Wheeler, 2010; Marshall & Rossman, 2011). On the other hand, measures of trustworthiness are the strategies or quality

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assurance mechanisms designed to ensure the overall scientific rigour and to instill confidence in the findings of the study (Holloway & Wheeler, 2010; Kumar, 2012). The nature of the study necessitated that both the qualitative and quantitative measures of trustworthiness be indicated. Quantitative researchers often doubt the trustworthiness of the results of qualitative research (Silverman, 2001). These researchers do not trust the qualitative research methods due to the fact that validity and reliability are not addressed in the same manner. For this reason, qualitative researchers have developed terminology that seeks to establish the rigour in qualitative research.

Kumar (2012) asserts that there are generally four measures of trustworthiness, namely: credibility, transferability, dependability and confirmability, “and it is these four indicators that reflect validity and reliability in qualitative research” (p. 172). The below-mentioned measures of trustworthiness reflect both the qualitative and quantitative variants. For instance, instead of internal validity, the researcher discussed the elements that establish the study’s credibility. Transferability was also discussed in the place of external validity by providing the context in which data was collected to allow for comparability of the findings in a different research milieu. The researcher also described the study’s dependability by presenting those measures of trustworthiness which allow for the study’s repeatability.

4.5.1 Credibility/ Internal validity

The credibility/ internal validity of the study is premised on the degree of accuracy and agreeability between the results and the quality the research instrument (Marshall & Rossman, 2011). Shenton (2004) reiterates that the credibility of the study is measured on account of its true reflection of the research process, particularly the empirical aspect.

All the data collected in this study has been kept as evidence and as a true record of the research process. Three forms of data were collected, from which this study’s findings are based. Firstly, it is the test that was written by 112 learners in grade 11 at the time of the data collection from four different schools within the town of Mthatha. Secondly, it is the written notes that were used during the task based interviews. Thirdly, there are videos and audios that were captured during the time of the data collections. Some evidence of the collected data was also included in the analysis section through excerpts of transcripts and pictures of both written and drawn work of the participants.

Finally, the findings of the study confirm what has been found by other studies which were conducted previously (Makgakga & Sepeng, 2013). One such study is that conducted by Essack (2015), which came close to this study. For instance, Essack (2015) found that learners tend to have ritualised routines, and they struggle with questions that seek to interrogate reasons for their particular action. Learners did extremely well on procedures that could be classified as

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‘classroom type’ and struggled with questions that were not normally attended to in everyday classroom situations. The researcher also allowed some participants to scrutinise the data of this project and ascertain that transcription was done correctly (member checking).

4.5.2 Transferability/ Generalisability

Transferability/ generalisability is viewed as the extent of the study’s findings being useful or applicable to others in similar contexts as those that prevailed at the original site(s) where the study was conducted (Marshall & Rossman, 2011). In a qualitative research, the findings are generally affected by the sample size, and cannot be applied to a wider population (Turner, 2010). Shenton (2004) on the other hand, states that the context where data was collected should be described fully, in order to enable those who wish to apply the findings of the study to check the applicability of these findings to their own contexts. It is the responsibility of the researcher to explain the study context fully (Walliman, 2011). The study was conducted in the Eastern Cape Province of South Africa. In this regard, the study’s generalisability was ensured by the consistency of the research instruments used (tests and interviews). Accordingly, the researcher ensured that all the questions focused on the mathematical discourse of the learners. No peripheral aspects of Mathematics were included in the repertoire of questions pertaining to learners’ mathematical discourse of functions and the asymptote.

4.5.3 Dependability/ Reliability

Dependability/ reliability refers to the extent to which a research instrument consistently measures the characteristics of a research variable or construct. Joppe (2000) defines reliability in research as the consistency of results over a given population that could be reproduced under the same conditions that prevailed at the time of study. For purposes of ensuring the repeatability of the study, the researcher has detailed the planning and execution of the research by means of an audit trail. In this regard, the researcher has also described the geographic area and conditions under which the study was conducted. Accordingly, all documents relating to the entire research process were kept for any further research on a topic bearing some degree of verisimilitude with the current study. The purpose of an audit trail is essentially to enable interested researchers and readers to trace all the processes which unformed the researcher’s decision-making throughout various stages of the entire research process (Holloway & Wheeler, 2010).