CONTEXTUALISATION AND METHODOLOGY
4.8 Quality considerations
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implementation of FA in the mathematics classroom. Karanasios et al. (2017) argue that contradictions and tensions “provide a lens for understanding how deviance from established rules and norms occur”, since individuals tend to move away from an established norm when tensions are increased and occur within an activity system.
Table 4.4: Pseudonyms and coding used for participants and their colleges
Name of college Code for college Name of participants Codes for participants
Roberkeyta college RCOE Sekyi S
Roberkeyta college RCOE Emily E
Oswald college OsCOE Wilson W
Oswald college OsCOE Fordjour F
PhilNeri college PnCOE Peprah P
PhilNeri college PnCOE Anani A
4.7.3 Interpreting and producing the report
MTEs’ understanding, and practices of FA were described and interpreted through the lens of sociocultural theories. When all data had been categorised, analysis of the data regarding the research question began. The researcher summarises and presents the data generated from all six participants in detail in Chapters 5, 6 and 7 of this report. Data were not presented using a case- by- case approach, since the themes that emerged from teacher educators were similar and, in some situations, repetitive. According to Braun and Clarke (2006) an analysis should embrace a concise, coherent, and non-repetitive account of the data represented through the specific themes. The researcher used vivid examples or extracts from the data to capture the essence of the themes.
Therefore, integral findings on data were presented to answer the research questions rather than present individual cases (Yin, 2011).
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studies to judge or justify the quality of the study and to answer the essential question of how good the study is (El-Sherif, 2017). According to Healy and Perry (2000) the terms reliability and validity are more situated in the quantitative study than the qualitative study. Lincoln and Guba (1985), as cited in (Maree, 2016) described the validity and reliability of the qualitative study as trustworthiness.
4.8.1 Trustworthiness
Trustworthiness is a set of standards that honour participants ethically through researcher sensitivity to the phenomenon and the settings (Rossman & Rallis, 2016). In Sinkovics and Alfoldi (2012) trustworthiness was defined as a process of maintaining the soundness of the findings of a study and the soundness of the arguments that conclude it. Trustworthiness or rigour of a study refers to the degree of confidence in data, interpretation, and methods used to ensure the quality of a study (Polit & Beck, 2014). The researcher relied on tape recordings of the interviews, field notes and participants' authentication to ensure that data gathered for the study were trustworthy.
Interview events were transcribed verbatim and copies were given to participants to clarify and validate their responses. Loh (2013) avers that trustworthiness consists of four components: (a) credibility, (b) dependability, (c) confirmability, and (d) transferability. Consistent with Loh (2013), Strauss and Myburgh (2001) explained that credibility, transferability, dependability, and confirmability ensure trustworthiness in a qualitative study. The sections that follow give an account of how the four components of trustworthiness were applied in this study.
4.8.1.1 Credibility
According to Wahyuni (2012) credibility deals with the accuracy of data in the context of social phenomena under study. In other words, credibility concerns itself with whether the study measures or tests what is intended to measure. Maree (2016) asserts that credibility can be established through the adoption of a well-established research method and research design that fit the research questions. Following Maree's view, the researcher adopted the exploratory case study design to investigate MTEs' understanding of FA and how their understanding translates into practice to ensure credibility of the study. In addition, Anney (2014) asserts that a qualitative researcher establishes the rigour of the inquiry by adopting the following credibility strategies:
prolonged engagement, triangulation, member checking, peer examination, reflexivity, and
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interview technique. Credibility was also enhanced via the development of an early familiarity with the participants. The rationale was to create trust that transcends the study in order for participants to have a feeling of togetherness and a good interpersonal relationship with the other participants. This provides a greater understanding of participants' culture and context (Anney, 2014).
In order not to underrepresent or misinterpret the participants, the researcher also adopted member checking. According to Yin (2011) member checking is the process of allowing the study participants to review and verify the data collected from interviews, participant observations, and documentation, to avoid the possibility of misinterpreting the data collected. Transcribed data and field notes were given to the participants to verify whether the answers presented represented what they had shared with the researcher. Member checking is a crucial process that any qualitative researcher needs to go through, because it is at the heart of credibility (Anney, 2014; Onwuegbuzie
& Leech, 2007). The researcher used multiple sources of data, obtained from interviews, observations and documentation to ensure credibility. El-Sherif (2017) explained that using multiple data sources to come to a conclusion about a phenomenon is called triangulation.
Triangulation "involves the use of multiple and different methods, investigators, sources and theories to obtain corroborating evidence" (Onwuegbuzie & Leech, 2007, p. 239). According to Anney (2014) triangulation helps the researcher to minimise bias, and cross-examines the integrity of participants' responses.
4.8.1.2 Transferability
Transferability refers to the degree to which the results of a qualitative study can be transferred to another context with other participants (Anney, 2014; Wahyuni, 2012). Thoma and Magilvy (2011) equated transferability in a qualitative study with external validity in quantitative research.
In line with Anney (2014) and Wahyuni (2012), Thomas and Magilvy (2011) also defined transferability as the ability to replicate research methodology and findings to another context.
However, Finfgeld‐Connett (2010) argued that in a naturalistic study a researcher cannot forestall in advance the extent to which the findings of a study will be transferable to another context.
Researchers are therefore required to provide thick responsive, thoughtful, and detailed descriptions of the study context to assist other researchers to judge the applicability of the research
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in a similar context (Thomas & Magilvy, 2011). According to Bitsch (2005), ensuring transferability requires ‘thick description’ and purposeful sampling. Thick description is achieved by delineating the phenomenon under investigation in detail, such that conclusions can be transferred to other situations, settings, people and times (Amankwaa, 2016). Similarly, Anney (2014) asserts that thick description involves the researcher giving an in-depth account of the whole investigation process, from the design and methodology to the production of the final report of the study, which offers other researchers the opportunity to replicate the study in similar contexts.
In this study, transferability was endorsed through a thick description of the processes that give in- depth meaning about the phenomenon of FA. Detailed descriptions of the study context, the intentions of the study, data generation method and research design and rich descriptions with extensive use of teacher educators' voices links the data to the analysis, claims, and interpretations.
Transferability was also sanctioned by choosing a purposive sampling technique in selecting the participants for the study. A detailed description of the research process and purposive sampling technique facilitate transferability in the study.
4.8.1.3 Dependability
Cope (2014) asserted that dependability refers to the consistency of data in a different context with similar conditions. To establish dependability, according to Amankwaa (2016), requires an inquiry audit with the aim of evaluating the research accuracy by examining whether data generated support the study findings, conclusions and interpretations. Dependability involves participants evaluating the findings and the interpretation and recommendations of the study to make sure that the findings are supported by the data received from the participants (Cohen et.al., 2011). To ensure qualitative research dependability requires an audit trail (Cope, 2014; Thoma & Magilvy, 2011). An audit trail involves an examination of the research process and products to validate the data, whereby an investigator accounts for every decision about the study such as how data were collected, recorded and analysed (Anney, 2014; Bowen, 2009). Thomas and Magilvy (2011) indicated that the audit trail is achieved by: (a) describing the purpose of the study; (b) discussing the sampling procedure to explain how and why the participants were selected for the study; (c) discussing the data collection method and the duration for data collection; (d) discussing the data
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analysis procedure for the study; (e) discussing in detail the interpretation and presentation of the findings of the study; and (f) communicating the procedures used in ensuring the data credibility in the study.
Dependability was established by giving a detailed description of the methodology and the contexts of the study. For instance, the purpose of the study, sampling frame and sampling criteria, as well as the rationale for the partiicpants’ selection, were discussed. In addition, the data collection method and the time for data collection were also discussed, together with the procedure for data analysis. Furthermore, the code-recode strategy was also adopted to ensure the dependability of the study. In this way data generated from the study were coded and recoded within two-week intervals to check for data consistency. The code-recode strategy involves the researcher coding the same data twice, and if the twice-coded results match or agree with each other, then the dependability of the result is enhanced (Ary, Jacobs, Razavieh & Sorensen, 2010).
The code-recode strategy helps the researcher to gain an in-depth understanding of data patterns to improve the presentation of the participants’ narratives (Anney, 2014).
4.8.1.4 Confirmability
Research confirmability is achieved when the credibility, transferability, and dependability of the study are established (Thoma & Magilvy, 2011). According to Tobin and Begley (2004, p. 392), confirmability is "concerned with establishing that data and interpretation of the findings are derived from the data and are not a creation of the researcher's imagination". Similarly, Cope (2014) explained that confirmability is achieved when the researcher demonstrates that the data represent participants' perspectives and are clear of researcher bias. Maree (2016) observed that confirmability can be increased in a qualitative study through triangulation. Triangulation involves the use of multiple and different methods, or different theories to obtain corroborating information (Onwuegbuzie & Leech, 2007). Carter, Bryant-Lukosius, DiCenso, Blythe, and Neville (2014) and Patton (1999) categorise triangulation as follows: (a) method triangulation, (b) investigator triangulation, (c) theory triangulation, and (d) data source triangulation. According to Polit and Beck (2014), method triangulation involves the use of multiple methods of data collection about the same phenomenon. Investigator triangulation concerns itself with two or more researchers engaging in the same study to provide multiple observation and conclusions (Carter et al., 2014).
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In addition, Carter and her colleagues also observed that investigator triangulation brings both confirmation of findings and different perspectives, adding breadth to the phenomenon under investigation. Theory triangulation uses different theories to analyse and interpret data, while data sources triangulation involves the collection of data from different people, including individuals, groups and communities, to gain multiple perspectives about the phenomenon (Carter et al., 2014).
Confirmability was established in this study through method triangulation and data source triangulation. Data were generated through interviews, observations and field notes as well as document analysis. The researcher studying this human phenomenon generated data through interviews with individual teacher educators from different Colleges of Education, based on the purpose of the study which offered the researcher the opportunity to gain an in-depth understanding of teacher educators' understanding and practices of FA from multiple perspectives.
Ho (2015) argued that another way of establishing the trustworthiness of data is awareness of the research limitations. Therefore, the limitations of the study are discussed in the next section.