3.7.1 Process of inductive analysis
With regard to data analysis for this particular study, an inductive process is appropriate, in order to uncover crucial themes regarding planning, classroom instruction and assessment, as components relating to the extent to which Grade 7 Mathematics and English First Additional Language educators use differentiated instruction to promote inclusive teaching and learning. Inductive analysis can be described as “The process through which qualitative researchers
41 synthesize and make meaning from the data, starting with specific data and ending with categories and patterns. In this way, more general themes and conclusions emerge from the data, rather than being imposed prior to data collection” (McMillan & Schumacher, 2010, p.367). Analysis and data collection should occur simultaneously, in a series of iterative phases, between collecting data and analysing information acquired earlier (Creswell, 2008, pp 244-245). Raw data is generated as the data collection tools seek to answer the research questions. Once the raw data is stored, where they can be traced back to a specific reference, analytical statements should be drafted. Next, an iterative process takes place, where “the draft analytical statements are tested against the data items, and amended or discarded as necessary” (Bassey, 1999, p. 85). The analytical statements are re-expressed as empirical findings once the iterative process has been exhausted. These findings are then expressed in the form of a narrative report.
In order to assist with the identification of themes, a code has been assigned to each behaviour index, listed in the Classroom Observation Checklist. In their article, Florian, Young and Rouse (2010, p. 714) describe how the codes which had been selected became further developed, leading to a deeper analysis of the data. From first of all being descriptive, the codes evolved to more complex levels, moving up a level to being functional and strategic, “to bridging and translating, to principles and theoretical codes based on philosophical underpinnings” (Florian et al., 2010, p. 714).
Data obtained from the interviews, lesson plans and the observations are compared to the analysis of the documents, namely, the assessment and assignment tasks set by the educators. This comparison in turn provides further insight into the extent to which differentiated instruction made a difference to teaching and learning. Evidence from the different types of data and methods of data collection in support of the themes which were uncovered are then corroborated. The information draws on multiple sources, which in turn will lend credibility and accuracy to reporting the findings (Creswell, 2008, p. 259).
3.7.2 Measures to ensure trustworthiness
Within the context of a case study, internal and external validity are problematic in terms of proving a cause and effect relationship that can be generalised to other contexts. Due to the fact that a case study is related to the intrinsic interest of the researcher, it is not a ‘typical example’ as is normally shown in an empirical manner. Reliability is also a problem, as the case, being unique, may make it difficult to replicate the research findings. Therefore, the researcher conducting a case study would strive for “trustworthiness” (Lincoln & Guba, 1985, cited in Bassey, 1999) as an alternative to validity and reliability. Eight questions, four of which are based on the work of Lincoln and Guba (1985), need to be taken into consideration, in order to facilitate ‘trustworthiness’. The questions (Lincoln & Guba, 1985, cited in Bassey, 1999) are based on persistent engagement with data sources, persistent observation of emerging issues, engaging a critical friend to challenge the findings and the existence of an adequate audit trail. Other aspects essential to ‘trustworthiness’ (Bassey, 1999, pp. 74-77) are checking raw data adequately with their sources, ensuring that there has been sufficient triangulation of raw data, providing an account of the research that is
42 sufficiently detailed and making sure that the hypothesis, evaluation or emerging story from the report , has been systematically checked against the analytical statements.
3.7.3 Triangulation
Triangulation, defined as “a process of using multiple perceptions to clarify meaning, verifying the repeatability of an observation or interpretation” (Stake, 1994, p. 241), should be used in order to lend trustworthiness to the data analysis. An important principle of case study research design is that the case is “viewed and explored from multiple perspectives”, through a variety of lenses, so uncovering and leading to an understanding of the “multiple facets” of the phenomenon itself (Baxter & Jack, 2008, p. 544). In their article, Baxter and Jack (2008, p. 556) argue convincingly that triangulation can be used to support this principle where the quality of the data is enhanced because it is based on “idea convergence and the confirmation of findings” (Knafl & Breitmayer, 1989, cited in Baxter & Jack, 2008, p. 556). When describing methodological triangulation, Stake (1995, p. 114) explains that by using multiple approaches within a single case study, some extraneous influences can either be nullified or illuminated. Observation, interviews and document reviews remain the principal methods in a case study for data collection. The process of triangulation highlights the fact that data analysis is not a simple process. As Stake (1995, p. 114) observes, “Triangulation regularly sends us back to the drawing board.”
During the process of triangulation, similarly coded data are grouped together into categories or themes, where the main ideas expressed by the data are represented by the themes. Following this, the objective is to seek to identify relationships between these categories, i.e. the focus is on discovering patterns. During the search for patterns, the intention is to “try to understand the complex links among various aspects of people’s situations, mental processes, beliefs and actions” (McMillan & Schumacher, 2010, p. 378). Once tentative patterns have been identified, they could be modified and some may even have been refuted, in the light of discrepant and negative evidence, where the evidence from the data contradicts the pattern. The next step is to shift back and forth between codes, categories and tentative patterns, to determine “how well the data illuminates the research problem and which data are central” (McMillan & Schumacher, 2010, p. 378).
Some codes are applicable to multiple patterns, as is demonstrated by means of their elasticity. Other codes which emerge from the research data may have to be excluded, as they might not be centrally related to the research questions. The content of each category on its own and in comparison with other codes and categories, give rise to “patterns of meanings” (McMillan & Schumacher, 2010, p. 378). After having investigated alternative explanations, only those patterns which provide reasonable explanations central to the research questions are considered. Such explanations are deemed to be ‘plausible’. ‘Plausibility’ can be defined as “a matter of judgement about the quality of the data” and is shown by how rigourous the data analysis is and the presentation of the data (McMillan & Schumacher, 2010, p. 380). Making such judgements involves carefully considering and selecting “what is really important and meaningful in the data” (McMillan & Schumacher, 2010, p. 378). Once the
43 final patterns have been selected, they serve as a framework for reporting the findings of the study and also to organise the research report (McMillan & Schumacher, 2010).
3.7.4 Triangulation process for this study
The codes pertaining to this particular research were pre-determined, as illustrated earlier when explaining the criteria relating to classroom observation and document analysis [Reference: Appendix 3, Appendix 4(a) and 4(b)]. The categories have also been pre- determined, in that they are directly related to the research sub-questions, as stated in Chapter One. Therefore, the three categories are; ‘Planning for Differentiated Instruction’, ‘Observing Differentiated Instruction in the Classroom’ and ‘Differentiated Instruction and Assessments’. An additional theme arising from the data gleaned from the questionnaire and preliminary interviews is “Participants’ Understanding of an Experience in Differentiated Instruction”. At first, a summative approach was taken, when analysing the data. Therefore, summaries were constructed of each preliminary interview and the field notes for every lesson observed. Following this preliminary analysis at a ‘vertical’ level, the data were then compared at a ‘horizontal’ level. All the information gleaned from the questionnaire was transferred onto a table grid, allowing the researcher to interpret the responses of the participants vertically, at an individual level and to also compare the participants with each other, horizontally. The summaries of the interviews were utilised to draft comparative notes, comparing the participants’ responses to every item of the preliminary interview. All the lesson observation checklists and field notes were compared, to determine which criteria for differentiated instruction were met consistently, which criteria were met occasionally and which criteria were not observed at all. This same process was also applied with regard to the lesson plans and assessment documents. The final patterns, which were identified, are a synthesis of the analysis of the codes. Figure 4.1, in the introduction of Chapter Four, is a summary of the triangulation process for this study.
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CHAPTER FOUR: PRESENTATION AND ANALYSIS OF DATA
4.1 Introduction
The quotation below reiterates the following principles of inclusive pedagogy: the importance of participation of all learners in the classroom and while differences are acknowledged, they are not the focus point.
“By focusing on how achievements in learning are realised through participation in the community of a classroom, the inclusive pedagogical approach acknowledges that there are individual differences between learners but avoids the problems and stigma associated with marking some learners as different.” (Florian, 2015)
Chapter Four commences with a diagrammatical illustration of the research findings, the four key themes which arose from the study and how these themes are supported by evidence from the data. Figure 4.1 on the following page, serves as a summary and is followed by the presentation and analysis of the data.
The sequence of the presentation of the data is as follows: Table 1 on page 45 presents the data from the questionnaire.
Table 2 on page 52 represents the findings of the analysis of the submitted GPLMS lesson plans and is followed by an explanation of these findings.
Table 3 on page 54 compares the eighteen criteria from the Lesson Observation Checklist that ideally should be met when teaching in a differentiated classroom, to what was actually observed during Grade 7 Mathematics and English lessons. This is followed by an analysis of the lesson observations.
The chapter is then concluded by means of an analysis of the assessment tasks submitted, represented by Table 4 on page 60, where feedback is provided in relation to the criteria for the analysis of the assessment tasks.
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4.2.2.1 Preconceived understanding 4.3.1 Planning flexible grouping 4.4.1 D.I. in practice 4.5.1 Setting assessment tasks 4.2.2.2 Perceptions D.I. strategies and classroom routines 4.4.2 Facilitating positive affects 4.5.2 Approaching assessments
4.2.2.3 Benefits of D.I. 4.3.2 Modifying the content within a differentiated classroom 4.5.3 Partial substantiation of required criteria 4.2.1.4 Reflecting on practice 4.3.3 Analysing the GPLMS 4.4.3 Challenges/issues regarding D.I. 4.5.4 Critical reflection regarding the ANA 4.2.2.5 Recommendations lesson plans 4.4.4 Meeting criteria
4.3.4 Participants opinions re. GPLMS 4.4.5 Providing support for learning lesson plans 4.4.6 A critique of the lessons
4.2 Theme One: