The research design indicates the general plan: how the research is set up, what happens to the subjects and what methods of data collection are used (Mcmillan & Schumacher, 2010: 20). One of the fundamental purposes of the research design is to avoid invalid inferences (Cook and Compell, 1979: 10). According to Punch (2009) the design sits between the research questions and the data, showing how the research questions will be connected to data, and what tools and procedures to use in answering them. See a model below in figure 7 below.
37
RESEARCH DESIGN
Data collected and analysed:
• Following what strategy? • Within what framework?
• From whom? • How?
Figure 7: Research design connects research questions to data: Adapted from Punch (2009: 114)
“Doing research involves choosing a study design that corresponds with your research questions”. These prudent words from Merriam (2009: 1) and the model in figure 8 above helped me to carefully structure the appropriate research design and method for this study. To answer the first question “following what strategy” from above model in figure 8, a qualitative research method that has adopted a case study approach was used. Qualitative research is defined by Van Maanen (1979) in Marriam (2009: 13) as an umbrella term covering an array of interpretive techniques which seek to describe, decode, translate, and otherwise come to terms with meaning, not the frequency, of certain more or less naturally occurring phenomena in the social world. Qualitative researchers seek to understand a phenomenon by focussing on the total picture rather than breaking it down into variables. The goal is holistic picture and depth of understanding (Ary, Jacobs, Razavieth & Sorensen, 2006: 31). Part of the reason for choosing qualitative research approach was that the qualitative designs allows gathering data on naturally occurring phenomena (Macmillan & Schumacher, 2010: 23). The design of this study was therefore driven by case study “strategy” (Punch, 2009).
In this study, grade 6 mathematics ANA scripts were rigorously analysed to extract the meaning from what learners were writing as responses to the questions asked to them because the key concern of this study was to understand the phenomenon from the participants’ perspectives, not from the researcher’s perspective.
Merriam (2009) further characterised Qualitative case studies as a form of qualitative research that search for meaning and understanding, the researcher as the primary instrument of data collection and analysis, uses an inductive investigative strategy, and the end product being richly descriptive (Merriam, 2009: 39). Qualitative case study as being particularistic, descriptive and heuristic.
• Particularistic means that the case studies focus on a particular situation, event, programme, or phenomenon. The case itself is important for what it reveals about the phenomenon.
DATA RESEARCH
QUESTIONS Q
38
• Descriptive means that the end product of a case study is a rich, “thick”
description of the phenomenon under study. thick description means the complete literal description of the incident or entity being investigated
• Heuristic means that case studies illuminate the reader’s understanding of the
phenomenon under study. They can bring about discoveries new of meaning, extend the reader’s experience or confirm what is known.
A case study approach
In this study, a case study research approach was chosen amongst the variety of the research approaches used in social science discipline. Yin (2009: 18) defines case study as an empirical inquiry that investigates a contemporary phenomenon in depth and within its real life context, especially when the boundaries between phenomenon and context not clearly evidence. Furthermore, (Ary, at al, 2006: 456) contends that case studies provide an in-depth description of a specific unit that may be selected because it is unique or typical or for a variety of other reasons. The three conditions to consider when deciding whether to use a case study approach or not proposed in Yin (2009) provided me with sufficient grounds for seeing a case study approach to be most pertinent for this study. Yin (2009) proposed the following three conditions when deciding on suitable method; (a) the type of a research question posed, (b) the extent of control the researcher has over actual behavioural events, and (c) the degree of on contemporary as opposed to historical events. This study focused on the Gauteng grade 6 learners’ low level of achievement in their mathematics ANA. I therefore found Case study approach to be more pertinent because the focus of this study was more on the contemporary phenomenon and I personally had no control over behaviours or the settings (Yin, 2009). Furthermore, the other reason for choosing a case study approach was that I also wanted to consider the context “schools” as it would have been impossible to have a true picture of the most common errors and their associated misconceptions contributing to low level of performance attained by Gauteng grade 6 learners at 5 selected school in Johannesburg South District in the mathematics ANAs without considering context (Baxter and Jack, 2008).
As mentioned already, the main research question for this study was:
What are the most common errors that contribute to low performance attainment in the mathematics grade 6 ANA at selected primary schools in a Gauteng Johannesburg South District?
The sub- question to the above major question was:
What possible misconceptions do learners possess that result into such errors?
To answer the research questions, I have chosen the Johannesburg South District (a bounded system) to be the “case” for this study. The grade 6 learners under Johannesburg South District are in effect, my unit of analysis (Baxter & Jack, 2008).
39
A case is defined by Miles & Huberman (1994) as a phenomenon of some sort occurring in a bounded context. They have indicated it in the figure 8 below as a circle with a heart at the centre. The heart in figure is regarded as the focus of the study, and circle defines the edge of the case “what will not be studied”.
Figure 8: A case as the unit of Analysis. Adapted from Miles & Huberman (1994: 25)
In this study, Johannesburg South District was chosen on the basis of being typically the lowest performing district amongst all Gauteng districts (Merriam, 2009). The study sought to find out the learners’ the most common errors and possible misconceptions associated with such errors that contribute to low performance in the ANA mathematics tests in grade 6. Therefore, I found it imperative to place the boundaries around the “case” to ensure that this study remained reasonable in scope (Baxter and Jack, 2008). Amongst the different grades in schools, different school subjects and variety of assessments used in the South African primary school sector, I have bounded the case of this study to Grade 6 Mathematics ANA. According to Baxter & Jack (2008), after determining that the study research question will be best answered using qualitative case study and the case and its boundaries have been determined, then one must come to consider what type of case study to be conducted. Varieties of case study types are distinguished (see Yin, 2009; Merriam, 2009; Punch, 2009; and others).
The type of case study used in this research was a single case with embedded units. The same single-case “Johannesburg South District” involved more than one unit of analysis “Different grade 6 learners under Johannesburg district” which I have considered to be my subunits (Yin, 2009). The subunits under the single-case have added significant opportunity for extensive analysis, enhancing the insights into the single case (Yin, 2009: 52). According to Baxter & Jack (2008), this ability of looking at sub-units that are situated within a larger case is powerful when considering that data can be analysed within the subunits separately (within case analysis), between the different subunits (between case analysis), or across all subunits (cross-case analysis). In this study my major unit of analysis were the grade 6 learners’ errors and possible misconceptions associated to such errors in the mathematics ANA.
40