Strategy for data presentation and analysis

A case study database was compiled for the study. This is a collection of all evidence collected during the study. It consists of all data, electronic and non-electronic, and all other evidence that has been collected by the researcher. Data analysis, according to (de Vos, 2002, p. 339) is the process of “bringing order, structure and meaning to the mass of collected data”. The entire set of data generated during the experiment was systematically analyzed while simultaneously documenting the grounds for particular assertions and inferences. Audio tapes were studied and transcriptions of interviews were done. The videotapes were also studied and information about the study was noted.

In mixed methods research, data may be analyzed differently in different designs. Creswell & Plano Clark (2011, p. 218) suggest the following model, which was adopted with modifications, in analyzing data for this exploratory design:

1) Collect the qualitative data;

2) Analyze the qualitative data qualitatively using analytic approaches best suited to the qualitative research question;

3) Design the qualitative strand based on the qualitative results; 4) Develop and pilot test the new instrument;

5) Collect the quantitative data;

6) Analyze the quantitative data quantitatively using analytic approaches best suited to the quantitative and mixed methods research questions;

7) Interpret how the connected results answer the qualitative, quantitative, and mixed methods questions.

(Creswell & Plano Clark, 2011, p. 218)

It is on the bases of this approach that qualitative and quantitative data are presented and analyzed separately in Chapters 4 and 5 respectively. Qualitative methods were used to analyze data from observations and interviews, while statistical numerical methods were used to analyze data collected from questionnaires. Some categories, guided by literature, were utilized to organize the information. Analysis of the quantitative data was done individually for each case, based on the model suggested by (Yin, 2009, p. 57). (See section 3.3.1). Integration of the qualitative and quantitative data took place during the analysis. The

findings, both quantitative and qualitative, were integrated during interpretation, and conclusions were drawn about the research. (Johnson & Christensen, 2004, p. 447).

When analyzing quantitative and qualitative data within the mixed methods framework, the researcher carried out the following processes: a) data reduction, b) data display, c) data transformation, d) data correlation, e) data consolidation, f) data comparison, and g) data integration (Onwuegbuzie & Leech, 2006, pp. 490-491; Onwuegbuzie & Teddlie, 2003). Figure 3.2 shows the steps in mixed methods data analysis process.

Figure 3. 2: The mixed methods Data Analysis Process (Onwuegbuzie & Leech, 2006, p. 492)

Data reduction involved reducing the number of dimensions in data by identifying and classifying it into themes, in the case of qualitative data or via descriptive methods in the case of quantitative data. According to Braun and Clarke, “a theme captures something important about the data in relation to the research question, and represents some level of patterned response or meaning within the data set” (Braun & Clarke, 2006, p. 10). It is worth noting, however, that the researcher’s judgment is necessary to determine what counts as a theme and what is not. A theme is not determined by the frequency of its prevalence within the data set, Note: Rectangles represent steps in

the mixed data analysis process; diamonds rere Triangles represent components. Data Integration Data Consolidation Data Correlation Data Comparison Data Display Data Reduction Data Transformation Multiple Data Type Single Data Type

but by whether it captures something important with regard to the overall research question” (Braun & Clarke, 2006, p.10)

Thematic analysis is defined as “a method for identifying, analyzing and reporting patterns

(themes) within data” (Braun & Clarke, 2006, p. 6). Thematic analysis of data may be

inductive or theoretically driven. In An inductive thematic approach, on one hand, the

themes are strongly linked to the data themselves, they emerge from the data, and are not necessarily driven by the theoretical interest of the researcher in the topic. On the other hand, a theoretically driven thematic analysis, which was followed in this study, is driven by the researcher’s theoretical or analytic interest in the area under study. The coding of themes is focused on those aspects as have been mentioned or implicated in the previous studies or literature in the area, as was the situation in the current study (Braun & Clarke, 2006, p. 12).

Thematic analysis in this study was done at the latent level. At this level, the identification of themes does not stop at surface (semantic or explicit) meaning of the data, but goes beyond and “starts to identify or examine the underlying ideas, assumptions and conceptualizations- and ideologies- that are theorized as shaping or informing the semantic content of the data” (Braun & Clarke, 2006, p. 13). As Braun and Clarke further affirm, “for latent thematic analysis, the development of themes themselves involves interpretive work, and the analysis that is produced is not just description, but is already theorized” (Braun & Clarke, 2006, p. 13). It is therefore imperative that in order for theoretically driven thematic analysis to be done successfully, thorough engagement with literature relevant to study be done.

The software, ATLAS.ti, was used to aid the process of data analysis. Data was then displayed or represented in the form of statements, tables and figures. This included discussion of the evidence of the themes, supported with actual quotations from the data. Quotations conveying the different themes or sub-themes were obtained from varying sources of data to provide multiple perspectives from individuals in the study. (Creswell & Plano Clark, 2011, p. 209). Interrelationships between themes and sub-themes were established.

During the transformation stage, quantitative data are converted into narrative data for analysis using quantitative methods and qualitative data are similarly converted to numerical data (coding) that can be statistically analyzed. Data correlation involves making correlation between quantitative and qualitative data. This could mean cross-classifying different data types, such as transforming qualitative data into categorical variables and examining their relationships with quantitative variables. In this particular study, however, no transformation of data occurred, qualitative data was analyzed using qualitatively and quantitative data was analyzed using analytic techniques best suited to the approach, as indicated earlier, and the results were then merged in order to draw conclusions for the whole study.

Table 3.3 shows phases of thematic analysis and corresponding descriptions of what happens at each phase.

PHASE DESCRIPTION OF PROCESS

1. Familiarization with data

Transcribing data, reading the data, noting down initial ideas 2. Generating initial

codes

Coding interesting features of the data in a systematic fashion across entire data set, collating data relevant to each code

3. Searching for themes

Collating codes into potential themes, gathering all data relevant to each potential theme.

4. Reviewing themes Checking if the themes work in relation to the coded extracts(level 1) and the entire data set (level 2), generating a thematic “map” of the analysis 5. Defining and

Naming Themes

Ongoing analysis to refine the specifics of each theme, and the overall story the analysis tells; generating clear definitions and names for each theme.

6. Producing the report

The final opportunity for analysis. Selecting of vivid, compelling extract examples, final analysis of selected extracts, relating back of the analysis to the research question and literature, producing a scholarly report of the analysis.

Table 3.3: Phases of Thematic Analysis (Braun & Clarke, 2006, p.:35)

Results from the data collected through the questionnaire were interpreted in terms of the themes used for the qualitative data. One-wayAnalysis of variance (ANOVA) was then carried out to determine the statistical significance of differences between means of responses

from the two schools. This is a statistical technique that can be used with two or more groups and uses the F-test statistic (Urdan, 2005, p. 101). Urdan further explains that “The F-value is the statistic used to indicate the average amount of difference between group means relative to the average amount of variance within each group”(Urdan, 2005, p. 114). The Mann-

Whitney U-test (U) was also used to determine whether there was any significant difference

between the groups. This is a nonparametric inferential statistic used to determine whether two uncorrelated groups differ significantly. This statistical test was used because the used data represented ordinal level scale and the sample sizes were small. Non-parametric tests are a class of tests that do not hold the assumptions of normality. (MacFarland, 1998)

In the last phase, findings from the qualitative and quantitative data were then triangulated, and collaboration and corroboration were sought. The exploratory nature of this study indicates that the aim was not to prove any proposition or generalization, but to seek better understanding of how learners experienced learning algebra in the spreadsheets environment, paying special attention to the type of obstacles they encountered and how they were be assisted, through instrumental orchestration, to overcome their problems. Here the researcher compared the results with the initial research problem and questions in the study and determined how these were answered. The results of the study were also compared with prior explanations from past research studies. In addition to these, the researcher also brought into picture, personal experiences and drew assessment of meanings of the findings.

3.4

Conclusion

This chapter provided an outline of how the study was conducted. The research commenced with a pilot study whose main purpose was to assess the appropriateness of the selection procedure for the participants, usability of the instructional materials and the questionnaire, in terms of language accessibility by the learners, and the appropriateness and applicability of the data collection protocol. The necessary modifications were done on some instruments and in the manner in which the study was conducted and the main study followed.

The main study progressed in three phases, the classroom observations, the administration of the questionnaire and the interviews. The design of classroom activities was provided. Data from the two schools, Retha and Palo High school was collected and analyzed through qualitative and quantitative methods. Triangulation of findings was done; comparisons were made to determine the differences, similarities, collaboration and correspondence between the findings from the different sources of data. Conclusions were drawn and recommendations were made concerning the study. The next chapter presents findings from the qualitative data.

CHAPTER 4

FINDINGS: QUALITATIVE DATA

4.1

Introduction

The previous chapter outlined how the empirical study was conducted. This chapter presents findings from the qualitative phase of the empirical study. The qualitative data was collected through classroom observations, learners’ responses to questions at the end of each worksheet, and in-person interviews. The findings provided in this chapter are from the sets of data from the two schools and are presented simultaneously for the two schools. This was done on realizing that there were overlaps in the data from the schools studied.

This presentation of findings is focused on:

1) The challenges that were encountered in the teaching and learning of grade 9 algebra through spreadsheets;

2) The strategies that enabled effective teaching and learning of Grade 9 algebra through spreadsheets, and

3) Learners’ attitudes and perceptions with regard to the teaching and learning of algebra through spreadsheets.

The discussion provided hereafter is focused on evidence of existence of the above aspects leading to answers to the main research question. The data in the form of extracts from each of these sources is provided and categorized according to the research sub-question they addressed. Letters R and P have been used to distinguish between data excerpts for learners from Retha and Palo High schools respectively.