According to Robson (2011), data in its raw state does not speak for itself unless it is analysed and interpreted. Data analysis is a process of organising, ordering and extracting information from raw data (Kendall and Kendall, 2009). This process involves a lot of thinking and re-organising, with the view of understanding what the data contains and what it does not contain. The process and product of analysis offers the basis for interpretation (Yin, 2003). The data in this study came in the forms of published statistical examinations results, transcriptions of audio tapes of interviews and responses to the self-completed questionnaires.
3.9.1 Analysis of statistical examination results
As stated previously, the main sources of the statistical examination results for this study are the published examinations results from the Joint Council for Qualifications (JCQ) from June 2005 to June 2011. The analysis of the data is based on descriptive, inferential statistics and statistics in perspective. Descriptive statistics are used to describe the essential features of the data and provide a summary about the sample. This summary can be stated in the form of the mean, frequency and mode (Fraenkel and Wallen, 2008). They can also be represented by a bar chart, pie chart or histogram. Inferential statistics are used if the researcher is interested in making inferences based on the findings from the sample, while with descriptive statistics the researcher is only
85 interested in the immediate data. With Inferential statistics however, the researcher is interested in conclusions that can be drawn beyond the immediate data. Using quantitative data to compare two or more groups with statistical parameters such as averages and frequencies helps to put the statistics in perspective. Fraenkel and Wallen (2008) suggest that quantitative data groups can be compared by using either percentages or frequencies. In their view, it is more appropriate to use graphical techniques before numerical to interpret the data.
Two forms of data were explored: GCSE and A-level Mathematics examination results. The first part of this analysis is the descriptive statistics, which involves exploring the GCSE results for Mathematics and Additional Mathematics. In exploring the data on GCSE Mathematics results, the limits were set to include grades B or higher. This is because throughout the interviews, it came to light that most sixth form schools use grade B as the cut-off point for students wanting to study A-level Mathematics. The data was recast to determine the total number of students who qualified to study A-level Mathematics for the various years. Based on this percentage, gender representations were determined for each year. All the information was then represented in graphical form. Drawing inference and putting the statistics in perspective involved the comparing of the data for different years. Grade limits were however not set for Additional Mathematics. This is because Additional Mathematics is an optional subject for students at GCSE and students without any grade in Additional Mathematics can still go on to do A-level Mathematics. But the essence of including Additional Mathematics in this analysis is because unlike compulsory Mathematics, students do it by choice. The aim was to find the proportional representation of males and females who took the subject for the various years and compare it with the numbers for compulsory Mathematics.
In exploring the A-level results, I first identified from the data the number of students who studied A-level Mathematics and Further Mathematics. The proportional representation of males and females was then determined. The derived data was then represented graphically before inferences were drawn. The analysis of statistical examination results is located in Chapter 4.
86 3.9.2 Analysis of interviews and self-completed questionnaires
The main approach for analysing the data from the interviews was based on Thematic Coding Analysis (TCA) (Silverman, 2011). The self-completed questionnaires were however analysed with both TCA and quantitative analysis. Robson’s (2011) assertions that the flexibility of TCA provides the means to summarise key features of large amounts of qualitative data have influenced my choice of this approach. Another reason for the choice of TCA is the ability to develop descriptive accounts, which can be refined where necessary (Silverman, 2011).
3.9.2 (i) Thematic Coding Analysis(TCA): interviews and Self-completed questionnaires
Based on the TCA, there were five stages involved with the analysis. Firstly the familiarisation stage, which involved the transcribing of the digitally recorded tapes and reading and re-reading of informants’ responses to the self- completed questionnaires (Robson 2011). The next stage involved generating codes; this is concerned with organising data into meaningful groups. In the study, this was guided by the research questions and previous research findings. This led to the third stage, involving the identification of the main themes (Silverman, 2011). The transcribed interview and self-completed questionnaires were examined critically to identify similarities, differences and any recurring information to establish themes. According to Silverman (2011), the main purpose of a theme is to capture important patterns in the data in relation to the research questions. In this study therefore, the aim of the study and the research questions influenced the theme selection. This formed the basis for identifying themes that could address the research questions and could also link to the literature in other to confirm or challenge previous findings and the theoretical framework. The fourth stage involved the contraction of the thematic framework and making comparisons. This stage of the study focused on finding out how the themes identified in the third stage could fit into each other to form one network. This led to the creation of sub-themes within each identified theme (Robson 2011). The final stage involved the integration and interpretation of the data. This aspect of the analysis involved making
87 comparison between the various views of the informants in the study by exploring, summarising, describing and interpreting identifiable patterns (Robson 2011).
In employing the TCA, genuine categories were discovered and given labels, which were then related to a theme. Sub-categories were created under categories. For example, in the questionnaires, female students who were not studying A-level Mathematics but who felt that Mathematics had nothing to do with gender were given codes. In this scenario, the main categories were males and females not studying A-level Mathematics. The sub-categories were the female students who felt that Mathematics had nothing to do with gender and those who held contrary views. In charting, I kept on arranging and rearranging my categories and sub-categories according to themes which hitherto were not seen to have had any bearing on the aim of the study, but which have now become important (Fraenkel and Wallen, 2008; Robson 2011).
3.9.2 (ii) Quantitative (Statistical) analysis of self-completed questionnaires
The quantitative analysis of the self-completed questionnaires was based on descriptive statistics, inferential statistics and statistics in perspective as described in 3.9.1. The main reason for analysing the self-completed questionnaires quantitatively in addition to TCA was to enhance trustworthiness (Section 3.11). The frequency of occurrence of some of the themes and sub- themes identified from the TCA formed the basis of the quantitative analysis, which included the use of pie and bar charts (located in Chapter 5/Section 5.1).