Methods of analysis

3.4.1 General approach to analysis

The analysis of the data needed to take into account the three elements within the chosen approach to the study: mixed methods, grounded theory and case study. Using a mixed methods approach meant that both qualitative and quantitative data would need to be analysed and integrated (Onwuegbuzie & Teddlie, 2003) but the two types of data would need different treatment at the first level of analysis. For the questionnaires a quantitative approach was appropriate but the interviews, focus groups and lesson observations required a qualitative method of analysis.

The analysis of qualitative data would involve trying to make sense of complex phenomena (Yates, 2004) and would not be limited to a single way of analysing (Wellington, 2000). Huberman and Miles (2002) state that analysis can be divided into three distinct stages: data reduction, displaying the data and drawing conclusions but with a mixed method, grounded theory approach it seemed that my analysis would resemble a more process. As an integral and interactive part of the research rather than a separate stage (Wellington, 2000)

102

the analysis might be better likened to arranging, rearranging and piecing together a patchwork quilt until it resembles a single, complete unit (Denzin & Lincoln, 2003).

The grounded theory approach meant that analysis would proceed alongside data collection to identify emerging themes and inform the direction of the research. My analysis would commence once the first data had been obtained and would continue throughout the fieldwork, shaping the data collection in a dynamic process of constant comparison and interaction (Bogdan & Biklen, 1992).

Classic grounded theory normally involves a particular systematic means of analysis based on an inductive approach (Newby, 2010) which uses coding, memos, categorising and comparison to derive theory from data (Strauss & Corbin, 1998). For my study, this provided a useful set of principles and an outline framework for the analysis. Features of qualitative research such as immersing oneself in the data, standing back to reflect and taking apart the data into manageable pieces (Wellington, 2000) could be incorporated into a more

structured process of coding, theming and theorising to explain patterns (Newby, 2010). By incorporating the main characteristics of theoretical sampling, coding, constant comparison and the identification of core variables (L. Cohen et al., 2007) then my analysis would have a recognised structure that would add validity to the findings.

The use of coding in qualitative analysis needed some closer examination since this would be fundamental to organising ideas and opening up the text (Newby, 2010; Richards & Morse, 2007). In a grounded theory approach three stages can be identified that would be useful to consider: substantive or open coding; selective or axial coding, in which codes are grouped together; and finally theoretical coding, in which a core idea is developed that connects the codes (Newby, 2010; Yates, 2004). My intention was to use this constant comparison method to guide the process of analysis so that, as different sections of qualitative data were gathered, they could be transcribed, coded, summarised and compared with other data whilst moving towards the development of theory. By this means, the wide and varied data from my research would be continually examined, coded, grouped and refined until theoretical ideas were established that were consistent with the data. This method of active inquiry should help to avoid the descriptive or shallow findings sometimes associated with qualitative methods (Richards & Morse, 2007) and, s

(L. Cohen et al., 2007, p.491), both qualitative and quantitative data could be incorporated.

103

The methods of analysis associated with grounded theory were suitable for the theory- seeking nature of my research but these needed to be compatible with the case study approach. Eisenhardt (1989) suggests that, with case studies, a similar, iterative approach is suitable for building theory in stages of divergence as data is compared and explored, but within an overall aim of achieving convergence into a single theoretical framework. Data collection and analysis may also overlap in a case study approach and there is a similar expectation that closure will occur when theoretical saturation is reached (Eisenhardt, 1989).

The distinctive features of case study analysis of value for my study were the opportunities - cross-case This would be a productive means of using the cases to develop further understandin Within-

analysis would focus on each case as a separate entity with its own patterns, whilst cross- case comparisons could be used to search for broader patterns, similarities and core themes.

These grounded theory and case study approaches to analysis each contribute to the overall plan in a complementary way and involve the interaction of analysis with data collection (Bogdan & Biklen, 1992). With the possibility of constraints on additional fieldwork then it seemed that iterations between data collection and analysis may need to be planned in phases so there was time to negotiate any changes to the original plan with colleges. There was also a risk that theoretical saturation may not be achieved within the time period agreed and this was a possible obstacle that would need resolving by negotiation with colleges if necessary or the limitations may be reflected in the findings.

3.4.2 Outline plan for analysis

The interaction between analysis and data collection made it difficult to prepare a precise plan and flexibility was needed since additional data collection or cases may be needed as the research progressed. The following stages of data collection provide an initial

chronological framework into which the analysis would be integrated:

 Interviews with managers

 Questionnaires for functional mathematics teachers  Interviews with functional mathematics teachers  First round of lesson observations

104  First focus group meetings

 Second round of lesson observations  Questionnaires for vocational teachers  Interviews with vocational tutors

 Additional observations, interviews or focus groups.

As the data from one element of this framework was obtained for a single college, then a first level analysis would be carried out. For interviews and focus groups this would entail full transcripts and initial open coding to elicit the main themes. Once a full set of data for an item had been collected from all the colleges then further analysis and comparisons could take place.

The questionnaire data would be coded numerically, using nominal codes for descriptive categories, such as gender and department. Numerical codes for responses on the Likert scale would be regarded as ordinal rather than interval. This data would then be entered into a spreadsheet and summarised so the key features or trends could be identified. A written summary of the results would be prepared and used to inform the on-going data collection, particularly the areas to be explored in the interviews. A similar method would be used for responses to the student card-sorting activity. With a full set of questionnaires from functional mathematics staff then a cross-college summary could be constructed so overall trends, similarities and differences could be examined. Some further analysis may be

possible at this stage using SPSS but since the data would be mainly ordinal and the numbers of responses would be relatively small, then statistical methods would be restricted to simple non-parametric tests appropriate for the size of the data set.

As interview and focus group data were gathered, transcribed and coded, then these open codes would be grouped into categories so the emerging themes could be identified. Using NVivo for the storage and coding of qualitative data would make the process easier to handle since it was anticipated that the volume of qualitative data would be substantial.

In some sections of the data there were specific comparisons that would be of interest. For example, comparing the responses of students to the same statements about school and college mathematics or comparing the questionnaire responses of vocational staff to functional mathematics staff. These would be important in identifying key differences or similarities and would need incorporating once the relevant data sets were complete.

In this way analysis would move forward whilst also feeding back into the data collection to ensure gaps were filled and additional data gathered, where appropriate. Meanwhile the

105

case studies of colleges and student groups would be developing, based on early interviews and lesson observations but continually being refined as additional data was analysed, compared and incorporated.