Data analysis

There is no particular moment when data analysis begins. Analysis is a matter of giving meaning to first impressions as well as to final

compilations.

(Stake, 1995, p.71)

This very much expresses the process I experienced with the analysis of my data. Each time I met with any of the participants in my research, I was mindful of my aims and the open structure of my dialogues allowed me to follow-up on questions both as they arose and in subsequent meetings. Thus the on-going, informal data analysis served to inform aspects of each meeting. The emphasis on this iterative process during research is also fundamental to constructivist grounded theory.

According to Stake (1995), case studies can be explored in two main ways. They can be explored as individual cases through “direct interpretation” which then allows for an “aggregation” of properties within each case and across different cases. With the children in my study, I wanted to explore each child in depth and identify any patterns or relationships in their development over time. I also wanted to then compare all my case studies to try to identify any common themes or strands that they shared.

After each visit, I transcribed the interview, reviewed my field notes and looked over any assessments I had done. As I transcribed each interview, I began to identify

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gaps and questions that I wanted to follow up in later visits. I also reviewed my notes from my meetings with staff, in order to identify areas of questioning which may have been missed. As I did this, I made notes to highlight points that seemed particularly significant. Thus some element of data analysis was on-going and iterative. This on- going analysis was also informed by my initial review of the literature, but as time went on and I read more, the detail of my analysis became more refined and fine- tuned, enabling me to explore more of the detail in the children’s responses and to find areas that had not been explored in the literature in such depth.

The process of analysis was challenging and, as stated by Cohen, Manion and Morrison (2007, p.368):

The great tension in data analysis is between maintaining a sense of the holism of the interview and the tendency for analysis to atomize and fragment the data – to separate them into constituent elements, thereby losing the synergy of the whole, and in interviews often the whole is greater than the sum of the parts.

As I analysed the data, it became clear that the children’s responses could not easily be reduced to just a few sentences. Rather, in order to understand the depth of the conversations, it was necessary to include complete episodes. In this way, it was possible to present aspects of the children’s personalities and observe their development over time. Over the 2 years that I worked with the children, I built relationships and watched them grow and change. It was important for me that the personalities of the children came through, as this was part of who they were and, therefore, an important part of the “context” for my analysis.

3.7.1 Interviews with the children

My first attempt to analyse the data as a whole took place during the spring, summer and autumn of 2014. During this time, I reviewed all my raw data (including

transcripts) and my notes. This helped me to decide which children I was going to focus on. I chose the five children for whom I had the richest data, in relation to my three research questions.

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My methods of data analysis were drawn from discursive analysis and thematic analysis, in order to identify themes to exemplify features, patterns and relationships that were relevant to my three research questions. The discursive approach enabled me to pay “more respectful attention to, and faithful representation of, participants’ meanings and understandings” (Wilkinson, 2000, p.454), rather than imposing my own. In thinking about themes, I was cognisant of the need to choose extracts carefully, in order to ensure that they illustrated the points being made (Braun and Clarke, 2006). With the transcripts for each child in chronological order, I read and reread them, in order to become more familiar with the data. This iterative process, enabled me to get a sense of each child’s journey, and to begin to identify extracts of dialogue that seemed to be mathematically significant, in terms of what I could infer about the child’s understanding and approach to problem-solving within the context of the mathematics we had explored. This was broadly a process of identifying themes according to “theory-driven” criteria (Braun and Clarke, 2006). In other words, although I was exploring each child’s mathematical journey and did not know what I would find in terms of the children’s mathematical development, I was working with the background knowledge of certain theories about mathematical learning that have been discussed in chapter 2. I therefore had some models to help identify particular characteristics of mathematical development in order to begin to explain the emerging trends in my data. The aspect that was not so developed in the literature, related to the development of the link between finger gnosis and finger mobility and understanding and skills in number and arithmetic.

A key focus of my analysis was an exploration of the children’s methods used during the interviews. This meant that transcription also had to include notes on the

methods used by children to help them work out their solutions to the problems posed.

Analysis of the transcripts also enabled me to identify changes in other areas, such as language development, which were not my focus, but which made a difference to how the children were able to approach the problems posed and articulate their thoughts. As these themes emerged during the process of analysis for each individual child, they were noted and then checked for all the children.

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Once this process had been completed, I was able to reflect on what was missing from my data. This reflects the theoretical sampling technique within constructivist grounded theory (Charmaz and Bryant, 2011). Following this I arranged to visit the children again, in order to complete my data collection and then finalise the analysis of the interviews, repeating the process outlined above. This process helped me to choose the five focus children for whom I had the richest data, in relation to the research questions.

My five focus children were spread across the age range and included four girls and one boy. At the beginning of the study, the girls were aged 5 years (Emily), 8 years (Isabelle), 9 years (Hannah) and 9 years (Tania) and the boy was aged 5 years (Luke). All the names are pseudonyms.

3.7.2 Interviews with parents and staff

The interviews with parents were reviewed to try to identify themes within each interview and also across the interviews. The interviews with staff have been used to provide some background information and have not been analysed in great depth. This was done in order to maintain the ethical position that the teaching and the provision was not being scrutinised. My role in the school was to observe the

children and any information provided by the school was provided voluntarily and in confidence.

3.7.3 In-class observations

In-class observations were analysed in a similar way to the interviews, where the search was for opportunities to identify moments of significance, in relation to the mathematics that the children were engaging with. Again themes were identified for later analysis and for comparison with the one-to-one interviews that I undertook. Although aspects of interactions with the staff have been identified, these are rarely

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discussed in a critical manner, in order to maintain the ethical position of the researcher.

3.7.4 Assessments

The standardised assessment scores were analysed in relation to what they told me about each child’s learning at a particular point in time. When exploring the data, I also reflected on the strategies and processes the children used.

The tests were carried out according to the instructions in the relevant manuals. For the WMTB-C all the practice trials were used when carrying out the tests. I moved on after four correct trials and observed the discontinuation rule if three or more errors were made in one block. For the WIAT-II Mathematical Reasoning test, I observed the discontinuation rule if three consecutive errors were made. For the WIAT-II Numerical Operations test, I told the children that they should complete the parts that made sense to them. Consequently, the children said when they could not complete any more of the calculations (usually because the calculations were presented in a way that was unfamiliar to them). If I felt that they could do more, I asked them to move on to questions which I knew they were more familiar with.

For Panamath, I was particularly interested in the children’s final scores and their reaction times. I also looked for any changes over time.

The number line estimation tasks were analysed individually, but also over time, so that changes in understanding could be more easily identified.

3.7.5 Putting all the results together

Once I had analysed all my data, I put all the information together for each child in chronological order. This helped place my interview notes and observations within the context of the views of the staff that were working with the children at the time. I was then able to look across the results for all the children to attempt to identify any

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patterns or similarities that were common for some or all of the children in the study. In other words, were any of my findings generalizable for the children? Had I found anything that could be described as a common feature of mathematical development in children with Apert syndrome?