Data Analysis

This section describes how the data captured from the qualitative and quantitative measuring instruments was analysed. The transparent

demonstration of the analysis process allows the reader to view how the data has been interpreted when identifying trends and relationships. The analysis of the quantitative data from the questionnaires was followed by an analysis of the qualitative data taken from the classroom work, teacher interviews, pupil feedback and lesson plans. It is important to remain aware of the fact that the data from the quantitative and qualitative sections are interconnected, in that the results of the quantitative data informed the development of the qualitative

research. In that respect the quantitative data was analysed prior to the collection of the qualitative data.

3.6.1 Analysis of the Data

Marshall and Rossman (1999, p. 150) describe data analysis as “the process of bringing order, structure and meaning to the mass of collected data. It is

described as messy, ambiguous, time-consuming, creative and a fascinating process”. The analysis of data invariably often does not proceed in a linear manner. It is a process of making sense, interpreting and theorizing about what the data is suggesting (Schwandt, 2007). Being from a mathematical background a logical, clinical, statistical approach to the data analysis seemed the obvious way forward, however, I soon found this to be an unhelpful course of action.

155 Verma and Mallick (1999) and Morrison (2012) remind us that data obtained from qualitative instruments require an interpretive approach with Baumfield, Hall and Wall (2008, p. 23) stating that “qualitative data tends to support inductive

reasoning as a basis for interpreting knowledge and constructing meanings”. Very often a researcher relies on their experience of a particular setting to be able to read, understand and interpret the data. Whilst this study does use a mixed method approach to the data collection, it focuses on the acceptance of a pragmatic position and uses a phenomenological approach for the data analysis. A pragmatic phenomenology allows not merely the opportunity to observe reality through a subjective data analysis but also to adjust and change the experience of reality for others involved. This approach is justified by its usefulness. That is to say we are not looking to see if some belief or approach is ultimately true but rather looking to see if it is justified by its use. Therefore, the adoption of a

pragmatic phenomenological approach to the analysis of the data allowed me the opportunity to research, observe and change practice. The final point here is the very essence of qualitative case study.

3.6.2 Analysing the questionnaire responses

The responses from 201 trainee teachers, 21 subject mentors, 3 school leaders and 9 departmental teachers from the study school were entered into a data file using the SPSS (Statistical Package for Social Scientists) programme. The contextual data from the first part of the questionnaire was also entered as free text. Each of the 26 survey questions were coded (‘S’, ‘T’ or ‘P’ and given a number 1-5 to correspond with the likert scale response). The coding became the 'case variable' in SPSS and was given a label to enable rapid logical retrieval (appendices 1, 2). Codes were also used for degree qualification subjects,

gender and age for the ease of analysis. It would have been perfectly possible to have gained a huge array of very powerful statistical measures from the SPSS program, but having decided to use a pragmatic, phenomenological approach to the data analysis I decided to look for trends and the interconnections in the quantitative data. So, simple statistical descriptive measures such as

frequencies, means, modes and standard deviations were all that I eventually required such as

156 Q u . No. Cat e g o ry Question Text Al m o s t Ne v e r O c c a s io n a lly Ab o u t h a lf o f th e ti m e M o s t o f th e t im e Al m o s t a lway s 1 S

I think learners should spend time in every lesson practising mathematics skills.

0 17 61 90 33

2 S

I think learners gain mathematical insight from practising skills.

3 53 51 71 23

3 S

I think learners should mainly work on their own when practising skills.

18 83 77 21 2

4 T I think learners should tackle tasks. 0 14 52 85 50

Part of Table 4.9a - Frequencies Table. All trainee respondents (n = 201) and Q u . No. Cat e g o ry Question Text

Mean Mode Std. Dev

1 S

I think learners should spend time in every lesson practising mathematics skills.

3.69 4 0.8452

2 S

I think learners gain mathematical insight from practising skills.

3.29 4 1.0278

3 S

I think learners should mainly work on their own when practising skills.

2.53 2 0.8368

4 T I think learners should tackle tasks. 3.85 4 0.8761

Part of Table 4.9l – (Mean, Mode and Standard Deviation, n=201)

The full analysis is show in tables 4.9a to 4.9v in the tables section of the thesis.

3.6.3 Analysing the videos

In total there was over 10 hours of video material from the two study lessons. The cameras were hand held by participating teachers, with each teacher being

allocated a number of pupil pairs to video. In the main they spent only 2 or 3 minutes with any pupil pair before moving on. I nevertheless watched the videos from each of the cameras on a minimum of four occasions, once to transcribe the pupils’ conversations and then to identify and measure other aspects of each child’s interactions (with the other pupils and teachers) and learning patterns. After each transcription was written, each pair of pupils was observed in turn from the videotape. Every interaction with the materials or as conversations between each pair of pupils or pupils and teacher was noted on the observation sheet with the transcription of what had been said or done (appendix 31). I used a

quantitative method to analyse the learning behaviour patterns of the pupils. The behaviours of each pair of pupils in the four parts of the lesson (activity, skill, exercise and task) were then coded using a letter system ‘A’ to ‘H’ (appendices

157 33 and 34). An arbitrary time of five seconds or more was arrived at from the

viewing of the videos as being a realistic amount of time that a particular observation could be coded as being ‘A’ to ‘H’. The two lessons were then analysed separately using exactly the same routines and coding mechanisms. Finally each video segment included a number of pairs of pupils so the results were then combined and summarised for each of the cameras (appendices 33, 34).

3.6.4 Analysing the semi structured interviews

Having made precise transcriptions of all of the semi-structured interviews I was mindful of Schmidt’s (2004, p. 253) warning that

The analytical techniques that are selected for semi-structured interviews within the framework of an investigation will depend on the goals, the questions and the methodological approach – and, not least, on how much time, research equipment and human resources are available. Nevertheless, Bengtsson (2016, p. 8) reminds us that qualitative research contributes to an understanding of context, but “there is no perfectly designed study, and unexpected events will always appear”. However, irrespective of the design the processing of the data reduces the volume of text collected, identifies and groups categories together and seeks some understanding of it. In some way, the researcher attempts to “stay true to the text and to achieve

trustworthiness” (Bengtsson, 2016, p. 8). A four staged approach to the analysis of textual data consisting of decontextualisation, recontextualisation,

categorisation, and compilation is advised by Burnard (1991) and Berg (2001). Stage 1 (decontextualisation) involves familiarisation with the data and reading through transcribed text to “obtain the sense of the whole” (Bengtsson, 2016, p. 10). Stage 2 (recontextualisation) everything is re-read. At stage 3

(categorisation) the data is synthesised into categories to condense the data without loss of content. Stage 4 (compilation) involves the analysis and writing up process and making sense of the data in an “attempt to find the essence of the studied phenomenon” (Bengtsson , 2016, p.11)

It was this approach I eventually used for the analysis of the data from the teacher semi- structured interviews, the pupil consultations and the video

158 as these are what Wolff (2004, p. 284) would call documents or “standard

artefacts” or textual material.

3.6.5 Pupil feedback

At the end of each lesson the pupils were ask to give feedback on the lesson using a prepared document (appendices 10, 27, 28 and 29). The pupil

consultation was designed to inform the teachers as well as valuing the contributions from pupils to the research. Flutter and Rudduck (2004, p. 5) remind us that the premise behind involving and consulting pupils rests on “the principle that pupils can bring something worthwhile to discussions about schooling and learning”, with Lee and Johnston- Wilder (2013, p.13) noting that the “pupil voice has a vital part to play in the continuous improvement of teaching and learning in mathematics”. These comments were foremost in my mind when designing the research instrument to be used with pupils as learning involves not only the teacher but also the pupil.