Reliability

The interview responses to this enquiry were considered largely, if not completely, to be subjective narratives which needed to be analysed thoroughly for examples of bias. However, I believed that a replication of this study with different interviewers

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and interviewees in alternative settings would almost certainly produce similarly subjective accounts (Kleven, 1995 cited in Cohen et al., 2011:203).

To limit personal bias and interviewees’ misinterpretations (Cohen et al., 2011), individual interview questions were kept short and pertinent with all responses recorded and later fully analysed.

I considered the responses provided to the questionnaires by the two pilot study pupils to be reliable, this because the pupils were not put under pressure and because people with Asperger Syndrome are generally honest (Asperger, 1979). I assumed that the data drawn for analysis, including the written sections of the questionnaires, provided dependable supporting evidence relating to each pupil’s personal views. For instance, both Andy from Arlidge Arts Academy and Ben from Bowman Hill School ticked the box indicating that they did not like to work in groups and in each case this was qualified by a written statement to explain why.

Reliability of observational data could have been affected by personal bias and important events might have been missed in the classrooms when I noticed or focused on alternative incidents. But triangulation in the form of findings from various data sources, (narratives and field notes), were expected to limit these effects. Disruption to classroom activities and the day-to-day lives of pupils and educators was kept to a minimum as I conducted each observation as naturalistically as possible with no indirect recording methodology or open discussions with pupils in the classrooms.

Cohen et al. (2011) suggest that reliability can be further compromised during the analysis by a number of other factors, some of which were of consideration in my study:

140 • Classification of narratives may be inconsistent due to coding variability; • Coding and categorising may result in the loss of richness of specific words

and connotations;

• In condensing data, incomplete portions of text are less reliable than

sentences and phrases that have the highest reliability. (Cohen et al., 2011:573)

In categorising and condensing the detail from the narratives in this work, some of the identifying features may have been lost but as far as possible, I tried to ensure that the original meanings remained clear. For affirmation, I asked a colleague to check that, in abridging some of the accounts, I had not removed any vivid data and also to confirm that the themes I saw emerging were indeed justifiable. This support ensured that personal beliefs were not colouring my perception of events. My own views could have unintentionally altered the intended meanings in write-up so it was vital that the final version was checked and re-checked for anomalies. The data, findings and analysis were personally and externally examined several times for inaccuracies, and checks to ensure that the main research questions were adequately addressed were rigorous.

Finally, while some of the narrative accounts from one particular external professional have been reported, not all of the data gathered from him were analysed as, according to him, despite a diagnosis of AS, his pupils had low functioning autism and not Asperger Syndrome (see also Chapter 2: Literature Review and Chapter 5: Limitations).

3.6 Summary

Although case study methodologies are sometimes considered as able to generate only subjectively functional conclusions (Hammersley, 2007), in order to facilitate consistency, I minimised bias by reducing the influence of personal belief systems.

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As a researcher, I was fully aware throughout of how I might have been constructing my enquiry’s micro-world through studying it. I have explained my own perspectives and personal decisions made about the advantages and limitations involved in observer participation (Hammersley, 2007). These clarifications were intended to limit adverse reaction and criticism regarding the potential for subjectivity in this piece of research. By specifying, in this chapter, facts about selection and sampling techniques as well as detailing factors influencing personal interpretation, I have justified my reasons for decisions and judgments made along with the principles applied to the study. At both the data collection and the analysis stages, subjectivity was, I believe, to a large extent eliminated; all background information has been provided and the data coding has been made explicit and straightforward for ease of replication as necessary. Adhering to my own methodological procedures closely, despite ongoing concerns regarding subjectivity and recall when notes were transcribed after the event, I managed to amass a considerable amount of data for analysis. The findings are conveyed in the next chapter and analysed ahead of the Discussion chapter which refers back to the Literature Review in support of some of the findings. Later, although there were no hypotheses to accept or reject, personal beliefs concerning pupils with Asperger Syndrome that changed following the analysis are reported accordingly.

142 Chapter 4: Analysis

4.0 Introduction

The Analysis chapter presents the findings from this research enquiry which was conducted to examine the situation in the contemporary mathematics classroom for pupils with Asperger Syndrome. Significant features of the new National Curriculum for Mathematics that developed into the research subquestions formed the lenses through which the narratives and field-notes were analysed. Including a section to compare common characteristics and learning styles, the eight themes which informed the subquestions and subsequently became the lenses are:

INTRINSIC EXTRINSIC

Common Characteristics Assisted Learning

Complex Problem Solving and Reasoning

Group Work

Rapid Processing Practical Mathematics

(including computer use)

Perseverance Real-World Learning

The data for analysis in this study were taken from:

• Narratives from questionnaires and interviews • Records of observations

• Diary entries

• Pupils' work (see examples in Appendices 4 & 5)

For triangulation purposes, the narrative data drawn from five questionnaire responses, (see Appendices 6 and 14 and Table 14), and interviews with three professionals, twenty-two staff, (see Table 9), one university student and six pupils (see Table 10 below) provided a variety of alternative views for analysis (Walker, 2007).

143 Table 10: Summary of Data Collection Methodologies

The external viewpoints enabled me to maintain both validity and an objective focus on pupils with the condition. The data arising from the interviews and questionnaires supported the records of classroom observations, (see Tables 12 and 13), and discussions with in-school educators. While the questionnaire and interview questions varied somewhat dependent on setting and respondent, (see Appendices 6, 9, 10, 11 & 14), a number of common features emerged from the narratives. The structure of this chapter is representative of the way in which I organised and amalgamated the data. Following these introductory paragraphs, I present, in Section 4.1, individual accounts of the classroom observations. In Section 4.2, a brief description of the classification process is provided to contextualise the analysis. An example of the coding system applied to the data ahead of the analysis is exemplified using a selected range of data drawn from the various observations, questionnaires and interviews. Next, in subsection 4.3, the various evaluated and generalised findings are linked to the themes. General practice that addresses the

Data Collection Methodology Number Observations Unstructured (Pre-pilot) 2 Observations Structured (Pilot) 2 Observations Semi-structured 8 Questionnaire Structured 3 Questionnaire Semi-structured 2 Interviews Unstructured 6 Interviews Semi-structured 26

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learning needs of pupils with Asperger Syndrome is presented in this section. Accounts of the findings from the various types of observation, interview and questionnaire can be found interleaved throughout for illustrative purposes. A further selection of supporting transcripts and field-notes, some unabridged, is to be found in the Appendices. For brevity, I have not included every sheet used in classification. Those provided are simply for clarification purposes. Categorised findings from all summary sheets are referred to throughout Section 4.3. Finally, the chapter closes with a comprehensive summation of the significant findings to come out of the analysis.