Componentes del Control Interno Coso I

As outlined in section 4.0, the opportunity sample was composed of volunteers who were taking a mathematics education module as part of their undergraduate mathematics degree. The purpose and form of this research were briefly described to the undergraduates towards the end of their course, and 13 students volunteered to take part in the research.

The prime ethical concern in this research arose from my personal dual role as researcher and course tutor; whilst both the content and direction of an interview are inescapably influenced by the interviewer, it is possible that if I were to conduct the interviews myself the participants might have been steered towards replicating discussions from the lecture course, or have felt pressured to offer the ‘correct’ response to a figure with some authority over their grades. To this end I recruited two colleagues each of whom interviewed half the sample. They were willing to act as co-researchers as they had some interest in the outcomes from their own research perspective. Hence whilst I, as lead researcher, organised and co-ordinated the sessions I was not present at any of the interviews.

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A selection of five students emerged through purposive sampling and limits on availability, both on the part of the co-researchers and the participants; this was reduced to four when one student repeatedly had practical problems with transport on the day. Although this was smaller than originally intended, after a review of the quality and nature of the data, it was determined that a second call for participants was not necessary.

4.3.2 Interview Design, Application and Analysis

The interviews were semi-structured. The absence of a single rigid structure was intended to allow the participants to express their narratives in their own ways, sharing discursive markers in both the form and content of their telling; conversely, the presence of some structure encouraged a greater degree of consistency between the interviewing co-researchers and facilitated comparisons and inquiry at the analysis stage. Each interview began with a short introduction which was intended to set the tone of the discussion and make clear its purpose:

The aim of this project is to listen to your stories about learning mathematics at school and at university, and to talk about how mathematics may or may not feature in what you choose to do next. We want to hear what you have to say about learning mathematics, what helped you to learn and what did not help you. We have some questions that we would like answered but what is most important is that we hear your story.

The interviews were conducted using a prompt sheet of six questions to ensure similar coverage. These were principally worded to warrant coverage of the local research questions, although the fifth of these was included in part to recognise the interests of the co-researchers. Whilst the questions were ordered to support a

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chronological recounting of each participant’s mathematical history, the interviewers were free to reword or reorder the questions in response to their sense of each participant’s emerging narrative:

 Tell me about your experiences of mathematics at school.

 What made you decide to do a mathematics degree?

 Tell me about your experience of learning mathematics at university.

 Was learning mathematics at university different from learning mathematics at school?

 Have you developed or used any particular strategies or approaches to help you make progress with mathematics at university?

 How do you feel about mathematics now?

Sub-questions could be added if this was deemed necessary at the interviewer’s discretion. The interviews typically took between half an hour and an hour. After transcription the interview data was coded and analysed in the same manner described in section 3.3.3.

4.3.3 Ethics

This research was designed and carried out in line with university guidelines regarding ethical research (the relevant ethics form is reproduced in Appendix C). Measures were taken at each stage to involve, respect and protect the participants; as well as the use of two co-researchers as interviewers detailed above, participants were invited in an e-mail which made it clear that they could opt out

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at any stage. This section of the thesis research was carried out in a particularly transparent manner which recognised that the participants themselves had some interest in mathematics education as a field; in line with the democratising ethos of critical theory the students were invited to ask any questions they had about either the analysis or the research and publication process.

The particular nature of the sample challenges claims to full anonymity, particularly as it applies to the educational institution. Nevertheless personal anonymity was supported through the use of pseudonyms both in written summaries of the research and in the interview transcripts. The interviews were timed in such a way as to have the minimum impact on any of the participating undergraduates’ examinations.

4.3.4 Validity and Reliability

A number of practical steps were taken in the design of this research to bolster the validity and reliability of the data. Principally, a semi-structured interview was chosen to try and hold validity and reliability in tension during the co-construction of the narratives. The imposition of structure was intended to limit interviewer bias and support consistency between the two interviewers, whilst the capacity for open-ended responses allowed the participants to demonstrate their unique perspective and thus supported content validity. The use of two co-researchers also supported the content validity of the findings. One co-researcher interviewed ‘Cathy’ and ‘Mark’ and the other interviewed ‘Adam’ and ‘John’; the presence of resonances both between and within these pairings corroborates their actuality. Finally, both co-researchers were experienced interviewers with a conscious

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awareness of their own biases, and my position as lead researcher facilitated additional checks and comparisons.

At the beginning of the analysis stage all three researchers coded all of the data and these preliminary codes were cross-referenced and compared. The closeness of the three sets of annotations further supports the internal validity of the resulting concepts.

The sample size was unequivocally small, and thus the research reported in this chapter makes no claims of generalisability in and of itself. Indeed, the potential value of this sample was in part related to its uniqueness. The fact that these students had attended a series of lectures on theories and research regarding mathematical learning meant that they had considered their own mathematical learning in depth prior to the interview; this bolstered the scope for both discussion and precision in the generation of shared meanings. The context of the sample also facilitated an uncommon level of access. In this way this sample fits the purpose of grounded theory research, in as much as it does not seek to generalise but to look for features in the available data; despite its size this sample thus contributes to the validity and reliability of the global research of this thesis.