Framework for analysing data

My research data is qualitative in nature as I seek to construct, through interaction and dialogue (Kvale & Brinkmann, 2009), the stories of teachers’ participation in the research project and the development over time of their conceptualisations of teaching mathematics for social justice and related classroom practices. These stories are captured through the use of semi-structured interviews, which are more suited to a desire to understand rather than to

explain (Fontana & Frey, 2008). I adopt an empathetic approach towards interviewing, for example by revealing my own feelings and opinions in order to build trust between myself and research participants, enabling a more meaningful representation of interviewees’ views to emerge (ibid.). I seek to maintain a caring and considerate approach during interviews, demonstrating sensitivity towards the interviewees and establishing an encouraging

environment, as these conditions have a significant influence on the outcomes (Dunne, et al., 2005).

My intention is to analyse and report research participants’ experiences as a “readable public story”, rather than to carry out a “detailed linguistic or conversational analysis” (Kvale & Brinkmann, 2009, p. 181). With these aims in mind, I consider it most appropriate to transcribe interviews and research group meetings using a literary style by, for example, ignoring pauses, fillers, intonations and colloquialisms during conversations. The resulting ‘unfocused

transcriptions’ outline “the basic ‘intended meaning’ of a recording of speech or action without attempting to represent its detailed contextual or interactional characteristics” (Gibson & Brown, 2009, p. 116). Whilst such an approach minimises the amount of time required for the transcribing process, it is important to recognise that all transcriptions are “impoverished, non- contextualized renderings of live interview conversations” (Kvale & Brinkmann, 2009, p. 178). I adopt a thematic analysis approach to analysing the transcripts, making use of “meaning condensation” and “meaning interpretation” (Kvale & Brinkmann, 2009, p. 197). The text is first of all reduced and broken down into units of meaning, for which preliminary themes are drafted. These are then compared across different units of meaning to create wider themes, which are then reported, through relating them to the research questions and theoretical framework underlying the research, in order to generate meaning (ibid.).

I incorporate methods drawn from ‘grounded theory’, described by Gibson and Brown (2009, p. 26) as “the process of developing theory through analysis, rather than using analysis to test preformulated theories”, in my thematic analysis. Such methods are consistent with my critical research methodology in that, whilst I assert that current practice should not be taken as given, there is no pre-existing hypothesis on how to translate a commitment towards teaching mathematics for social justice into practice. My initial conceptualisation (see Section 2.8) offers a starting point for envisioning a more desirable alternative, however this conceptualisation is expected to develop during the course of the research and there is no pre-determined notion of what it might ultimately look like. Thus theories and hypotheses are free to emerge through the research project, albeit with an initial theoretical framework informing and guiding the initial action research cycle.

I make use of the ‘constant comparative method’ from grounded theory which Gibson and Brown (2009, p. 28) describe as “comparing findings or observation with other instances in which those findings might be applicable” and involving three stages: “Creating categories, properties and theoretical relations; Solidifying the theory; Writing”. Theoretical relations are expressed through hypotheses, which are relationships between categories and properties. The theory and its components (categories, properties and hypotheses) are then solidified, or firmed up, by removing non-relevant properties and categories and continuing the analysis until theory saturation is achieved, i.e. further analysis “comprises nothing new in the form of properties but simply reaffirms what is already known” (ibid., p.28).

Categorisation is used in order to enable the emergence and development of themes from the data. Since my intention is to reconstruct the stories of research participants in a way that will provide meaning, I am wary of using rigid and simplistic coding, that can be easily quantified. Such a reductionist approach, whilst allowing easy comparison of large amounts of data, may lead to an impoverishment of the stories of the research participants which I am aiming to report: “By creating a generalized ‘set’ of data that speaks to a range of participants’

experiences, researchers lose focus on the particularities of the cases being examined” (Gibson & Brown, 2009, p. 128). Hence codes and categories are used only to facilitate the exploration of “commonalities”, “differences” and “relationships” (ibid., p. 129) between emerging themes, by enabling easy comparison between inter-related units of meaning. Such comparisons take into account the context of each unit of meaning belonging to a particular category, where necessary returning to the original text and audio-recordings, and may lead to new readings of the data not apparent when units of meaning are considered in isolation (ibid.).

Bergstrom (2012) argues that inductive coding, in which the codes are derived from the data, is more useful for generating meaning in thematic analysis associated with design-based research, than deductive coding, in which the codes are derived from the initial theory. I consider an inductive approach to data analysis more useful for analysing and reporting research participants’ experiences within the participatory action research model I am

adopting, which shares with design-based research the characteristic of “working with iterative cycles for developing both theory and practice equally” (ibid., p.25). However, I consider a deductive approach to coding more appropriate for evaluating the credibility of research processes, since criteria for establishing such credibility have already been articulated by action researchers (see Section 3.6).

Since my research methodology rests on the collaborative construction of knowledge, data analysis includes iterative processes, in which initial findings are presented back to teacher

researchers for comment. This is intended to promote discussion during interviews and meetings of the research group, thus generating further data related to the findings. Presenting findings to other university-based academics, not involved in the project, also provides opportunities to consider alternative interpretations of the data from various theoretical perspectives within mathematics education. Jackson and Mazzei (2012, p. viii) outline the need to avoid the “simplistic treatment of data and data analysis in qualitative research that … reduce complicated and conflicting voices and data to thematic “chunks” that can be interpreted free of context and circumstance”. As an alternative they suggest “plugging in” the data to the texts of theorists whose work underlies the research. This process,

characterised by “reading-the-data-while-thinking-the-theory” (ibid., p.4) allows new analytical questions to emerge that can give new meaning to the data. Findings from the research project are therefore related back to theories underlying my pedagogical positioning, including those of Bourdieu, Bernstein, Boaler, Ernest, Freire, Gutstein and Skovsmose (see Chapter 2), as well as those theories underlying my methodological positioning discussed in this chapter. In this way, the data is interrogated in relation to the “self-understanding” of teacher

researchers, the “critical commonsense understanding” of the wider mathematics education community, as well as the “theoretical understanding” derived from the theories underlying the research (Kvale & Brinkmann, 2009, p. 214).

3.8 Concluding remarks

In this chapter, I have outlined how my own experiences as a mathematics teacher educator have influenced my methodological positioning in relation to this research study. I have used this positioning to explain my choice of the ‘critical research’ model (Skovsmose & Borba, 2004) of participatory action research as the basis for my research design. I have given careful consideration to my role as researcher and to issues of validity and trustworthiness of

research. I have developed a framework for ensuring the trustworthiness of my research and outlined how this has been applied to the research design. Finally, I have discussed and explained the framework for analysing data which I have adopted. In the next chapter, I describe in more detail the research design and the data analysis processes employed in this study.