Research purpose and methodology

Through this research project I sought to explore the notion of motivation in relation to adults learning mathematics, what sort of teaching and learning approaches influenced this motivation(s) and how their membership of their particular trade union, who organised the opportunities to learn the subject, shaped it. Motivation to learn mathematics is often seen as problematic (Dweck, 2008; Boaler, 2009), so I chose to interview a group of people who I thought might be highly motivated to learn to try to understand the issues. These adults were learning mathematics at or below GCSE level, while in the workplace, through opportunities negotiated by trade unions and employers. Having experienced previous ‘failure’ when learning this subject, which I discussed in chapter three, these learners have chosen to re-engage with mathematics, overcoming practical barriers such as shift work and caring responsibilities and other more emotional barriers. I was driven to explore what motivated these adults to learn and in the process learn more about what motivation actually is and what teacher and teacher trainers involved with adults might learn from this research.

4.1.1 Me as the researcher

As someone who has had a career in mathematics, I am regularly in dialogue with trainee teachers exploring my own and their worldview, in relation to the ways of understanding the subject and the positivist tradition of scientific exploration it encourages. Walkerdine (1990) describes this way of thinking as ‘the path to rationality, displayed best in

mathematics, is a path to omnipotent mastery over a calculable universe’. (p. 23)

I was inclined to a positivist worldview while studying A level Mathematics, Physics and Geography but when undertaking a university degree in Government and Economics, where I studied mathematics in the first year, and later my MA in Vocational Education, I challenged my then way of seeing the world and I started to consider ‘that humans learn through their experience and that the nature of the experience influences the nature of the resulting knowledge’(Crawford, 1996, p. 96). The contemporary positivist ontological and epistemological tradition has come under severe criticism in research as a ‘reductionist and mechanistic’ view of nature, defining ‘life in measureable terms rather than inner

experience’ relying on the interpretation of quantitative information (Cohen et al., 2011, p. 14). Ernest (1996) further suggests ways of knowing and understanding are about

recognising how the social domain influences the formation of the individual, and how the individual constructs themselves in response. I take that idea a step further and suggest that the individual also influences the social context in which they develop, as I do in my discussion on identity development in chapter three, closer to what Lerman might claim to be the ‘person-in practice-in person’(2000, p. 38).In this sense the research falls within an interpretive research paradigm in that ‘it is primarily concerned with human understanding, interpretation, intersubjectivity, lived truth (i.e. truth in human terms) (Ernest, 1996, p. 24).

However, in this research, I seek to understand what people think and feel, so I wish to explore their understandings of motivations through stories and narratives, told by the people who are learning mathematics at work.

4.1.2 Being sensitive and creating joint representations of experiences

Interpretivism, or antipositivism was developed within the Social Sciences, and in the fields of Psychology and Sociology particularly and is more concerned with understanding people and their behaviour. It focuses on individuals and their interpretations of situations, so naturally relies on qualitative data, which can come from a variety of sources including transcripts from case studies and focus groups, (Denzin and Lincoln, 2000; Bryman, 2012) but in my research mainly one-to-one interviews were prevalent.

However this approach to research is criticised for being too subjective and specific to offer useful insights into group behaviour (Bryman, 2012, p. 405), but Corbin (2008) argues that the notion of objectivity is not a useful way to assess the quality of qualitative data; rather a researcher has to develop sensitivity to his or her data. She describes sensitivity as ‘having insight, being tuned into, and being able to pick up relevant issues, events and happenings in the data’. (Corbin and Strauss, 2008, p. 32). But a criticism of being too subjective could be made, so I agree with Cohen et al. (2011) when they recognise Bernstein’s argument that a researcher becomes part of the research when they are negotiating with participants, yet the research is often written as though the researcher is ‘outside’ the situation’. I do not claim I am outside the process; rather I seek to develop ‘representations’ of the situation (Dowling and Brown, 2010, p. 3), which produces text from data analysis overlaid with my own interpretation based on my own history and experiences. So my perspective and interpretation will not be objective but will have what Donna Harraway (1998) calls a ‘view from somewhere’ (Olesen, 2003, p. 357). Somewhere, in this research, is a teacher of maths to adults with over twenty-five years experience and a teacher trainer with over ten years experience, as well as being a trade unionist for over thirty-five years and a political activist for over twenty years. The research I have undertaken is relevant to my work and my life experiences and therefore cannot help but be influenced by my own knowledge and biographies. So my interpretation of the learners’ narratives could be seen as biased but I agree with Sarkar and Cybulski(2004) when they cite Heidegger (1962) stating it is also impossible to take away all of the preconceptions and presuppositions of the researcher. I accept the need to write in such a way that my bias as the researcher is explicit and not

complicit. I return to this notion of subjectivity when discussing confirmability of the data later in section 4.3.4. (on page 54).

4.1.3 Becoming more critical

Another criticism aimed at both the positivist and anti-positivist paradigms is that they tend to explain rather than change situations, to describe rather than to emancipate (Clough and Nutbrown, 2008; Bryman, 2012). As a lifelong trade unionist and one time political activist I am interested in the potential of this research to identify ideas used in trade union

education that might usefully influence more traditional adult education settings.

The context of this study is adults learning in the workplace, which is often, along with vocational learning and apprenticeships, perceived as having lower quality and value than academic knowledge (Wolf, 2011; TES, 2012). Rather than developing the whole person to think critically and freely,(Hirst and Peters, 1970) learning at work is more often linked to an ‘individual’s economic progress and performance in the workplace’(Shelley, 2007, p.

117).However trade unions were more involved with training for activism and

empowerment, as discussed in section 2.1 (on page 14) so this research and the teaching approaches used in mathematics classes are of interest to my work. I want to explore if this research could usefully improve mainstream mathematics education practice. Hence the study adopts a critical approach in that I am seeking to ‘understand, interrogate, critique and transform actions and interests’ (Clough and Nutbrown, 2008, p. 17).

The learning described in this research occurs because the conventional route has failed the people I interviewed and learning at work has offered those adults a second chance to achieve. Hence I am interested to use the learners’ narratives to describe what they define as 'other’ and ’different’ that has motivated this achievement. It can be argued that the learning that takes place in the workplace has been ‘marginalised’ through the ‘powerful dominant discourses’ of formal education (Cole, 2010, p. 60) but I want to help inform

educators about these ‘other’ forms of teaching and learning, which have proven to be so useful to adult learners.

This research is also underpinned by my own personal belief that learning mathematics, at whatever level, is only valuable if it is related to the empowerment of that person and enables them to live a fuller life that contributes to the betterment of themselves, their environment and society. Because of this I understand trade union learning as a way of enabling people ‘to achieve social justice and challenge societal norms through collective action’ (Shelley, 2007, p. 117). My personal belief about education is also close to that expressed by D’Ambrosio, who wrote about the goals of education being ‘to promote creativity, helping people to fulfil their potentials, but being careful not to promote docile citizens’ (D'Ambrosio, 2007, p. 26) and more particularly that ‘Mathematicians and math educators must accept, as priority, the pursuit of a civilization with dignity for all, in which inequity, arrogance and bigotry have no place’(D'Ambrosio, 2007, p. 25). So my research is also critical in the sense that the researcher is also concerned about the ethical and political dimensions of mathematics education itself

4.1.4 Influenced by feminist research perspectives

Feminist ways of understanding the worldview have been useful to me to help understand my own history of learning experiences, for example when I was training to teach in 1981, a mathematics teacher trainer explained to my learning group that “girls were innately less able to do mathematics than boys”. Hence Burton’s (1987) ideas resonated with me when she theorized that ‘education systems, staff attitudes and pedagogies all reinforce the selection of females and minority groups away from mathematics’ (p. 29). Hacker (1990) understood society as a place where both technology and mathematics was also used to exclude women from other professions, such as engineering. But Benn (2004) went

further, arguing that mathematics was a tool in the construction of a ‘male dominated euro- centric, patriarchal and hierarchical society’ (p. 109). My own experience and being

exposed to these ideas has helped me develop my own thinking about the role of power and culture within society. Social attitudes may now be changing and this analysis may need updating, but feminist thinking was influential in my early teaching career and

continues to inspire my teaching and research in mathematics today. Indeed feminist research has also always sought to explore personal viewpoints, because as Reinhartz (1992) suggests when citing Datan (1989, p. 175) ‘ it is an axiom of feminism that the personal is political’ (p. 234). This is one reason why I carry out analysis in my work at the individual level because I want to use personal viewpoints to consider the influence of affect on motivation. But I stress, as does Benn (2004), that I reject any attempt to locate the problem of not being motivated to learn mathematics within the learner. Being

subjective does not mean blaming the learners rather it seeks to understand their viewpoints.

Throughout this section I have sought to explore and explain my own ‘world view’ and show that my approach to this research, influenced by feminism, aims to be critical and interpretist.