Interpretación De Los Resultados De Las Encuestas

In order to operationalise this stage of the research it was first necessary to consider what particular perspectives and insights these learners might shed on the global research questions. These questions were first stated in section 1.3 as follows:

- How do the experiences and mathematical trajectories of learners reflect the competing goals and roles of mathematics education?

- How do learners navigate and make sense of competing or co-existing goals and roles of mathematics education? In particular, how do they make sense of their own mathematical purpose?

The common incident central to this group, and that which arguably has the potential to reflect most clearly the competing goals and roles of mathematics education, is each prodigal’s decision to return to mathematics. A close association between the purposes of mathematics education and the prodigals’ decisions is both consonant with, and theoretically plausible within, different schools of thinking regarding decision making (for instance, Hastie and Dawes 2010). In psychological models which conceptualise decisions as responses to personally constructed sets of needs and preferences, the goals and roles of mathematics education can be understood as contributing to this construction, such as in the case of the teaching assistant who took GCSE mathematics as she wanted to feel more confident when supporting pupils in class. In cognitive

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models where decision making is a process that responds to external or environmental stimuli, the goals and roles of mathematics education could be thought of as contributing either directly or indirectly to these stimuli. Similarly, in normative models of decision making such as mathematical game theory where decisions are seen as logical choices designed to maximise some form of profit or advantage, the goals and roles could be seen as qualifying or even quantifying different outcomes and achievements as things of worth. In these ways, the actress who returned to education to improve her GCSE mathematics grade might be construed as either responding to the stimuli of the demands of the job market (demands which are closely associated with some of the goals and roles outlined in chapter one,) or acting to maximise her cultural capital by obtaining a key mathematical qualification.

The centrality of the decision making process thus gave rise to three localised research questions, of which the first two are:

 Who are the prodigals?

 What motivates the prodigals to return to learning mathematics; in particular, what roles or goals are at play in these decisions?

The second of these questions is a focused wording designed to facilitate exploration into both the prodigals’ mathematical trajectories and their sense- making processes, so as to elucidate the global research concerns. The introductory and complementary first question is then necessary to offer context and clarify the data so that its messages are more fully understood. As well as reporting on demographic characteristics such as age and gender, this question

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involves the prodigals’ educational biographies and thus offers important context; it would be difficult to infer or discuss confidently the place and relevant impact of a mathematics qualification for an individual without considering first their prior qualifications.

Whilst the decision to return to mathematics is fundamental in exploring the influence of the goals and roles of mathematics education on the prodigals, this group offers opportunity beyond simply considering the decision itself; having experienced mathematics education in two contrasting environments, and in two institutions which are likely to respond differently to the varied purposes of mathematics education, these learners can offer a useful perspective on the similarities and differences which they have observed:

 How do the prodigals’ experiences of learning mathematics as an adult compare to, and contrast with, their experiences of learning mathematics at school? What changes are there in the ways that the goals and roles of mathematics education are navigated or made sense of by these learners?

The intention here was that establishing a direct comparison between the two sets of experiences would highlight differences that can then in turn be understood as resulting, at least in part, from a shift in the balance of the contending goals and roles outlined in chapter one. For instance, it might be expected that the goal of inculcating a sense of numeracy might be differently emphasised in adult education institutions as compared to school, since the majority of adult learners are likely to have a wider body of experiences to draw on; similarly the prevalence and presentation of this particular goal might vary between an adult

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numeracy course and a course for adults which culminates in the GCSE mathematics examination.

In this way these three localised research questions offered meaningful explication of the global research questions of this thesis, and could be in turn operationalised into a localised methodology which is described below in section 3.3. The findings of this research are presented in sections 3.4 and 3.5; the contributions of these results to the global research questions are then discussed in section 3.6.