Theoretical frameworks

2.6.1 Numeracy as a Social Practice

There is a large body of literature commonly referred to as the ‘New Literacy Studies’ which have suggested the idea of literacy (and numeracy) as consisting of social activity which cannot be disentangled from the situation in which it occurs. This development has largely been in response to government policy that conceptualises learning numeracy as primarily about the acquisition of ‘skills’ that are independent of context and value free (Street, 1984, 1993). What follows from this ‘skills’ viewpoint is a belief that possession of these skills can easily be measured through assessment and statistical surveys; a tendency to see people as either

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‘having’ or ‘lacking’ them. The focus inevitably is on what people cannot do rather than on what they can do; a ‘deficit’ model. This position is reflected in policy documents that refer to ‘low- skilled adults’; a term that is both disrespectful and inaccurate (Mallows, 2016). The implication of rejecting this ‘skills’ view is that, for adults, it is unhelpful and inaccurate to conceive of a linear progression for numeracy from ‘basic’ numberwork through to GCSE level mathematics. These are ‘school numeracies’ which reflect just one type of social practice that may not be relevant for adults (Goulet and St. Clair, 2009). A socio-cultural view would also suggest that assessment itself is a social practice and cannot be viewed as neutral (Elwood and Murphy, 2015). Conceptualising assessment as a social practice allows for inclusion of power relations and requires us to acknowledge that the practice of assessment is a ‘complex capability’ rather than ‘acquisition of a set of skills’ (Wall et al, 2014, p.10). This idea is developed further and specific assessment literacies are discussed in chapter six. How we write and talk about people is important and revealing; to describe someone as having ‘low skills’ is an insulting and

inaccurate way to describe a person who has many life skills but whose numeracy is below an arbitrary norm that is expected of adults (Duncan and Schwab, 2015).

Some of the ideas generated by the New Literacy Studies can be usefully applied to numeracy (Baker, 1995; Baker, 1998; Baker & Street, 1994; Johnston et al, 1997). A social practice view of numeracy considers numeracy as more than a set of skills which someone either has or lacks. It considers the situation where numeracy is happening and the power relations, beliefs, agendas, fears and relationships of those carrying it out (Oughton, 2013). One of the

implications of this social view is that it does not expect ‘skills’ learned in one context to be automatically transferable to another, for example between ‘street maths’ and ‘school maths’ (Nunes et al, 1993). The social practices model may begin to provide answers to the ‘apparent contradiction between many adults being blocked in relation to mathematics in formal settings and being competent in their everyday life’ (Wedege, 1999, p.205). Very often adults do not

recognise their everyday numerate practices as mathematics and, conversely, when a piece of mathematics has been successfully applied, it becomes common sense (Wedege and Evans, 2006). The consequence is that for some adults being successful at mathematics is always out of reach; ‘mathematics – that’s what I cannot do’ (Wedege, 2002, p.63).

Adult education has historically been associated with a critical stance and movements for social justice. There have been calls for a return to this wider purpose for adult education that goes beyond economic agendas (Oughton, 2007; Lima, 2014). For example, mathematics/numeracy classes could provide opportunities for students to ‘question how numbers, measurements and statistics are being used within power relations’ (Ackland, 2014, p. 17) which would also be consistent with a social practices view.

A social practice view of numeracy would suggest that curricula and assessment should relate to learners’ own purposes. If learners were given a choice of assessments, they could choose ones that aligned with their home literacy and numeracy practices (Brzeski, 2008). For some learners, this could involve academic, school mathematics and a timed test if their purpose is to gain a qualification or to prove that they can succeed. For others, it could involve directly

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supporting their numerate practices in a job or activity outside the classroom. As O’Donoghue argues;

There is no gain if the argument polarizes around context and decontextualized mathematics. The point is that some but not all learners are served in either case. Numeracy as an issue in mathematics education must treat these aspects as complementary. (O’Donoghue, 1996, p.81).

Research has shown that tutors sometimes experience a professional dilemma between the need to prepare adults to pass qualifications and to respond to them as individuals who bring their own motivations and purposes for attending mathematics classes (Appleby and Barton, 2008; Ivanic et al, 2006). Swain et al (2005) remind us that learners themselves do not always want mathematics that is practical and related to their everyday lives: meaningfulness for an individual learner relates to their individual purposes and the quality of their engagement with learning. Green and Howard (2007, p.15) summarise this well; ‘A theme that runs through this NRDC research is that matching learning activities to learners' interests, values and purposes is an effective teaching strategy’. Why not also match assessment to learners’ interests, values and purposes? This is also recognised in the same publication;

Perhaps the next task for assessment development is how to combine these creatively to offer a menu of assessment options, spoken and written, teacher-and peer-led, portfolio and exam, formative and summative, that will best support learning. (ibid, 2007, p.19).

2.6.2 Human and Social Capital

According to some authors the issue of capital is central to debates around policy and assessment of adult basic skills programmes (Yasukawa and Black, 2016; NRDC, 2011). Broadly speaking these revolve around whether adult education (and indeed education more generally) should have goals that relate mainly to preparing individuals to contribute to the nation’s economy (increasing human capital) or have goals that relate to shared norms and values and ways to connect and cooperate with each other (increasing social capital). Some definitions of human capital are quite broad such as this one from the Centre for Educational Research and Innovation; ‘The knowledge, skills, competencies and attributes embodied in individuals that facilitate the creation of personal, social and economic well-being’ (CERI, 2001, p.18). However, policy makers tend to see human capital in much narrower terms that relate exclusively to providing skilled workers for the economy (NRDC, 2011). This view prevails despite government research suggesting that ‘literacy and numeracy provision should not be framed solely in terms of increasing human capital.’ (BIS, 2013, p. xi). It has been suggested that benefits to individuals from this approach are there ‘more by chance than design’ (Yasukawa and Black, 2016, p. xiv). This emphasis on the creation of human capital is also inextricably linked to the high stakes testing regime and accountability measures that are dominant in our education system.

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There is considerable research to support the benefits of participating in learning for adults beyond improved ‘skills’ or achievement of qualifications (for example BIS, 2015; Tett and Maclachlan, 2007). In addition, a review carried out in New Zealand makes the point that there is clearer evidence for a link between participation in education and a change in practices than for participation leading to an increase in skills/proficiency (Alkema and Rean, 2013). This finding is supported by longitudinal research carried out in England (Wolf and Jenkins, 2014) and the United States (Reder, 2009). The implications are clear; attempting to measure only improved skills is likely to severely underestimate the benefits to individuals of taking part in adult education. This leads to a dilemma for adult education programmes which are funded largely on their ability to improve proficiency in line with the dominant human capital discourse outlined above (Reder, 2009). The Skills for Life strategy in England that ran from 2001 to around 2012 was deemed to have ‘failed’ in terms of improving numeracy based on a survey of proficiency in 2011 (BIS, 2012) that showed a slight worsening of numeracy skills in the working population compared to the survey from 2003 undertaken at the beginning of the strategy (DfES, 2003). Yet, in terms of participation and broader ways to define ‘success’, the strategy could be deemed to have been very successful (BIS, 2013). Of particular relevance to this research is the fact that the Skills for Life strategy met all its targets in terms of qualifications achieved. These facts taken together support the view taken in this research that qualifications (usually achieved through timed tests) may be a poor proxy for the development of lasting skills/proficiency. The negative interpretation of the survey results of 2011 also reflects the ‘binary’ view that individuals are either ‘numerate’ or ‘innumerate’ and underestimate how proficiency levels for individuals can change over time and may need ‘ongoing attention’ (Carpentieri et al, 2015, p.10). This ‘binary’ view is closely related to the deficit model of education that sees learners as either having or lacking mathematical skills and views poor basic skills as a crisis that can be dealt with by short term measures such as increased achievement of approved qualifications. Carpentieri et al suggest;

Instead of being a ‘crisis’ low basic skills is more accurately understood as a societal condition that requires a comprehensive, lifelong and life-wide strategy that addresses concerns of supply and demand, and brings together a range of policy stakeholders to address these issues. (ibid, p.63).

Supporting social capital goals for adult education would be consistent with choices for adults about modes of summative assessment and, indeed, whether to be summatively assessed at all. This perspective does not dismiss the importance of developing human capital but takes the view that improving social capital is likely to be a requirement for increasing human capital; they are ‘mutually reinforcing’ (The Centre for Literacy, 2010, p.4) and one cannot happen without the other (Balatti et al, 2006). In addition, there is an argument that adult learners are

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et al, 2005) and a move away from what Alex Dunedin11 calls an ‘unnatural gravity around

employability’ (Dunedin, 2015).