Chapter 2. Assessment Matters: A Literature Review
2.8 What Mathematics/Numeracy is Needed?
2.8.2 Workplace Mathematics
Given the dominance of the human capital ‘deficit’ model of adult numeracy in England that places so much emphasis on productivity and economic outcomes, it is useful to examine research on the mathematics/numeracy needed in the workplace. Is there evidence here for a ‘skills crisis’ or pointers for what could be included in curricula and assessments?
Research conducted in English workplaces in 2008 strongly refuted the idea of a skills crisis. The research concluded that adults generally ‘make do’ very effectively with the skills they have and respond to the demands of their jobs through informal learning if and when necessary (Evans and Wait, 2008). A large scale, longitudinal study of workplace literacy and numeracy in England concluded that employers are not concerned about the literacy and numeracy skills of their employees and that there was no discernible link between the small literacy gains from work based basic skills programmes and improved productivity (Wolf et al, 2010). Similar findings have been reported in Australia where the assumption that improving literacy and numeracy will increase productivity is also a key element in policy discourse (Black et al, 2013). A more recent study claimed that ‘One in eight (12%) workplaces in England report a literacy and/or numeracy gap whereby at least one member of staff is unable to perform certain literacy or numeracy tasks to the level required in their day-to-day job’ (BIS, 2016a, p.7).The same study goes on to reveal that less than 7% of workplaces report a ‘numeracy gap’ and found no significant relationship between workplaces declaring a skills gap and their productivity (ibid). These figures, considered alongside the highly situated nature of numeracy practices within the workplace, are less than convincing of the existence of a ‘skills crisis’. Furthermore, this report reveals a ‘deficit discourse’ by suggesting that limited numeracy skills are ‘masked’ by the use of technology and peer support (ibid). However, it could be argued that use of technology and collaboration with peers is a normal part of any workplace and does not need to be interpreted as evidence of a deficit.
19 See, for example, the Open Science movement; http://www.openscience.org 20 Project sponsored by Cisco, Intel and Microsoft.
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A study on workplace numeracy in Denmark (Wedege, 2007) highlighted key differences between ‘school mathematics’ and ‘workplace numeracy’ as shown in Table 1 below. Analyses such as this are consistent with a view of numeracy as a social practice and thus highly relevant to this research.
Table 1: Difference between numeracy at work and mathematics in school (Wedege,
2007, p.22)
Numeracy at Work
Mathematics in School
All numbers have units of measurement or refer
to something concrete.
The numbers often appear as pure numerical
quantities.
Numbers and tasks have to be constructed.
Numbers and tasks are given.
A task often has different solutions.
A task only has one correct solution.
Accuracy is defined by the situation.
Right/wrong is negotiable.
Accuracy is defined by the teacher. Right/wrong
is not negotiable.
Solving tasks is done through collaboration.
Solving tasks is an individual matter, i.e.
competition.
Tasks are full of ‘noise’. The numbers are often
‘dirty’.
Tasks are cleared of ‘noise’. The numbers are
‘clean’.
Reality requires the use of mathematical ideas
and techniques.
Reality is a pretext to use mathematical ideas
and techniques.
Solving tasks has practical consequences.
Solving tasks has no practical consequences.
Working tasks are defined and structured by the
technology.
Mathematical tasks structure the teaching.
It seems less surprising, having read the table, that individuals who have ‘performed well’ in school, perhaps gaining a high grade at GCSE mathematics, are not always immediately successful with the mathematics needed in the workplace (Hogden and Marks, 2013); as Wedege reveals, they are two distinct kinds of mathematics. Steen points out that the mathematics itself used in the workplace is not necessarily at a high level;
Mathematics in the workplace makes sophisticated use of elementary mathematics rather than, as in the classroom, elementary use of sophisticated mathematics. Work- related mathematics is rich in data, interspersed with conjecture, dependent on technology, and tied to useful applications. Work contexts often require multi-step solutions to open-ended problems, a high degree of accuracy, and proper regard for required tolerances. None of these features is found in typical classroom exercises. (Steen, 2003, p.55)
This finding is supported by research in workplaces in Ireland that reveals a ‘spectrum of factors that complexify’ routine mathematics and potentially add to the tendency for mathematics at work to become invisible (Keogh et al, 2014, p.85). Recent research from England confirms that workplaces require ‘simple mathematics in complex settings’ and that for most jobs the level of
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mathematics does not go beyond GCSE (Hogden and Marks, 2013, p.5). However, the same research recommends further mathematics courses following the achievement of GCSE that involve collaboration, the application of mathematics to complex authentic problems and the use of technology (ibid).
2.9 Summary
This literature review shows that, despite significant research on adult numeracy in recent years, there has been very little that directly relates to evaluating or developing different assessment models. There has been some research on adults’ attitudes and preferences for assessment in mathematics and this suggests that adults do not always want to work towards qualifications and that many prefer assessment that does not take the form of a timed test. However, some adults and young people like the fact that a test is a one-off event and feel that this form of assessment suits them.
The importance of affective aspects of learning mathematics are reflected clearly in the literature with particular attention being given recently to developing resilience and a growth mindset. Negative attitudes have been attributed in part to high stakes timed tests and the detrimental effect this has on classroom teaching. Mathematics anxiety and test anxiety are serious issues that affect a significant number of people and these too have been linked to the use of frequent timed tests. The literature suggests positive attitudes towards mathematics can be supported by the use of open tasks and less emphasis on speed of calculation and the need for memorisation.
The historical review of examinations showed how they were used from the outset as
accountability measures and for ranking and sorting students within the English school system. This is still the case today to a large extent and some literature questions whether this is a solution to a past problem that is no longer appropriate.
The literature revealed two approaches to assessment of particular relevance to this research; divergent assessment involving an open-ended approach to finding out what someone knows or can do and the concept of eliciting a ‘best performance’ from an individual.
The theoretical framework of numeracy as a social practice provides an alternative view of numeracy to the dominant discourse of ‘skills acquisition’. This view has profound implications for assessment and supports a more holistic approach that incorporates choice, collaboration and a variety of assessment tasks rather than a one-off event such as a timed test. Such approaches, evidenced in the international literature, also have the potential to support the development of social capital as well as human capital. There is considerable literature to show that attempting to evaluate adult education programmes by measuring improvements in the mathematical ‘skills’ of the students is problematic and reflects an unhelpful binary view of adults as ‘having’ or ‘lacking’ such skills.
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Similarly, within all phases of education, there is overwhelming research evidence that using high stakes timed examinations for accountability is damaging. The literature relates this high stakes approach to a culture of performativity and concerns about ‘standards’ and international competitiveness.
The literature makes a distinction between attempting to assess mathematical performance and competence and suggests that a timed test is perhaps limited to assessing only performance. To assess competence more broadly tasks need to be open ended and include realistic scenarios that require students to make connections between mathematical topics. There is considerable support for this approach in the literature on 21st century skills which suggests that
what is needed is the ability to solve problems rather than memorise facts and methods and demonstrate speedy calculation. Literature on mathematics needed for the workplace also supports this approach and reveals that usually the highest level of mathematics needed is Level 2/GCSE but within what is likely to be a ‘complex’ setting.