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Gail E. FitzSimons
Abstract
The construct of numeracy, where this term or similar has been adopted, is
necessarily situated socially, culturally, historically, and politically. It
is also contested, especially in relation to decisions concerning teaching
and assessment (at a local or an international scale). My own definition is
as follows:
Numeracy is a horizontal discourse which draws upon foundations of
mathematical knowledge developed by individuals over a lifetime of personal
experience and enculturation but which, unlike the vertical discourse
of the discipline of mathematics, relies on common sense and is
context-specific and -dependent, directed towards the achievement of
specific, immediate, and highly relevant goals.
Background
In English-speaking countries the term ‘numeracy’ was coined in the 1959
Crowther Report, as a counterpart to ‘literacy’. This has led to a range of
implications. On one hand, it may be regarded as an attempt to popularise
mathematics — a discipline commonly seen as impersonal and difficult to
learn, and of little use in everyday life. On the other hand, one outcome
has been that the nexus between numeracy and literacy has focused attention
on the communicative aspects of mathematics (mathematics as another literacy)
at the expense of other aspects. Another outcome has been in terms of
research and professional development funding, where numeracy has been able
to benefit from the social importance placed on literacy, but often at the
cost of being just an ‘add-on’. People receiving the funding may have little
or no academic qualifications in mathematics or mathematics education, and
produce findings and/or programs which really only address the literacy
questions, mentioning numeracy in passing.
Over the years the conceptualisation of numeracy has broadened from being
concerned with numbers and perhaps some measurement ¾ that is, the ‘basics’
of the four operations on whole, then rational, numbers ¾ to include, in
some cases, aspects of algebraic, geometric, statistical thinking (or
quantitative literacy in the USA since the 1980s; now used more
generally as a synonym for numeracy), as well as problem solving. As an
indication of the contested nature of numeracy, there are many related terms
used in English, including: functional mathematics, mathematical literacy,
techno-mathematical literacies, democratic mathematics, and mathemacy.
In Denmark the term numeralitet was coined in the mid-1990s [see Tine Wedege
& Lena Lindenskov’s contributions], in France the term ‘numeracie’ is used,
and in the Netherlands, the term gecijferheid was in use prior to the
Crowther Report [see Mieke van Groenestijn’s contribution]. In some
countries, such as Greece and Switzerland, there appears not to have been
any perceived need for this particular conceptualisation of mathematics.
Recently, even the discipline of mathematics was interrogated by Gelsa
Knijnik as to whether it could be solely a unitary construct or one of
several alternative systems developed by people in different social and
cultural settings (Knijnik, 2006). In this regard she argued that terms such
as ‘applied mathematics’, ‘ethnomathematics’, ‘folk mathematics’, and even
‘critical mathematics’ do not disturb the supremacy of the discipline which,
according to Knijnik, masks the power relations which underpin its white,
urban, male roots.
It is clear that all members of the EMMA Consortium value the right of
access to mathematics/numeracy education by adults who, for a variety of
social, cultural, and/or economic reasons, not always under their control (e.g.,
age, gender, race, poverty), may not have had access to the mathematics they
or others perceive as necessary for participation as citizens/workers in
contemporary, increasingly technologised society. It is also clear that
who gets access to what content and why are political
decisions — increasingly so in many English-speaking countries at least — ,
according to the power relations between the various stakeholders in each
country or locality. Nowadays, the pedagogy of numeracy eschews the deficit
model of the learner as needing diagnosis and remediation, and attempts to
take into account the learners’ existing competencies, life experience, and
interests. However, each actual teaching-learning situation — whether in
classroom, workplace, community setting, home; online or face-to-face — will
obviously depend on the individuals who participate, working within (or
around) the parameters of funding guidelines. These guidelines are often
tied to assessment processes and measurable outcomes — but these can never
reflect the actual learning taking place in terms of cognitive, affective,
and social development. Neither can formalised assessment take into account
the flow-on effects of the adult learner’s enhanced contribution to the
family, the workplace (paid or unpaid), and the community at large.
In essence, numeracy is dynamic, and contextually bound to time and place
(van Groenestijn, 2002) [See also Mieke’s contribution to this page.]
My Own Perspective on Numeracy
In order to theorise the ongoing discussion and debate about
distinctions between numeracy and mathematics, I have drawn upon the work of
Basil Bernstein (2000). He describes the discipline of mathematics as an
example of a vertical discourse due to its systematic, coherent, and
explicit structure. That is, more conceptually advanced knowledge builds
upon and integrates foundational knowledge. In formal education, the
discipline of mathematics is recontextualised by teachers for the purpose of
enculturation of learners. However, just as the school subject of woodwork
is qualitatively different from the trade of carpentry, so school or formal
adult mathematics education is different from professional mathematics or
statistics; also from workplace numeracy.
Following Bernstein (2000), I argue that the construct of numeracy is
an example of a horizontal discourse. This follows from my extensive
reading of the literature and my own research into how mathematics is used
and constructed in the workplace to address the ever-evolving problems which
arise there. These include routine checks which indicate the need for
action, communication between workers and with management or clients —
particularly in the case of breakdown in equipment or understanding —, and
creative design or process improvement. Bernstein describes horizontal
discourses as comprising strategies which are local, segmentally organised
(i.e., there is no necessary connection between the solution to one task and
the next), context specific and dependent, designed to both draw on and
respond to encounters with people and the local environment in an optimal
way. The knowledges of horizontal discourses are embedded in on-going
practices rather than abstractions, they usually have strong affective
loadings (i.e., there is usually some degree of emotional involvement), and
are directed towards specific, immediate goals, highly relevant to the
particular context of the learner (i.e., the outcome really matters).
Numeracy is not necessarily explicit or precise (but can be if required),
and its capacity for generating formal models may be limited to the context
at hand rather than generalisable.
In summary, numeracy is a horizontal discourse which draws upon
foundations of mathematical knowledge developed by individuals over a
lifetime of personal experience and enculturation but which, unlike the
vertical discourse of the discipline of mathematics, relies on common
sense and is context-specific and -dependent, directed towards the
achievement of specific, immediate, and highly relevant goals.
Pedagogical
Implications
From an individual’s perspective, Bernstein (2000, p. 160) claims that
“there is not necessarily one and only one correct strategy relevant to a
particular context.” Whereas the transmission of formal mathematics
knowledge is likely to progress from the concrete to the mastery of simple
operations, to more abstract general principles, the teaching of numeracy to
adults may have more in common with the reverse processes which take place
in workplace learning. In other words, based on experience, general
principles may be understood but need to be made concrete in order to be
realised. Ultimately, the learner will be expected to develop a repertoire
of context-dependent strategies, based on experiential learning from a more
‘knowledgeable’ person (or persons) in a given situation, where achieving
the task itself is the priority — not the learning of mathematics per se.
Common sense is highly valued. In my opinion, in order to develop adults who
are considered numerate in contemporary society, there needs to be a
convergence between teaching of the vertical discourse of mathematics and
the horizontal discourse of numeracy. For further discussion see FitzSimons
(2006).
For further information on adult numeracy research from an Australian
perspective, see http://www.ncver.edu.au/teaching/31035.html
Acknowledgement
This paper is based upon work funded by a grant from the Australian Research
Council (ARC) Discovery Project, DP0345726: Adult Numeracy and New
Learning Technologies: An Evaluative Framework.
References
Bernstein, B. (2000). Pedagogy, symbolic control and identity: Theory,
research, critique (Rev. ed.). Lanham, MD: Rowman & Littlefield.
Crowther Report. (1959). 15 to 18: A report of the Central Advisory
Council for Education. London: Her Majesty’s Stationery Office.
FitzSimons, G. E. (2006). Divergence and convergence in education and work:
The case of mathematics and numeracy. VET & Culture conference 2006:
Divergence and convergence in education and work. [Retrieved August 9,
2006 from the World Wide Web: http://www.peda.net/veraja/uta/vetculture]
Knijnik, G. (2006). Cultural differences, adult education and mathematics.
Keynote address presented at ALM 13, Queens University, Belfast, 16th-20th
July.
Van Groenestijn, M. (2002). A gateway to numeracy. A study of numeracy in
adult basic education. Utrecht: CD b Press, Universiteit Utrecht.
4th October 2006 |
