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Gail E. FitzSimons
Monash University
Australia
What is numeracy and how might it be related to mathematics? Numeracy is
logically connected with mathematics just as literacy is logically connected
with language (Lee, Chapman, & Roe, 1996). Mathematics is said to be a
pan-cultural competence. According to Bishop (1988), all people — young or old,
schooled or unschooled — in all cultures normally perform what he claims to be
six ‘universal’ mathematical activities: counting, locating, measuring,
designing, explaining, and playing.
Bernstein (2000) describes mathematics as being a vertical discourse due to its
coherent, explicit, and systematically principled structure. It takes the form
of a series of specialised, codified languages, with many sub-disciplines (e.g.,
algebra, geometry, trigonometry). In formal education, the discipline of
mathematics is recontextualised for the purpose of enculturation. 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 is due to the strong affinity between the
burgeoning corpus of research reports on workplace and everyday activities
involving the use and re/construction of mathematical knowledges and Bernstein’s
description of a horizontal discourse as “a set of strategies which are local,
segmentally organised, context specific and dependent, for maximising encounters
with persons and habitats” (p. 157). He continues that the knowledges of
horizontal discourses are “embedded in on-going practices, usually with strong
affective loading, and directed towards specific, immediate goals, highly
relevant to the acquirer in the context of his/her life” (p. 159).
Compared to the discipline of mathematics, numeracy is weakly classified in
terms of its necessary integration with context. Whereas in mathematics there is
a well-known hierarchy from s common sense up to so-called uncommon sense, in
numeracy common sense is of the essence. High level abstractions alone are
insufficient and may even prove counter-productive. Numeracy cannot be said to
have a specialised language, except at the most local level of use in context.
For example, the use of the term “thou” [i.e., thousandths] is widely used in
the building and automotive industries, but may not have meaning elsewhere.
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 essence, then, 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
Vertical discourses such as mathematics consist of specialised symbolic
structures of explicit knowledge; its procedures are linked hierarchically. The
formal pedagogy is directed towards some unspecified projected application and
is an on-going process, generally continuing over an extended period of time.
By contrast, according to Bernstein (2000), the pedagogy of horizontal
discourses is usually carried out through personal relations, with a strong
affective component. It may be tacitly transmitted by modelling or showing, or
by explicit means. The pedagogy may be completed in the context of its enactment,
or else it is repeated until the particular competence is acquired. From an
individual’s perspective, “there is not necessarily one and only one correct
strategy relevant to a particular context” (p. 160). Bernstein concludes that
horizontal discourse “facilitates the development of a repertoire of strategies
of operational ‘knowledges’ activated in contexts whose reading is unproblematic”
(p. 160).
In summary, 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, general principles are 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. As
discussed above, context-specific and localised models may also be developed and
practical knowledge/expertise, together with common sense, is highly valued.
References
Bernstein, B. (2000). Pedagogy, symbolic control and identity: Theory,
research, critique (Rev. ed.). Lanham, MD: Rowman & Littlefield.
Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on
mathematics education. Dordrecht: Kluwer Academic Publishers.
Lee, A., Chapman, A., & Roe, P. (1996). Pedagogical relationships between
adult literacy and numeracy. Sydney: University of Technology Sydney, Centre
for Language & Literacy.Juergen Maasz
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