id: 06270988
dt: j
an: 2014b.00297
au: Foster, Colin
ti: Mathematical études: embedding opportunities for developing procedural
fluency within rich mathematical contexts.
so: Int. J. Math. Educ. Sci. Technol. 44, No. 5, 765-774 (2013).
py: 2013
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: D40 C30 D50
ut: Cartesian coordinates; enlargement; fluency; learning for understanding;
practice; solving equations; task design; traditional and progressive
approaches to the teaching of mathematics
ci:
li: doi:10.1080/0020739X.2013.770089
ab: Summary: In a high-stakes assessment culture, it is clearly important that
learners of mathematics develop the necessary fluency and confidence to
perform well on the specific, narrowly defined techniques that will be
tested. However, an overemphasis on the training of piecemeal
mathematical skills at the expense of more independent engagement with
richer, multifaceted tasks risks devaluing the subject and failing to
give learners an authentic and enjoyable experience of being a
mathematician. Thus, there is a pressing need for mathematical tasks
which embed the practice of essential techniques within a richer,
exploratory and investigative context. Such tasks can be justified to
school management or to more traditional mathematics teachers as vital
practice of important skills; at the same time, they give scope to
progressive teachers who wish to work in more exploratory ways. This
paper draws on the notion of a musical étude to develop a powerful and
versatile approach in which these apparently contradictory aspects of
teaching mathematics can be harmoniously combined. The author
illustrates the tactic in three central areas of the high-school
mathematics curriculum: plotting Cartesian coordinates, solving linear
equations and performing enlargements. In each case, extensive practice
of important procedures takes place alongside more thoughtful and
mathematically creative activity.
rv: