id: 06617723
dt: j
an: 2016e.00756
au: Wilkie, Karina J.; Clarke, Doug M.
ti: Developing students’ functional thinking in algebra through different
visualisations of a growing pattern’s structure.
so: Math. Educ. Res. J. 28, No. 2, 223-243 (2016).
py: 2016
pu: Springer Netherlands, Dordrecht; Mathematics Education Research Group of
Australasia (MERGA), Wahroonga, New South Wales, Australia
la: EN
cc: H20 C30
ut: algebra; functional thinking; pattern generalisation; visualisation; middle
years of schooling
ci:
li: doi:10.1007/s13394-015-0146-y
ab: Summary: Spatial visualisation of geometric patterns and their
generalisation have become a recognised pathway to developing
students’ functional thinking and understanding of variables in
algebra. This design-based research project investigated upper primary
students’ development of explicit generalisation of functional
relationships and their representation descriptively, graphically and
symbolically. Ten teachers and their classes were involved in a
sequence of tasks involving growing patterns and geometric structures
over 1 year. This article focuses on two aspects of the study:
visualising the structure of a geometric pattern in different ways and
using this to generalise the functional relationship between two
quantifiable aspects (variables). It was found that in an initial
assessment task ($n=222$), students’ initial visualisations could be
categorised according to different types and some of these were more
likely to lead either to recursive or explicit generalisation. In a
later task, a small number of students demonstrated the ability to find
more than one way to visualise the same geometric structure and thus
represent their explicit generalisations as different but equivalent
symbolic equations (using pronumerals). Implications for the teaching
of functional thinking in middle-school algebra are discussed.
rv: