id: 06243026
dt: j
an: 2014a.00557
au: Kullberg, Angelika; Runesson, Ulla
ti: Learning about the numerator and denominator in teacher-designed lessons.
so: Math. Educ. Res. J. 25, No. 4, 547-567 (2013).
py: 2013
pu: Springer Netherlands, Dordrecht; Mathematics Education Research Group of
Australasia (MERGA), Wahroonga, New South Wales, Australia
la: EN
cc: F42 D72
ut: fractions; learning; teaching; variation theory; difficulties
ci:
li: doi:10.1007/s13394-013-0080-9
ab: Summary: This study concerns pupils’ experience of unit and non-unit
fractions of a discrete quantity during specially designed lessons. The
aim was to explore pupils’ understanding of operations such as $b/c$
of $a$ in lessons where the teachers were aware of some pupils’
difficulties beforehand and what needed special attention. Five classes
were involved in the study and 10 video-recorded lessons and written
pre- and post-tests were analysed. Even though the lessons were
designed for learning how to operate with both unit and non-unit
fractions, we found that more pupils could solve items with unit
fractions than with non-unit fractions. We found that few pupils in
this study had difficulties with equal partitioning. Instead, it seemed
difficult for some pupils to understand the role of the numerator and
denominator and to differentiate between the amount of parts and the
amount of objects in each part, and some pupils did not differentiate
between the numbers of units and the amount of objects within a unit.
This study identified some critical aspects that the pupils need to
discern in order to learn how to operate with unit and non-unit
fractions of a discrete quantity.
rv: