id: 06271227
dt: j
an: 2014c.00770
au: Mofolo-Mbokane, Batseba; Engelbrecht, Johann; Harding, Ansie
ti: Learning difficulties with solids of revolution: classroom observations.
so: Int. J. Math. Educ. Sci. Technol. 44, No. 7, 1065-1080 (2013).
py: 2013
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: I55 D75
ut: Riemann sums; solids of revolution; skill factors; 3D visualization
ci:
li: doi:10.1080/0020739X.2013.823253
ab: Summary: The study aims to identify areas of difficulty in learning about
volumes of solids of revolution (VSOR) at a further education and
training college in South Africa. Studentsâ€™ competency is evaluated
along five skill factors which refer to knowledge skills required to
succeed in performing tasks relating to applications of the definite
integral, in particular to VSOR. The paper reflects on reasons for the
difficulties that students experience in this topic. The study reveals
that many students are not competent in drawing graphs and in
interpreting the region bounded by the given graphs. If the graphs are
given, students have difficulty in selecting the representative strip
that is used in approximating the bounded region. Although many
students are able to produce the correct formula to calculate the
volume, be it a disc, washer or shell, they find it problematic to draw
the three-dimensional (3D) representation of the rotated strip and the
generated solid of revolution. Students seem to succeed better with
tasks requiring simple manipulation skills. The study illustrates how a
measure (the skill factors) can be put into practice for establishing
exactly where the problems lie when students under-perform in the topic
of VSOR. The results can serve as guide on how conclusions can be drawn
by assessing the problematic situation through breaking it down along
the framework of skill factors.
rv: