This research focuses on the development of the concept images of the
derivative concept of students enrolled in the in-service programme
'Advanced Certificate in Education' at University of KwaZulu-Natal,
Pietermaritzburg campus. In addition, two qualified teachers not enrolled
in the programme were included.
A theoretical framework which describes the derivative as having three
layers - the ratio, limit and function layers - that can be represented by a
variety of representations - graphical, rate, physical and symbolic - is
used to analyse the development of the students' concept images. This
framework was adopted from previous research, but expanded to allow
for situations where a student's concept image did not fall into any of the
layers or representations. In those cases, the concept image was classified
into the non-layer section or the instrumental understanding section.
The findings of this research show that of the five ACE students who
were interviewed, only one had a profound concept image in all the three
layers of the derivative, with multiple representations as. well as
connections among representations within the layers. This one student
also passed the calculus module with a distinction. The other four
students had the ratio layer and graphical representation profound in their
concept images, while the other layers and representations were pseudostructural
with very few connections. Two of these students passed the
calculus module while the other two failed.
All the students showed progression in their concept images, which can
only be credited to the ACE calculus module. However, it is clear that
even upon completion of this module, many practicing teachers have
concept images of the derivative which are not encompassing all the
layers and more than one or two representations. With the function layer
absent, it can be difficult to make sense of maximization and
minimization tasks. With the limit layer absent or pseudo-structural , the
concept Itself and the essence of calculus escapes the teachers - and
therefore also will be out of reach of their learners. / Thesis (M.Ed.)-University of KwaZulu-Natal, Pietermaritzburg, 2006.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/8498 |
| Date | January 2006 |
| Creators | Likwambe, Botshiwe. |
| Contributors | Christiansen, Iben Maj. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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