Institute for Educational Development - The Aga Khan University
Flinders University of South Australia
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of this paper was supported by the Cultural Inclusivity through
Publishing Project and funded by a Flinders
University Diversity Initiative Grant.
The purpose of this study was to determine prospective teachers'
knowledge about the concept of division. One focus of interest was
whether the prospective teachers were able to represent division of
fractions. The participants were introduced to an alternative model
for representation of fractions based on a rate or ratio model of
division involving whole numbers. A second focus of interest was
whether the prospective teachers would be able to apply this model to
problems of division of fractions. The findings revealed that the
prospective teachers' successfully represented division of whole
numbers using models of fair sharing and, to a lesser extent, repeated
subtraction. However, they had difficulty in successfully representing
division of fractions. Some improvement was observed in participants'
performance in attempts to represent division of fractions after
introduction of the rate/ratio model. However the prospective teachers
often used the rate or ratio model mistakenly where the situations
were not appropriate for the model, which appeared to be associated
with difficulty in multiplicative thinking.
Concept of division, multiplicative thinking,
conceptual knowledge of mathematics, pedagogical content knowledge of