International Education Journal

Educational Research Conference 2006 and Cultural Inclusivity through Publishing Special Issue



download View Complete Article

Acrobat Reader Install Acrobat Reader

Prospective teachers' knowledge: Concept of division

Nusrat Fatima Rizvi 
Institute for Educational Development - The Aga Khan University 

Michael J. Lawson 
Flinders University of South Australia


download Read complete article


Preparation 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 mathematics


Rizvi, N.F. and Lawson, M.J. (2007) Prospective teachers' knowledge: Concept of division. International Education Journal, 8 (2), 377-392.

All text and graphics 1999-2007 Shannon Research Press. ISSN 1443-1475.