Prospective primary school teachers’ knowledge of the ratio concept

Abstract

Prospective primary school teachers learn about some mathematics concepts in several courses besides the mathematics ones. This happens with the ratio concept which is a cross subject and instrumental concept. Research has shown that this concept is quite hard to master event though it is often used in school as well as in everyday life. This research aims at investigating prospective primary school teachers knowledge on the ratio concept, namely with regard to their ability to interpret and compare ratios in two different contexts. Data were collected from 50 prospective primary school teachers attending a Portuguese university by means of a questionnaire. Participants were asked to answer to two questions that involve the ratio concept: one of them deals with a pizza division and requires a comparison of homogeneous quantities; the other one deals with the speed concept and involves a comparison of heterogeneous quantities. Both questions require information from a graph to be picked up. Data analysis showed that, in the pizza question, participants in the study tend to use numerical representations under the format of a fraction, which led them to do correct comparison between two ratios. In the case of the speed question, prospective teachers showed more difficulties which seem to have been caused by the physical meaning of speed. Thus, the results suggest that most of these prospective teachers hold a limited and rigid knowledge of the ratio concept that may be due to learning process based on numerical representations and carried out within mathematics courses. An implication of this is that teacher educators need to find ways of developing prospective teachers’ cross subject knowledge of the ratio concept so that they can be better prepared to teach this concept to young children embedded into cross disciplinary everyday life contexts.