An exploration of learners’ theorems-in-action used in problems on ratio and proportion

Abstract

The purpose of this study is to explore Grade 9 learners’ understanding of ratio and proportion. The sample consists of a group of 30 mathematics learners from a rural school inthe province of KwaZulu-Natal, South Africa. Data were generated from their responses totwo missing value items, adapted from the Concepts in Secondary Mathematics and Sciencetest set in the United Kingdom over 30 years ago. The study utilised Vergnaud’s notion oftheorems-in-action to describe the learners’ strategies. It was found that the most commonstrategy was the cross multiplication strategy. The data reveal that the strategy was reducedto identifying and placing (often arbitrarily) three given quantities and one unknown in fourpositions, allowing the learners to then carry out an operation of multiplication followedby the operation of division to produce an answer. The study recommends that the role ofthe function underlying the proportional relationship should be foregrounded during theteaching of ratio and proportion