Learner errors and misconceptions in ratio and proportion : a case study of grade 9 learners from a rural KwaZulu-Natal school.

Abstract

Proportionality is the content domain of mathematics that is rooted in ratio and proportion. It is believed to be vital for problem solving and reasoning, which are key cognitive domains of mathematics teaching and learning. Hence, ratio and proportion forms part of curricula for all countries. Studies carried out in different parts of the world found that while learners can do simple and routine manipulations of ratio and proportion, they struggle to solve problems that involve these concepts. Researchers apportion the blame for this to the strategies that learners use to solve the problems. Researchers found that learners use flawed strategies due to misconceptions that learners have on ratio and proportion. The purpose of the study is to explore learner errors and misconceptions on ratio and proportion. A test that comprised of questions that are appropriate to the National Curriculum Statement (NCS), for General Education and Training (GET) band, was used to collect data. Items in the instrument were selected and adapted from a tool used in Concepts in Secondary Mathematics and Science (CSMS) study. The participants in the study are 30 Grade 9 learners from a rural school in KwaZulu-Natal (KZN). The findings of the study are that learners have a limited knowledge and understanding of ratio and proportion, hence their performance in items on the topic is poor. A great proportion of the learners have serious misconceptions of ratio and proportion. They use incorrect strategies to solve problems on ratio and proportion that produce errors. The errors and misconceptions they exhibit are not different from those observed by similar studies conducted in other parts of the world. The study recommends a structured focus on ratio and proportion because the topic is fundamental to proportional reasoning. It recommends clarity for teacher trainers, textbook writers and teachers on what learners need to learn on ratio and proportion. It recommends serious exploration of errors and misconceptions on ratio and proportion, and a teaching approach that considers errors and misconceptions as opportunities for learning.