Ratio is one of the key mathematics concepts included in the South African Mathematics curriculum. It is applied in other topics of the Grade 7 curriculum, including geometry, functions and relationships, algebra, similarity and congruency.
The aim of this qualitative research study was to explore the difficulties that learners experience in learning ratio. The primary research question for the study was: What is Grade 7 learners’ knowledge of ratio? This research question was answered through the following secondary research questions: How do learners solve problems involving ratio? What is learners’ conceptual knowledge of ratio? And what learning difficulties do learners experience when learning about ratio?
The study was informed by Kilpatrick, Swafford and Findell’s (2001) five strands of mathematical proficiency; however, the focus was on conceptual and procedural knowledge of ratio. The interpretivist paradigm and the single exploratory case study design were used to gain insight into the learning of ratio. Data was collected from Grade 7 learners (23 of the 35 learners originally sampled) through a self-developed test that followed the prescripts of the Grade 7 Mathematics curriculum in South Africa and through semi-structured interviews. The test scripts were analysed using the Atlas.tiTM windows coding system and the results were used to construct questions for the semi-structured interviews. The interviews were used to corroborate data emerging from the test.
The results of the study indicated that Grade 7 learners can do simple and routine manipulations of ratio as well as non-proportional ratio problems but struggle to solve problems that require multiplicative thinking and proportional reasoning skills. Although there could be other factors contributing to learners’ struggle to tackle proportional ratio problems requiring multiplication and proportional reasoning, a lack of conceptual knowledge seemed to contribute significantly.