Investigating some grade 9 learners’ challenges in Algebra with specific reference to integers

Abstract

The teaching of integers is essential in the accumulation of mathematics knowledge among learners in primary and early secondary school years. In Grade 9, it is expected that learners develop a sound understanding of integers, which is needed in Further Education and Training as well as tertiary education, for those who opt for pure mathematics or mathematical literacy. To provide a strong mathematical foundation among Grade 9 learners, teachers and learners have to overcome several challenges that affect learners’ understanding of fundamental concepts including that of integers. Qualitative research methodology within the interpretivist paradigm was used to address the problem being addressed by this study. The purpose of this study was to explore the challenges experienced by Grade 9 learners in understanding integers in Algebra. The target population for this study consisted of 120 Grade 9 learners. A written test on integers, Algebra, was administered to a sample of 40 learners. The face-to-face interview method was used in collecting data from a purposive sample of 5 learners, upon which the Early Algebraic Conceptual Framework by Kaput (2008) was used to analyses data and interpret results. The trustworthiness of the data and results used in this study was achieved through triangulating instruments. Data from the algebra test, and that from interviews, were analysed using open codes, from which themes were generated, interpreted and discussed based on the reviewed literature and theoretical framework. This study confirmed that Grade 9 learners experienced challenges when learning integers in early algebra. Furthermore, it was found that learners struggle to use symbols to generalise, act on symbols, and follow the appropriate rules. The findings were similar to those made in the Early Algebraic Conceptual Framework. The study concluded that the major challenge faced by Grade 9 learners was in understanding the properties of integers, and this resulted in errors such as incorrect application of rules. The study further concluded that the failure of learners to find relationships between variables and numbers was due to a poor understanding of integers. Moreover, when using distributive property, learners tended to ignore the minus sign preceding the integer they were multiplying with, formed part of the product. These findings of the study underscore the need for teachers to discourage learners from memorising rules, but to understand and be able to apply them correctly when given complex integer problems. The study recommended that an integer baseline assessment need to be administered to Grade 9 learners to create a picture of competence in integers. Early detection of integer knowledge gaps among Grade 9 learners, could help learners who were struggling to become achieve better results. It is further recommended that, with suitable instructional guidance from the educators, learners can formulate their definitions that will help them solve even complex integer problems.