Implementing an intentional teaching model to investigate the algebraic reasoning of grade 9 mathematics learners
Davids, Jade Ethel
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This research has employed an intentional teaching model to investigate the algebraic reasoning of grade 9 learners from a low socio-economic background. It has also sought to study how learners engage with algebra to make generalizations and to scrutinize any misconceptions deriving from the experience. They looked for patterns, paid attention to aspects of the patterns that are important and then generalized from familiar to unfamiliar situations. Algebraic reasoning underpins all mathematical thinking including arithmetic because it allows us to explore the structure of mathematics. This study is based on the Curriculum and Assessment Policy Statement which states that learners are expected to investigate patterns to establish the relationships between variables, as well as represent and analyse the change of patterns. The study also had a huge emphasis on algebra. According to Mphuthi & Machaba (2016): “Algebraic expressions form part of the senior phase CAPS curriculum in South Africa. A substantial amount of time is allocated to this section on evaluating expressions and simplifications of algebraic expressions in grade 7-9.” The study is premised on a qualitative research paradigm and a design-based research methodology for data collection. A set of tasks based on algebraic patterns and generalizations was given to an opportunistic sample of 20 grade 9 learners in a school in Delft, a low socio-economic suburb about 30 kilometres from Cape Town in the Western Cape Province of South Africa. Three weeks after completing the tasks, learners were interviewed to identify their reasoning and how they felt about the tasks. The results of the study show that the majority of the learners struggled with tasks especially when asked what the rules they could derive from the patterns. Learners did not seem to understand what they were doing because they were unable to articulate the given tasks in words and did not have knowledge of concepts like the perimeter.