Magister Educationis - MEd / In South Africa it is widely known that most learners struggle with mathematics. The results for mathematics are poor. The department of basic education offers a number of intervention programmes to assist learners in mathematics but the problem still persists. Algebra is the most basic and important topic in mathematics as it becomes an element in almost all the other topics in mathematics curriculum. Algebraic fractions in particular are a challenge for most leaners. Research shows that learners commit a number of errors when they work with algebraic fractions. The study investigated the implementation of an intentional teaching model into grade 9 mathematics learners’ ways of working with rational algebraic fractions. An intentional teaching model is a teaching strategy which emphasizes teaching intentions or teaching objectives are brought to the fore during a lesson, the model emphasizes the use of spiral revision and assessment for learning. Ways of working in this study refers to the way in which learners deal with algebraic fractions when they simplify them including the errors they commit from the misconceptions they have about aspects of working with fractions. The study was conducted in a group of grade 9 mathematics learners at Gugulethu High school, which is located in Guguletu, a township in the Western Cape Province of South Africa. The study is premised on a qualitative research paradigm which focuses on studying situations in their natural settings and applying an interpretive perspective. Data was collected by means of observation and video recording of lessons while learners were engaged in working with algebraic fractions. Learners’ written work was analysed as part of the data collection. The results of the study show that leaners commit a number of errors when they manipulate algebraic fractions. Among other errors are: (i) Cancellation errors which had the highest frequency of occurrence (ii) Defractionalisation (iii) No recognition of the common factor and (iv)Exponential laws error. It was found that the learners’ ways of working with algebraic fractions are mostly characterised by their misunderstanding of exponential laws and difficulty in working with fractions needing the use of factorisation to simplify and find the lowest or highest common denominator during addition or subtraction. The results of the study also reveal that learners struggle to articulate extensively or in detail what they are actually doing as they simplify rational algebraic fraction.

Magister Educationis - MEd / This research investigated how grade 7 learners dealt with introductory aspects of integers when they are introduced through a temperature model. In particular, the study analysed the effect of an intentional teaching strategy on learners' engagement with integers. The idea of combining an intentional teaching strategy with the introduction of integers in grade 7 learners using a temperature model is what makes this study unique. A qualitative study was adopted. Data was collected by means of audio and video and also by means of learners' completed worksheets. The results of the study indicate that the majority of learners could recognise, compare and order integers. It is recommended that the application of intentional teaching with a temperature model is a viable strategy to introduce grade 7 learners to integers.

Magister Educationis - MEd / 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.