Magister Educationis - MEd (Mathematics)
http://hdl.handle.net/11394/4940
2021-06-25T13:55:05ZConceptions of conservation of energy among grade seven learners in two cape town schools
http://hdl.handle.net/11394/8047
Conceptions of conservation of energy among grade seven learners in two cape town schools
Okoroh, Nwakaego Esther Malin
The clamour in the country about the poor performance of learners in the area of physical science is a concern and this problem had been attributed to different facets of learning which include the amendment of curriculum over the years. But my question is; can the curriculum amendment succeed without effective teaching approaches? This poignant question formed the central concern for this investigation. This study examined two cohorts of grade seven learners’ conceptions of conservation of energy using a Dialogical Argumentation Instructional Model (DAIM) as well as the Traditional Lecture Method (TLM). The study involved 48 learners selected from two public schools in Cape Town. Using a quasi-experimental (Non-equivalent groups) design, the study examined the two groups from different schools (24 learners in each). It exposed one group to the Traditional Lecture Method (TLM) and the other group to a Dialogical Argumentation Instructional Model (DAIM) which was based on two argumentation frameworks– Toulmin’s Argumentation Pattern (TAP) and Contiguity Argumentation Theory (CAT).
Magister Educationis - MEd
2021-01-01T00:00:00ZMathematical modelling with simultaneous equations – An analysis of Grade 10 learners’ modelling competencies
http://hdl.handle.net/11394/7276
Mathematical modelling with simultaneous equations – An analysis of Grade 10 learners’ modelling competencies
Machingura, Dzivaidzo
Mathematical modelling is gaining extensive interest across the schooling sector worldwide, as it is deemed to develop learners with competencies set to deal with the demands of the fourth industrial revolution and being creative problem solvers. As mathematical modelling has only recently gained momentum across the mathematics curricula for schools in South Africa, many teachers may not be aware of the competencies that are needed to be developed in their learners through solving word problems, and even learners may not be aware of these essential modelling competencies. Hence, this mixed-methods approach study adopted a case-study design located within an interpretative paradigm to explore the levels of mathematical modelling competencies a sample of Grade 10 learners attending a Western Cape School demonstrated as they solved a set of word problems associated with the use of simultaneous equations. Additionally, data collected through observations and limited sets of semi-structured interviews were considered in the data analysis processes, which were largely driven by qualitative content analysis methods and supplemented with elementary descriptive statistical methods.
The findings of this study showed that most of the learners demonstrated non-competency in modelling mainly because of their inability to understand the problem as evident in their failure to comprehend the context of a problem, inability to recognise important quantities associated with a problem, and muddled relationships if any. The study conjecture that the use of the English language could have been a barrier to the sample of English second language speakers understanding the problem. However, a very limited number of students showed partial modelling competency, as they were only able to understand the problem and build a correct model to solve the problem. Regrettably, these students lacked the knowledge of the heuristics for solving a system of linear equations correctly and completely and did not check or verify their answers. The extremely small number of learners, who demonstrated sufficient modelling competency, demonstrated sufficient understanding of the problem, built and solved the system of simultaneous linear equations successfully without necessarily checking or testing whether their answers satisfied the conditions of the problem. Hence, this study recommends that adequate focus be given to the role of language in understanding a problem, heuristic competencies to solve a system of linear equations should be strengthened, and the habit of checking the reasonableness of the solution should be encouraged and developed continuously across problem-solving tasks. Studying learners’ modelling competencies requires further work to add to the repertoire of this knowledge domain.
Magister Educationis - MEd
2020-01-01T00:00:00ZThe impact of using technology through cooperative learning on learners’ performance on grade 11 circle geometry
http://hdl.handle.net/11394/7254
The impact of using technology through cooperative learning on learners’ performance on grade 11 circle geometry
Shonhiwa, William
Euclidean geometry was recently re-introduced as a compulsory topic in the Mathematics Curriculum for learners in the Further Education and Training (FET) band in 2012. The diagnostic analysis reports on the National Senior Certificate (NSC) Mathematics Paper 2 examinations since 2014 has repeatedly expressed concern of the poor performance of leaners in proof and reasoning items linked to circle geometry. Various efforts have been made to examine the composition of the curriculum to find ways of motivating learners in the study of circle geometry and enhancing their performance but not much has been realized. The use of technology or cooperative learning approaches for the teaching of geometry is beneficial for pedagogical purposes, particularly for improving learners’ performance in geometry. Hence, this study investigated the impact of using technology through cooperative learning on learners’ performance on grade circle 11 geometry. It was thus an attempt to focus on blending these two teaching methods with an emphasis on the use of technology. The research took place at a Khayelitsha school and the scope of technology was limited to using a mathematical computer programme called Heymath.
Magister Educationis - MEd
2020-01-01T00:00:00ZImplementing an intentional teaching model to investigate grade 9 learners’ ways of working with rational algebraic fractions
http://hdl.handle.net/11394/6943
Implementing an intentional teaching model to investigate grade 9 learners’ ways of working with rational algebraic fractions
Maphini, Nwabisa Vivian
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
2019-01-01T00:00:00Z