Theses and Dissertations (Mathematics Education)http://hdl.handle.net/10500/64402015-03-31T13:19:15Z2015-03-31T13:19:15ZRelationship between learners' mathematics-related belief systems and their approaches to non-routine mathematical problem solving : a case study of three high schools in Tshwane North district (D3), South AfricaChirove, Munyaradzihttp://hdl.handle.net/10500/184132015-03-26T08:46:54Z2014-06-01T00:00:00ZRelationship between learners' mathematics-related belief systems and their approaches to non-routine mathematical problem solving : a case study of three high schools in Tshwane North district (D3), South Africa
Chirove, Munyaradzi
The purpose of this study was to determine the relationship between High School learners‟ mathematics-related belief systems and their approaches to mathematics non-routine problem-solving. A mixed methods approach was employed in the study. Survey questionnaires, mathematics problem solving test and interview schedules were the basic instruments used for data collection.
The data was presented in form of tables, diagrams, figures, direct and indirect quotes of participants‟ responses and descriptions of learners‟ mathematics related belief systems and their approaches to mathematics problem solving. The basic methods used to analyze the data were thematic analysis (coding, organizing data into descriptive themes, and noting relations between variables), cluster analysis, factor analysis, regression analysis and methodological triangulation.
Learners‟ mathematics-related beliefs were grouped into three Learners‟ mathematics-related beliefs were grouped into three categories, according to Daskalogianni and Simpson (2001a)‟s macro-belief systems: utilitarian, systematic and exploratory. A number of learners‟ problem solving strategies were identified, that include unsystematic guess, check and revise; systematic guess, check and revise; trial-and-error; logical reasoning; non-logical reasoning; systematic listing; looking for a pattern; making a model; considering a simple case; using a formula; numeric approach; piece-wise and holistic approaches. A weak positive linear relationship between learners‟ mathematics-related belief systems and their approaches to non-routine problem solving was discovered. It was, also, discovered that learners‟ mathematics-related belief systems could explain their approach to non-routine mathematics problem solving (and vice versa).
2014-06-01T00:00:00ZAn investigation into the factors impacting on the selection and adoption of constructivist teaching methods by mathematics teachers in selected Gauteng urban schoolsMoyo, Innocenthttp://hdl.handle.net/10500/141942014-10-30T09:35:14Z2014-05-01T00:00:00ZAn investigation into the factors impacting on the selection and adoption of constructivist teaching methods by mathematics teachers in selected Gauteng urban schools
Moyo, Innocent
Constructivist teaching strategies are undeniably accepted as effective in achieving the desired
educational goals of constructing knowledge through active and creative inquiry. Inasmuch as
teachers would love to adopt these strategies in their teaching, mathematics teachers find themselves
in a situation where they are forced not to use them. This study investigated the factors that impacted
on the selection and adoption of constructivist teaching strategies in selected Gauteng’s urban schools.
Four (4) public schools and sixteen (16) mathematics teachers participated in the study. The parallel
mixed methods design was employed in the study to produce both quantitative and qualitative data.
The data were therefore analysed both quantitatively and qualitatively. It was found that the
participating mathematics teachers had an understanding of constructivist theories of teaching and that
they perceived their classroom environments to be constructivist in character. The study also found
that the adoption of constructivist teaching strategies was hindered by teachers’ lack of skills and
competencies to handle a curriculum that they felt was handed down to them without their full
involvement at all the stages of its development. Learners’ family backgrounds were also identified as
a major social factor that impacted negatively against selection of constructivist strategies. Based on
these findings, recommendations were made on how constructivist views can be realised in the
teaching of mathematics in South African schools.
2014-05-01T00:00:00ZA framework for the development of pedagogical content knowledge for secondary school statistics teachersMakina, Antoniahttp://hdl.handle.net/10500/138512014-08-23T22:01:38Z2013-11-01T00:00:00ZA framework for the development of pedagogical content knowledge for secondary school statistics teachers
Makina, Antonia
The study developed and designed a pedagogical content knowledge framework to guide and support the professional development of pedagogical content knowledge to about 130 statistics teachers. It captured the experiences of teachers during the development of pedagogical content knowledge, to come up with the main themes that describe pedagogical content knowledge as the relevant knowledge for teaching Grade 11 and 12 statistics.
The study was overall qualitative in nature and supported by some quantitative data. Questionnaires, in-class facilitated tasks/activities, in-class facilitated discussions and observations were used as the main data collection instruments. This process revealed some significant themes, described as “missed opportunities”, which were defined as incidents in which pedagogical content knowledge was needed but not used. The thesis contributes to the theoretical and knowledge base of secondary school statistics teachers in the education system by providing measures that can be used to determine professional development needs of teachers.
2013-11-01T00:00:00ZExploring solution strategies that can enhance the achievement of low-performing grade 12 learners in some mathematical aspectsMachisi, Erichttp://hdl.handle.net/10500/132442014-04-23T15:18:09Z2013-06-01T00:00:00ZExploring solution strategies that can enhance the achievement of low-performing grade 12 learners in some mathematical aspects
Machisi, Eric
The purpose of this study was to explore solution strategies that can enhance the achievement of low-performing Grade 12 learners in the following mathematical aspects: finding the general term of a quadratic sequence, factorising third degree polynomials, determining the centre and radius of a circle, and calculating the angle between two lines. A convenience sample of twenty-five low-performing Grade 12 learners from a secondary school in Capricorn District of Limpopo Province participated in the study which adopted a repeated-measures research design. Learners were exposed to multiple solution strategies and data were collected using achievement tests. Findings indicated significant differences in learners‟ average scores due to the solution strategies used. In determining the general term of a quadratic sequence, learners‟ scores were significantly higher when they used formula and the table method than with the method of residues and solving simultaneous equations. Synthetic division made learners to achieve better scores than long division and equating coefficients in factorising third degree polynomials. The use of formulae to find the centre and radius of a circle made learners to have better achievement scores than completing the square. In calculating the angle between two lines learners‟ scores were better using formula and the cosine rule than using theorems. It was concluded that exposing low-performing Grade 12 learners to multiple solution strategies would enhance their achievement in the mathematical aspects explored in the study. Some of the solution strategies that made learners to achieve better results were not in the prescribed mathematics textbooks. The study therefore recommends that mathematics teaching should not be textbook-driven and that low-performing Grade 12 learners should not be regarded as beyond redemption.
2013-06-01T00:00:00Z