Theses and Dissertations (Mathematics Education)http://hdl.handle.net/10500/64402014-08-29T22:52:12Z2014-08-29T22:52:12ZA 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.
2013-06-01T00:00:00ZImplementing the National curriculum statement : how is instructional capacity in the teaching and learning of mathematics constructed, organised and replenished in secondary schools?Chiconga, Benardhttp://hdl.handle.net/10500/131002014-04-23T15:18:23Z2013-05-01T00:00:00ZImplementing the National curriculum statement : how is instructional capacity in the teaching and learning of mathematics constructed, organised and replenished in secondary schools?
Chiconga, Benard
A study was undertaken to explore what constitutes instructional capacity in the teaching and learning of mathematics (TLM), with a focus on how schools (as institutions of teaching and learning) integrate resources for a particular configuration of capacity to promote high achievement levels of Grade 12 students in mathematics. Data were collected in ten public secondary schools, mostly in a disadvantaged context, in the Vhembe District in Limpopo Province, South Africa. The study explores strategies for constructing, organising and replenishing instructional capacity in TLM. Five low- and five high-performing schools were selected, based on the pass rate in mathematics in high stakes examinations. The researcher observed lessons and interviewed ten Grade 12 mathematics teachers, ten principals, five curriculum advisors and a sample of forty Grade 12 mathematics students.
The research revealed that the capacity to encourage the new curriculum reform practices in TLM within different schools is often inadequate, and largely fails to compensate for organisational effects and arrangements that shape the capacity to create quality instruction in mathematics. However, high-performing schools were somewhat ahead of low-performing schools in terms of encouraging reform-oriented teaching and learning in mathematics. Recommendations include:
Principals should initiate the development and implementation of a school-based clinical supervision programme through collaborative decision-making to promote a sense of ownership by all mathematics teachers. Such a supervision programme would enhance commitment and ensure that all efforts are unified towards improving the quality of TLM.
There is a need for the DoE in Limpopo Province to coordinate teacher professional development workshops, where effective practising mathematics teachers model how they teach mathematics in the classroom, while other teachers observe.
Context-based strategies to enhance student outcomes in mathematics should be devised, such as modelling good practice by effective teachers in terms of: lesson preparation; subject knowledge; pedagogic approach; assessment and monitoring of classroom practice, including direct observation of teaching by HoDs and principals. It is proposed that attention to these issues, amongst others, would limit the impact of an unpromising context on student achievement levels in mathematics in high stakes examinations in the Vhembe District and elsewhere.
2013-05-01T00:00:00ZThe development of mathematical problem solving skills of Grade 8 learners in a problem-centered teaching and learning environment at a secondary school in GautengChirinda, Brantinahttp://hdl.handle.net/10500/118762014-04-23T19:09:37Z2013-06-01T00:00:00ZThe development of mathematical problem solving skills of Grade 8 learners in a problem-centered teaching and learning environment at a secondary school in Gauteng
Chirinda, Brantina
This mixed methods research design, which was modelled on the
constructivist view of schooling, sets out to investigate the effect of developing
mathematical problem solving skills of grade 8 learners on their performance
and achievement in mathematics. To develop the mathematical problem
solving skills of the experimental group, a problem-centred teaching and
learning environment was created in which problem posing and solving were
the key didactic mathematical activity. The effect of the intervention
programme on the experimental group was compared with the control group
by assessing learners’ problem solving processes, mathematical problem
solving skills, reasoning and cognitive processes, performance and
achievement in mathematics. Data were obtained through questionnaires, a
mathematical problem solving skills inventory, direct participant observation
and questioning, semi-structured interviews, learner journals, mathematical
tasks, written work, pre- and post- multiple-choice and word-problem tests.
Data analysis was largely done through descriptive analysis and the findings
assisted the researcher to make recommendations and suggest areas that
could require possible further research.
2013-06-01T00:00:00Z