Department of Mathematics Educationhttp://hdl.handle.net/10500/64242015-11-28T11:21:16Z2015-11-28T11:21:16ZAssessing the algebraic problem solving skills of Grade 12 learners in Oshana Region, NamibiaLupahla, Nhlanhlahttp://hdl.handle.net/10500/192252015-10-19T01:09:25Z2014-06-01T00:00:00ZAssessing the algebraic problem solving skills of Grade 12 learners in Oshana Region, Namibia
Lupahla, Nhlanhla
This study used Polya’s problem-solving model to map the level of development of the algebraic problem solving skills of Grade 12 learners from the Oshana Region in Northern Namibia. Deficiencies in problem solving skills among students in Namibian tertiary institutions have highlighted a possible knowledge gap between the Grade 12 and tertiary mathematics curricula (Fatokun, Hugo & Ajibola, 2009; Miranda, 2010). It is against this background that this study investigated the problem solving skills of Grade 12 learners in an attempt to understand the difficulties encountered by the Grade 12 learners in the problem solving process. Although there has been a great deal of effort made to improve student problem solving throughout the educational system, there is no standard way of evaluating written problem solving that is valid, reliable and easy to use (Docktor & Heller, 2009).
The study designed and employed a computer aided algebraic problem solving assessment (CAAPSA) tool to map the algebraic problem solving skills of a sample of 210 Grade 12 learners during the 2010 academic year. The assessment framework of the learners’ problem solving skills was based on the Trends in International Mathematics and Science Study (TIMSS), Schoenfeld’s (1992) theory of metacognition and Polya’s (1957) problem solving model. The study followed a mixed methods triangulation design, in which both quantitative and qualitative data were collected and analysed simultaneously. The data collection instruments involved a knowledge base diagnostic test, an algebraic problem solving achievement test, an item analysis matrix for evaluating alignment of examination content to curriculum assessment objectives, a purposively selected sample of learners’ solution snippets, learner questionnaire and task-based learner interviews.
The study found that 83.8% of the learners were at or below TIMSS level 2 (low) of algebraic problem solving skills. There was a moderate correlation between the achievement in the knowledge base and algebraic problem solving test (Pearson r = 0.5). There was however a high correlation between the learners’ achievement in the algebraic problem solving test and achievement in the final Namibia Senior Secondary Certificate (NSSC) examination of 2010 (Pearson r = 0.7). Most learners encountered difficulties in Polya’s first step, which focuses on the reading and understanding of the problem. The algebraic strategy was the most successfully employed solution strategy.
2014-06-01T00:00:00ZThe impact of constructivist-based teaching method on secondary school lerners' errors in algebraOwusu, Jameshttp://hdl.handle.net/10500/192072015-10-23T10:31:12Z2015-02-01T00:00:00ZThe impact of constructivist-based teaching method on secondary school lerners' errors in algebra
Owusu, James
The aim of this study was to investigate the comparative effects of Constructivist-Based Teaching Method (CBTM) and the Traditional Teaching Method (TTM) on Grade 11 Mathematics learners’ errors in algebra. The constructivist learning theory (CLT) was used to frame this study. Mainly, CLT was used to influence the design of CBTI to hone participants’ errors in algebra that militate against their performance in Mathematics. The study was conducted in the Mpumalanga Province of South Africa with a four-week intervention programme in each of the two participating secondary schools. Participants consisted of n=78 Grade 11 Mathematics learners and one Grade 11 Mathematics teacher. A non-equivalent control group design consisting of a pre-test and post-test measure was employed. The Grade 11 teacher in the control school employed the TTM while the researcher implemented CBTM in the experimental school.
The main aspects of CBTM entailed participants’ construction of their own knowledge from the base of prior knowledge and through group learning approach and exploratory talk in which discussions included argumentation, verbalising explanations, justifications and reflections. Participants in experimental school became familiar with the basic principles of CBTI such as group work, which enhanced the construction of conceptual understanding of algebraic concepts. This reduced most of the errors they commit in algebra and elevated their performance in Mathematics. The principal instruments for data collection consisted of a standardised Algebra Concept Achievement Test and lesson observations.
The pre-test was used to determine participants’ initial errors in algebra before the intervention. A post-test was given at the end of intervention to ascertain change in participants’ errors in algebra over a four-week intervention period. Using descriptive and inferential statistical techniques, the study found that participants in experimental school significantly reduced their errors in algebra than those in control school. The study showed that CBTM was a more effective pedagogy that improved the errors Grade 11 learners commit in algebra than the TTM.
2015-02-01T00:00:00ZAn evaluation of a mathematics professional teacher development programmeNel, Benita Portiahttp://hdl.handle.net/10500/190482015-10-13T11:12:54Z2015-06-01T00:00:00ZAn evaluation of a mathematics professional teacher development programme
Nel, Benita Portia
Although South African teachers have ample opportunities for professional development (PD), weak results of learners show that these opportunities have had a limited effect on the development of the Mathematics teachers’ instructional skills. The improvement of the teaching of Mathematics is regarded as a solution to learners’ poor performance, because teachers play a key role in the improvement of pupils’ learning. In the light of this, a Mathematics PD programme implemented in a province of South Africa was evaluated and served as a case study. The aim of this evaluation was to probe the quality of the programme since it had been suggested that improving the quality of teaching can be achieved by offering effective PD programmes. Thus, the evaluation was done in an attempt to establish the academic value of the intervention. The investigated programme – which was implemented in a rural and under-resourced setting – focused on FET Mathematics teachers and used mentoring and workshops as its key intervention implementers. Five teachers were involved in this programme. Data collection methods included semi-structured interviews, lesson observations, mentoring and workshop reports, the results of learners, and pre- and post-test results of the participants. The evaluation of the PD programme revealed the following: that the workshops addressed the participants’ content knowledge gap to a limited degree; that mentoring was able to assist with the individual classroom-related needs of the participants, and that the community of practice formed in the workshops helped the participants to develop by means of working together on lesson preparation, micro-teaching, and content knowledge exercises. Other findings revealed that the duration of the workshops were adequate, however their intensity was insufficient to effectively address the participants’ needs, and that the workshops were carefully planned, given that the same topics were repeated. The mentor teachers and other facilitators encountered challenges relating to the long intervals between the mentoring sessions, the limited post-lesson-observation discussion time, the significant distances between the involved schools and the heavy teaching load of the participants. Nevertheless, recommendations on improving the effectiveness of future PD programmes included careful selection of the dosage of interventions, site-based mentoring, to incentivise participants of PD programmes, alleviating the teaching load of overburdened participants and the creation of conducive environments in rural areas for the formation of communities of practice.
2015-06-01T00:00:00ZThe effect of using a computer assisted instruction on teaching circle geometry in grade 11Gweshe, Lovejoy Comforthttp://hdl.handle.net/10500/190052015-10-13T11:12:51Z2014-12-01T00:00:00ZThe effect of using a computer assisted instruction on teaching circle geometry in grade 11
Gweshe, Lovejoy Comfort
South African learners continue to perform poorly in high school Circle Geometry. Lack of learner confidence and motivation in Mathematics may be the contributing factors to the low success rate in Circle Geometry. These factors, coupled with Conventional Teaching Instructions (CTI), may have contributed to the significant reduction in the number of learners enrolled for Mathematics, and provided a rationale for the study that explored a possible alternative teaching pedagogy to motivate and eventually improve learner performance in Circle Geometry. The study aimed to investigate the comparative effects of Computer Assisted Instruction (CAI) and CTI on the performance and motivation of Grade 11 learners in the topic of Circle Geometry. The population of the study consisted of Grade 11 Mathematics learners from 65 secondary schools in the Ekurhuleni North District of Gauteng province in South Africa. Using convenience sampling techniques two schools with n=136 Grade 11 Mathematics learners and two teachers participated in the study. One school formed the experimental group (n=71) and the other school formed the control group (n=65).
The study followed a quasi-experimental design with a non-equivalent control group approach consisting of pre-and post-test measures. Intact classes participated in the study as it was not possible to randomly select participants for the study. Both groups wrote a standardised achievement pre-test to ascertain their performance status at the beginning of the study. CAI was implemented in the experimental school while CTI was implemented in the control school. A similar post-test was administered on both groups to measure the comparative effects of each teaching method on the performance of learners. A questionnaire was also administered to both groups to measure the motivation of learners. A purposive sample (n=12) was selected from both groups to participate in semi-structured interviews to account for the results of the test and the questionnaire. A socio-constructivist theory framed the study. Analysis of Covariance (ANCOVA) was used to analyse data. The results of this investigation indicated that the use of the computer software, GeoGebra, in the teaching and learning of Circle Geometry improved the performance and motivation of Grade 11 learners.
2014-12-01T00:00:00Z