M.Ed. / Please refer to full text to view abstract

The goal of this research study was to provide psycho-educational guidelines that will facilitate synergy between the stakeholders involved with the teaching and learning of mathematics at a school. The stakeholders in this research study are members of the management team, the educators and the learners. Synergy simply defined means that the whole is greater than the sum of its parts. Covey (in Moore, 2003:1) states that synergy is the fruit of mutual respect, of understanding and valuing the differences in one another as well as different approaches to problem solving. I believe that when one creates an environment that is more open, more trusting, less judgemental, more loving and more caring in the classroom synergy will occur. This environment will produce learning outcomes beyond expectation. In other words, when the members of the groups of stakeholders at a school participate synergistically the results that are produced and outcomes that are achieved will be much higher then the total results of the inputs of their individual efforts. It is evident from the description, evaluation and interpretation of the collected data that learners and educators do not experience their interactions as situations where their potential is acknowledged and improved. Once again: if there is no effective interaction and appreciative understanding between the different stakeholders, successful integration cannot take place. There is almost no indication of any collaboration between the participants in the teaching and learning situation. In fact, the analysis of the data show that educators and learners experience the teaching and learning process as a process of disempowerment, which is Theme One of the analysed data. Almost all the sub-categories under Theme One provide evidence that the input of the different role players in the teaching and learning environment is not considered. These categories are: • learners experience that they have to do activities without the necessary pre-knowledge; • learners experience the teaching and learning of Mathematics as a process of victimization; • learners experience that educators ignore their learning needs; • learners experience inadequate communication and inappropriate guidance in the classroom; • educators portray an uncaring attitude; • learners do not portray a positive attitude towards the teaching and learning of mathematics; • educators do not experience job satisfaction; and • educators do not experience support from the parents. However, all the stakeholders that participated in this research study made recommendations that could contribute to a constructive teaching and learning climate. These recommendations were: • educators should play a supportive role; • learners and educators must be motivated; • learners should participate in the teaching and learning situation; o educators should implement new teaching strategies; o educators and learners should value co-operative learning and group work; and • team work between educators and learners should be enhanced; These recommendations indicate that the stakeholders would like the teaching and learning situation to become more constructive and meaningful through active participation. These are essential ingredients for synergy to take place. Educators and learners also indicated that they experience frustrations due to the socio-economic situation of the learners that impact negatively on the teaching and learning of mathematics and contribute to disempowerment of these stakeholders. It seems therefore that the community as well as the parents of these learners are stakeholders that should be considered when the guidelines are formulated. I experienced this research study as an eye-opener with regard to the development of the teaching and learning process into a constructive and meaningful activity. I realised that for sustainable development it is essential to develop all the stakeholders and not only the educators. / Prof. C.P.H. Myburgh

M.Ed. / Please refer to full text to view abstract

This qualitative study reports on critical reflective teaching by three mathematics teachers and how it shapes their classroom practice. The study was carried out in three secondary schools in Rundu in northern Namibia. The study employed a case study method. The selection of teachers was based on their rich practical professional knowledge and exemplary teaching practices. Data collection and analysis was done through an interpretive approach. Interviews and document analyses were the two research tools used, not only for the collection of data but for triangulation also. Interpretations of the findings were validated through member checking. Critical reflective teaching involves thought and action, and it raises teachers’ consciousness of what they do. Through critical reflective practice, teachers scrutinize their beliefs and knowledge of the subject and their practice. Furthermore critical reflective practice may get teachers into a disposition to find alternatives to improve their teaching. In this study, the findings are that participants reflect extensively on their classroom practice. The teachers pointed out that reflection on practice enables them to analyse and evaluate their teaching in line with effective mathematics teaching. They emphasised that critical reflection leads to the identification of weaknesses in teachers’ classroom practice. This culminates in better planning whereby alternative approaches to teaching are exercised. Because of its potential to improve teaching and enhance professional development it is therefore recommended that mathematics teachers be exposed to skills that enhance critical reflective teaching practice. Teachers need to familiarise themselves with the concept of critical reflective teaching in mathematics to meet the demands of superior quality teaching.

Visualisation in general and visualisation processes in particular have received much attention in the mathematics education research literature. Literature suggests that the appropriate use of visualisation helps learners to develop their conceptual understanding and skills of geometry as it allows them to visually interpret and understand fundamental mathematical and geometrical concepts. It is claimed that visual tools play an important role in communicating mathematical ideas through diagrams, gestures, images, sketches or drawings. Learning mathematics through visualisation can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. This interpretive case study focused on how selected teachers taught concepts in geometry through visualisation processes for conceptual understanding as a result of an intervention programme. The study was conducted at four high schools by four mathematics teachers in the Kavango East Region in Northern Namibia. The participants were involved in a three-week intervention programme and afterwards taught three lessons each on the topic of geometry. The data collection method of this research was: focus group and stimulus recall interviews, classroom observations and recorded videos. This research is located in constructivism. I used vertical and horizontal analysis strategies to analyse the data. My analytical instrument consisted of an observation schedule which I used in each lesson to identify how each of the visualisation processes was evident in each of the observed lessons. This study revealed that the participant teachers used visualisation processes in most of their lessons and these processes were used accurately in line with the requirements of the grade 8 mathematics syllabi. The visualisation processes were used through designed visual materials, posters and through the use of geometrical objects such as chalkboard ruler, protractor and compass. The results from this study also confirmed that visualisation processes can be a powerful instructional tool for enhancing learners’ conceptual understanding of geometry.

M.Ed. (Mathematics) / The rising of the problem whether competency based education (CBE) programs produce better results than conventional edu - cational report. methods has been investigated and discussed in this A comprehensive literature study indicated that the upholders of the CBE program advocated beter results than the conventional educational methods. Research showed positive results. An empirical research on the micro-level was launched to de - termine whether this was the case or not. The procedure was to use a group N1-students, at a technical college of the Department of Education and Training, who were not familiar with the N1-Mathematics syllabus. An experimental group as well as a control group was selected at random. The experimental group was subjected to the CBEmethod and the control group to the conventional method of teaching of N-Mathematics. Prior to the research both groups were subjected to a standard N1-Mathematics test without preparation. These results were used for the pretest. The national N1-Mathematics examination was used for the post test, after completion of the course. The pretest results were compared to determine whether there was a significant difference in the level of the foreknowledge of the two groups...

M.Ed. (Computer-Based Education) / Please refer to full text to view abstract

M.Ed. (ICT in Education) / Information and Communication Technology has made its way into almost all fields of human interactions. The leading field, where ICT is most commonly practiced, is that of business and industry. In contrast, Mostert and Nthetha (2008) assert that the in the field of education, ICT is used minimally and mainly for administrative purposes. At present, the use of ICT is not common in the mathematics classroom and can be attributed to initial teacher training programmes that did not include the integration of ICTs into the curriculum until more recently. Pre-service student teachers, who have been exposed to ICT modules in preparation for using it in their practice, thus stand a better chance to utilise ICT resources because of their previous exposure. This dissertation aims to identify current pre-service mathematics student teachers acceptance of ICT`s in their classroom. The focus will be on mathematics teaching and learning as this is one of the subjects in which learners perform below expectation in the South African context. The positive contribution of ICT in the mathematics classroom firstly relies on the individual teacher’s belief in the effectiveness of ICT and secondly on the teacher’s competence to utilise ICT tools and services. An imbalance in the equation will ultimately influence a teacher’s perception on ICT integration for pedagogy. Teachers, who have ICT competency skills but do not believe in its effectiveness, are bound to reject its integration in as much as teachers who believe in ICT but lack competency in using ICT resources. Therefore, teachers need to have a positive attitude and the technical knowhow on how to successfully integrate ICT in their teaching and learning of mathematics. This is the theoretical framework that underpins ICT integration in education ...

M.Ed. (Mathematics in Education) / In spite of the efforts of the South African government, the Gauteng Department of Education and many business and private funders to place a high emphasis on mathematics performance, the mathematics achievement of South African learners is still less than desirable. In fact, the results of the three Third International Mathematics and Science Study (TIMSS) (Howie, 2001, 2003) reports in 1995, 1999 and 2003 reported South African learners as the lowest performing in those tests; performing well below the international average amongst the countries that participated. The Southern African Consortium for Monitoring Quality 2004 and Center for Development in Education 2004, 2010 and 2011 reports results show similar results (Moloi, 2005). The research study sought to get a deep understanding of why learners1 continue to perform poorly, and what the factors are which contribute to poor performance. While there are a number of factors responsible for the poor performance, one of the least researched areas is answered examination scripts. This research entailed a detailed error analysis of four items of the 2008 mathematics paper 1 senior certificate examination scripts, to see the trends and patterns of written responses with regards to the types of errors made by learners. The study was aimed at investigating South African Grade 12 learners‘ errors exhibited when solving quadratic equations, quadratic inequalities and simultaneous equations. Findings of this investigation shed light of the kind of knowledge learners bring into their learning experiences and this knowledge affects how they encode and later retrieve new information learned (Davis, 1984). While the study was not a mixed methods one, the data was analysed quantitatively using frequency counts and qualitatively by studying selected learners‘ solution of examination tasks. The study also identified common errors in the learners‘ work. The four items analysed in the study comprised of questions from three important areas of algebra namely: quadratic equations, quadratic inequalities and simultaneous equations. The scripts were analysed for carelessness, conceptual and procedural errors. The learner misconceptions were discovered in learners‘ work; v these comprised the notions of equality and inequality, the construct of the variable, order of operations, factorisation, and solution of equations instead of inequalities. From this, the researcher noted that learners' learning difficulties are usually presented in the form of errors they show. Not all the errors that learners had are the same; some errors in procedures can simply be due to learners' carelessness or overloading working memory (Davis, 1984). Some errors in procedures can be caused by faulty algorithms or "buggy algorithms". Other errors can have certain conceptual basis and can be termed as ‗misconceptions‘. The results obtained indicated a number of error categories under each conceptual area, namely, quadratic equations and inequalities and simultaneous equations. Some errors emanated from misconceptions. Under the conceptual areas indicated above, the main reason for misconceptions seemed to be the lack of understanding of the basic concepts including numbers and numerical operations; functions; the order of operations; equality; algebraic symbolism; algebraic equations, expressions and inequalities; and difference between equations, expressions and inequalities. The abstract nature of algebraic expressions posed many problems to learners such as understanding or manipulating them according to accepted rules, procedures, or algorithms. Inadequate understanding of the uses of the equal sign and its properties when it is used in an equation was a major problem that hindered learners from solving equations correctly. The main difficulty in inequalities was manipulating the inequalities correctly and converting the inequality to an equation. Recommendations to the mathematics educational community based on this research were made.

Ph.D. / The purpose of this study was to investigate the ways in which Social Network Analysis can be used to enhance the conitinuous professional development of the Mathematics teachers of a secondary school. With this in mind a literature study was first undertaken in order to clarify exactly what is meant by a Social Network Analysis perspective, online social networks and the continuous professional development of teachers. The study was framed in a Multi Method Mixed Methods framework to enable the integration of a Design Based (DBR) study and Social Network Analysis (SNA) in different phases of the overarching research. The purpose of the DBR study was to design and develop an online social network to provide the Mathematics teachers of sufficient opportunities for continuous professional development. The assumtion was made that the online social network will develop into a Learn 2.0 technology if a) it could provide access to appropriate content, b) teachers could use it to develop own professional development opportunities, c) it could provide opportunities for collaboration between the teachers and d) if it could provide opportunities to connect with those teachers who could contribute their Professional Development. This study refers to the ties which were used to enable the flow of information, knowledge, advice, leadership, support, experience and concrete artefacts (documents) as a teachers’ Personal Development Network. From a SNA perspective the personal development networks of the teachers cannot be fully understood without studying the social network in which these ties are embedded. I refer to this network as the Development Network. The development network is at any given point a stable social construct, but it changes as soon as new ties vii are formed or old ties disintegrate. Therefore a Social Network Analysis was done before, during and after the intervention to explore the development network to understand, explain and predict the effectiveness of CPTD. The findings show that DPO.com (the online social network) provided the teachers of sufficient CPTD opportunities and developed during the course of the study into a Learn 2.0 technology. It also shows that SNA provides an effective method to understand and predict the CPTD of the Mathematics teachers.