Euclidean Geometry is a challenging topic for most of the learners in the secondary schools. A qualitative case study explores the reasoning skills of ninth graders in the proving of congruent triangles in their natural environment. A class of thirty-two learners was conveniently selected to participate in the classroom observations. Two groups of six learners each were purposefully selected from the same class of thirty-two learners to participate in focus group interviews. The teaching documents were analysed. The Van Hiele’s levels of geometric thinking were used to reflect on the reasoning skills of the learners. The findings show that the majority of the learners operated at level 2 of Van Hiele’s geometric thinking. The use of visual aids in the teaching of geometry is important. About 30% of the learners were still operating at level 1 of Van Hiele theory. The analysed books showed that investigation help learners to discover the intended knowledge on their own. Learners need quality experience in order to move from a lower to a higher level of Van Hiele’s geometry thinking levels. The study brings about unique findings which may not be generalised. The results can only provide an insight into the reasoning skills of ninth graders in proving of congruent triangles. I recommend that future researchers should focus on proving of congruent triangles with a bigger sample of learners from different environmental settings. / Mathematics Education / M. Ed. (Mathematics Education)

Learners in South Africa underachieve in Mathematics. Amidst many other factors that influence the Mathematics scenario in South African schools, one major aspect of the Mathematics classroom culture is the Language of Learning and Teaching (LoLT). For many learners the LoLT, namely English, is not their main language. The question arises of whether Setswana learners with Limited English Proficiency (LEP) are disadvantaged because the LoLT is English and if so, what could be done about it. The interaction between language and thought is discussed against the background of the learning theories of Piaget, Vygotsky and van Hiele, as well as the Network Theory of Learning. From this study the importance of language for conceptualisation becomes clear, especially that of the mother tongue. The circle is then narrowed down to take a look at the vital part that language plays in Mathematics and the problems that exist for the learner when negotiating meaning during the journey between natural language and the mathematical register. Focusing on the situation of the Setswana Mathematics learner with English as LoLT, the views of parents and teachers come under scrutiny as well as government policies regarding the LoLT. The techniques and strategies of teachers in the English Second Language Mathematics classrooms (ESL-classrooms) are investigated. In this regard code-switching is of importance and is discussed extensively. These theoretical investigations led to an empirical study. Firstly, a quantitative study was undertaken by means of a survey to investigate the language situation in schools where Setswana is the main language. Furthermore, the views of those teachers, who teach Setswana learners with English as LoLT, on how English as LoLT influences Setswana Mathematics learners' conceptualisation were investigated. A sample of 218 teachers in the North-West Province of South Africa was used in this survey. A complex language situation crystallises where no one-dimensional answer can be recommended. Code-switching has clearly made large inroads into the Mathematics classroom, but teachers' views on the expediency of using Setswana, especially for formal notes, terminology and tests, vary considerably. Secondly, a qualitative study was undertaken in two schools. The study investigated the possibility that notes in Setswana as well as in English, and the aid of an English/Setswana glossary of Mathematical terminology in daily tasks as well as in tests, would be of value to learners. It was clear from the sample that the new terminology is difficult for the teachers in question because they are used to the English terminology. Some learners also find the Setswana terminology difficult. However, the learners experience the use of the Setswana in the notes positively. It was clear from the interviews with the learners that by far the most of the learners in the sample felt that the Setswana/English notes as well as the glossary helped them to understand better. The learners oscillate between English and Setswana to understand the explanation given or the question asked. Most of the learners are of opinion that tests where questions are asked in both languages contribute to a better comprehension of what is asked. They also experience the glossary of English/Setswana terminology supplied in the test as an important aid. Recommendations comprise that the Setswana Mathematics register should be expanded and final examinations set in both Setswana and English. Furthermore, teachers should be educated to use new terminology effectively as a scaffold to ensure adequate conceptualisation, as well as to manage code-switching in a structured way. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2005.

Learners in South Africa underachieve in Mathematics. Amidst many other factors that influence the Mathematics scenario in South African schools, one major aspect of the Mathematics classroom culture is the Language of Learning and Teaching (LoLT). For many learners the LoLT, namely English, is not their main language. The question arises of whether Setswana learners with Limited English Proficiency (LEP) are disadvantaged because the LoLT is English and if so, what could be done about it. The interaction between language and thought is discussed against the background of the learning theories of Piaget, Vygotsky and van Hiele, as well as the Network Theory of Learning. From this study the importance of language for conceptualisation becomes clear, especially that of the mother tongue. The circle is then narrowed down to take a look at the vital part that language plays in Mathematics and the problems that exist for the learner when negotiating meaning during the journey between natural language and the mathematical register. Focusing on the situation of the Setswana Mathematics learner with English as LoLT, the views of parents and teachers come under scrutiny as well as government policies regarding the LoLT. The techniques and strategies of teachers in the English Second Language Mathematics classrooms (ESL-classrooms) are investigated. In this regard code-switching is of importance and is discussed extensively. These theoretical investigations led to an empirical study. Firstly, a quantitative study was undertaken by means of a survey to investigate the language situation in schools where Setswana is the main language. Furthermore, the views of those teachers, who teach Setswana learners with English as LoLT, on how English as LoLT influences Setswana Mathematics learners' conceptualisation were investigated. A sample of 218 teachers in the North-West Province of South Africa was used in this survey. A complex language situation crystallises where no one-dimensional answer can be recommended. Code-switching has clearly made large inroads into the Mathematics classroom, but teachers' views on the expediency of using Setswana, especially for formal notes, terminology and tests, vary considerably. Secondly, a qualitative study was undertaken in two schools. The study investigated the possibility that notes in Setswana as well as in English, and the aid of an English/Setswana glossary of Mathematical terminology in daily tasks as well as in tests, would be of value to learners. It was clear from the sample that the new terminology is difficult for the teachers in question because they are used to the English terminology. Some learners also find the Setswana terminology difficult. However, the learners experience the use of the Setswana in the notes positively. It was clear from the interviews with the learners that by far the most of the learners in the sample felt that the Setswana/English notes as well as the glossary helped them to understand better. The learners oscillate between English and Setswana to understand the explanation given or the question asked. Most of the learners are of opinion that tests where questions are asked in both languages contribute to a better comprehension of what is asked. They also experience the glossary of English/Setswana terminology supplied in the test as an important aid. Recommendations comprise that the Setswana Mathematics register should be expanded and final examinations set in both Setswana and English. Furthermore, teachers should be educated to use new terminology effectively as a scaffold to ensure adequate conceptualisation, as well as to manage code-switching in a structured way. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2005.

The subject of teacher competencies or knowledge has been a key issue in mathematics education reform. This study attempts to identify and analyze teacher competencies necessary in the orchestration of a problem-centred approach to dynamic geometry teaching and learning. The advent of dynamic geometry environments into classrooms has placed new demands and expectations on mathematics teachers. In this study the Teacher Development Experiment was used as the main method of investigation. Twenty third-year mathematics major teachers participated in workshop and microteaching sessions involving the use of the Geometer's Sketchpad dynamic geometry software in the teaching and learning of the geometry of triangles and quadrilaterals. Five intersecting categories of teacher competencies were identified: mathematical/geometrical competencies. pedagogical competencies. computer and software competences, language and assessment competencies. / Mathematical Sciences / M. Ed. (Mathematical Education)

There are numerous problems associated with the teaching of Euclidean geometry at secondary schools today. Students do not see the necessity of proving results which have been obtained intuitively. They do not comprehend that the validity of a deduction is independent of the 'truth' of the initial assumptions. They do not realise that they cannot reason from diagrams, because these may be misleading or inaccurate. Most importantly, they do not understand that Euclidean geometry is a particular interpretation of physical space and that there are alternative, equally valid interpretations. A possible means of addressing the above problems is tbe introduction of nonEuclidean geometry at school level. It is imperative to identify those students who have the pre-requisite knowledge and skills. A number of interesting teaching strategies, such as debates, discussions, investigations, and oral and written presentations, can be used to introduce and develop the content matter. / Mathematics Education / M. Sc. (Mathematics)

The subject of teacher competences or knowledge has been a key issue in mathematics education reform. This study attempts to identify and analyze teacher competences necessary in the orchestration of a problem-centred approach to dynamic geometry teaching and learning. The advent of dynamic geometry environments into classrooms has placed new demands and expectations on mathematics teachers. In this study the Teacher Development Experiment was used as the main method of investigation. Twenty third-year mathematics major teachers participated in workshop and microteaching sessions involving the use of the Geometer’s Sketchpad dynamic geometry software in the teaching and learning of the geometry of triangles and quadrilaterals. Five intersecting categories of teacher competences were identified: mathematical/geometrical competences, pedagogical competences, computer and software competences, language and assessment competencies. / Mathematics Education / M. Ed. (Mathematics Education)

There are numerous problems associated with the teaching of Euclidean geometry at secondary schools today. Students do not see the necessity of proving results which have been obtained intuitively. They do not comprehend that the validity of a deduction is independent of the 'truth' of the initial assumptions. They do not realise that they cannot reason from diagrams, because these may be misleading or inaccurate. Most importantly, they do not understand that Euclidean geometry is a particular interpretation of physical space and that there are alternative, equally valid interpretations. A possible means of addressing the above problems is tbe introduction of nonEuclidean geometry at school level. It is imperative to identify those students who have the pre-requisite knowledge and skills. A number of interesting teaching strategies, such as debates, discussions, investigations, and oral and written presentations, can be used to introduce and develop the content matter. / Mathematics Education / M. Sc. (Mathematics)

No description available.

This study examined “problem solving skills in circle geometry concepts in Euclidean Geometry. This study was necessitated by learners’ inability to perform well with regards to Euclidean Geometry in general and Circle Geometry in particular. The use of naturalistic observation case study research (NOCSR) study was employed as the research design for the study. The intervention used for the study was the teaching of circle geometry with Polya problem solving instructional approach coupled with social constructivist instructional approach. A High School in the Northern Cape Province was used for the study. 61 mathematics learners (grade 11) in the school served as participants for the first year of the study, while 45 mathematics learners, also in grade 11, served as participants for the second year of the study. Data was collected for two consecutive years: 2018 and 2019. All learners who served as participants for the study did so willingly without been coerced in any way. Parental consent of all participants were also obtained. The following data were collected for each year of the research intervention: classroom teaching proceedings’ video recordings, photograph of learners class exercises (CE), field notes and the end-of-the- Intervention Test (EIT). Direct interpretations, categorical aggregation and a problem solving rubric were used for the analysis of data. Performance analysis and solution appraisal were also used to analyse some of the collected data. It emerged from the study that the research intervention evoked learners’ desire and interest to learn circle geometry. Also, the research intervention improved the study participants’ performance and problem solving skills in circle geometry concepts. Hence, it is recommended from this study that there is the need for South African schools to adopt the instructional approach for the intervention: Polya problem solving instructional approach coupled with social constructivist instructional approach, for the teaching and learning of Euclidean geometry concepts. / Mathematics Education / M. Sc. (Mathematics Education)

No description available.