The aims of this study were to investigate the effects of drama based instruction on seventh grade students&rsquo / achievement on geometry (angles and polygons / circle and cylinder), retention of achievement, van Hiele geometric thinking level, attitudes toward mathematics and attitudes toward geometry compared to the traditional teaching / to get the students&rsquo / views related to the effects of drama based instruction on their learning, friendship relations, awareness of themselves, and the role of teacher and students / and to get the view of teacher who was present in the classroom during the treatment on drama based instruction. The study was conducted on three seventh grade classes from a public school in the 2002-2003 academic year, lasting 30 lesson hours (seven and a half week). v The data were collected through angles and polygons / and circle and cylinder achievement tests, the van Hiele geometric thinking level test, mathematics and geometry attitude scale, and interviews. The quantitative analyses were carried out by using two multivariate covariance analyses. The results revealed that drama based instruction had a significant effect on students&rsquo / angles and polygons achievement, circle and cylinder achievement, retention of these achievement, van Hiele geometric thinking level, mathematics attitude, and geometry attitude compared to the traditional teaching. According to the interview responses of the experimental group students and the classroom teacher, significantly better performance of the experimental group students was attributable to the potential of the drama based instruction to make learning easy and understanding better by / supporting active involvement, creating collaborative studying environment, giving chance to improvise daily life examples, giving opportunity to communicate, providing meaningful learning, supporting long-lasting learning and providing selfawareness.

Summaries in Afrikaans and English / Outcomes-Based Education forms the foundation of South Africa's revised national education curriculum, known as The Revised National Curriculum Statement Grades R-9. The Van Hiele Model, developed for the teaching and learning of geometry, has already been used successfully in the school curricula of the Netherlands and Russia. Strong support for this theory exists in leading countries like America and Europe. This study has investigated the possible relationship between the Van Hiele theory and the "Revised National Curriculum Statement Grades R-9" and through critical evaluation found a great compatibility between them. Both are giving strong support for the spiral approach to mathematics education. It is recommended that all geometry learning programmes and teaching units be moulded on the Van Hiele Model. / Suid-Afrika se hersiene nasionale onderwyskurrikulum, die "Revised National Curriculum Statement Grades R-9" word deur uitkomsgebaseerde onderwys gefundeer. Die Van Hiele Model vir die onderrig en leer van meetkunde, is suksesvol in skoolkurrikula van Nederland en Rusland toegepas en geniet wye steun in lande soos Amerika en Europa. Hierdie navorsing het die moontlike verband tussen die Van Hiele raamwerk en die nuwe kurrikulum ondersoek en deur kritiese evaluering baie sterk versoenbaarheid tussen die "Revised National Curriculum Statement Grades R-9" en die Van Hiele Model gevind. Verder is ook aangetoon dat beide sterk gebruik maak van die spiraalbenadering in wiskundeonderwys. Aanbevelings in die verband is dat leerprogramme en onderrigeenhede wat die kurrikulum vir meetkunde in skole implementeer op die Van Hiele Model geskoei word. / Mathematical Sciences / M. Sc. (Mathematics Education)

This research originated from a question by a student of the night shift Elementary School for using mathematics to a plank floor. This led the research problem “as an educational approach to promote the concept of area in order to provide the student with the solution of problem solving of everyday life” We selected two classes (thirty students) for the sixth year of elementary school night, a public school in the city of Maceió, Alagoas. The research is an documentary literature and exploratory type. We chose didactical engineering as methodology. The subjects were selected through interviews and data collection by means of recorded audio file (LG GX 200) depositions/interviews of the subjects, recorded video file (Kodak EasyShare C180 digital camera 10.2 mp) productions the subjects throughout the process and tests Van Hiele – applied before, during and after the completion of the process of investigation. The theoretical approach adopted was Constructivism and Vygotsky’s theory of Van Hiele. Several researchers such as Nasser and Sant’anna, Lorenzato among others, agree that the development of geometric thinking is essential for the student to perform a reading of his daily life, viewing analytical and geometrical aspects in the search for solutions to problem situations. The workshops or the moments of experimentation (ME) – which comprise the didactical sequence (the educational product) – translate the actions perfomed in the classroom on topic-focus with dedication by the students and teacher, and the teaching to make analysis and/or adaptation in accordance with the reality of each school. / A presente pesquisa teve origem por meio de uma indagação de um aluno do turno noturno do Ensino Fundamental sobre a aplicação da Matemática para assoalhar um piso. Isto gerou o problema de pesquisa “como promover uma abordagem didática do conceito de área de modo a propiciar ao estudante a solução de situações-problema do seu cotidiano?”. Foram selecionadas duas turmas (trinta alunos) do sexto ano do Ensino Fundamental noturno, de uma escola pública do município de Maceió, em Alagoas. O tipo de pesquisa é de cunho documental, bibliográfica e exploratória. Decidimos por um recorte da engenharia didática como metodologia. A seleção dos sujeitos foi por meio de entrevista e a coleta dos dados por meio de gravações de arquivo de áudio (celular LG GX 200) de depoimentos/entrevistas dos sujeitos; gravações de arquivo de vídeo (câmera digital KODAK EasyShare C180 10.2 mp) das produções dos sujeitos ao longo do processo e testes de Van Hiele - aplicados antes, durante e depois da realização do processo investigatório. O aporte teórico adotado foi o Construtivismo de Vygotsky e a Teoria de Van Hiele. Vários pesquisadores tais como Nasser e Sant’anna, Lorenzato entre outros, concordam que o desenvolvimento do pensamento geométrico é fundamental para que o aluno realize uma leitura de seu cotidiano, visualizando aspectos analíticos e geométricos na busca de soluções de situações-problema. As Oficinas de aprendizagem ou os momentos de experimentação (ME) - que compõem a sequência didática (o produto educacional) – traduzem as ações realizadas em sala de aula sobre a temática-foco com dedicação por parte dos alunos e professor, e o fazer pedagógico para análise e/ou adaptação de acordo com a realidade de cada unidade escolar.

This text discusses final results from empirical studies, scientific articles and literature from the period 1990-2023, concerning teachers’ knowledge, students’ misconceptions and various teaching methods related to geometric objects. The results highlight challenges for both teachers and students in understanding and defining geometric shapes and figures. The work elucidates students in grade 4-6 difficulties and knowledge in identifying geometric objects in varied positions, as well as their understanding of the properties of geometric shapes and figures. The teacher’s understanding is crucial för imparting accurate information to students in instruction. Therefore, effective teaching methods such as practical activities, everyday connection and Van Hiele’s instructional model are suitable to apply in practice. This instructional model has been effective in students education and is therefore a good example for a teaching method.  In summary, the results are based on the abilities of teachers and students and their abilities can be enhanced by adapting teaching methods related to geometric objects, and how misconceptions are something that should be taken seriously and be prevented.

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)