Traditionally, geometry at school starts on a formal level, largely ignoring prerequisite skills needed for formal spatial reasoning. Ignoring that geometry conceptualisation has a sequential and hierarchical nature, causes ineffective teaching and learning with a long lasting inhibiting influence on spatial development and learning. One of the current reform movements in mathematics education is the appropriate use of dynamic computer technology in the teaching and learning of mathematics. Concerning mathematics education, the lecturers may involve the introduction of both dynamic computer technology and mathematics in meaningful contexts that will enable interplay between the two. Pre-service mathematics teachers (PMTs) can be encouraged to become actively involved in their learning and, therefore, less frustrated in their study orientation in mathematics. Therefore, such learning environments may be essential to enhance the conceptual understanding of PMTs. To be able to reach their eventual learners, PMTs' own conceptual understanding of geometry should be well developed. When PMTs have conceptual understanding of a mathematical procedure, they will perceive this procedure as a mathematical model of a problem situation, rather than just an algorithm. This study aimed at investigating the effect of a technologically enhanced learning environment on PMTs' understanding of geometry concepts and their study orientation in mathematics, as prerequisite for deep conceptualisation. A combined quantitative and qualitative research approach was used. The quantitative investigation employed a pre-experimental one-group pre-test post-test design. A Mayberry-type test was used to collect data with regard to PMTs' conceptualisation of geometry concepts, while the Study Orientation in Mathematics (SOM) questionnaire was used to collect data with regard their study orientation in mathematics. The qualitative investigation employed phenomenological interviews to collect supplementary information about the participating PMTs' experiences and assessment of the influence of the use of the dynamic software Geometer's Sketchpad (GSP) on their learning and conceptualisation of geometry concepts. During post-testing the participating group of PMTs achieved practically significantly higher scores in the Mayberry-type test, as well as in all fields of the SOM questionnaire. Results seem to indicate that PMTs gained significantly in the expected high levels of conceptualisation, as well as high degrees of acquisition of those levels during the intervention programme. The main conclusion of the study is that a technologically enhanced learning environment (such as GSP) can be successfully utilised to significantly enhance PMTs' conceptualisation and study orientation, as prerequisite for deep conceptualisation, in geometry. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006

Cette recherche se propose de tester en CM2 et en 6ème un nouveau cadre théorique construit à partir d'une part de la théorie des paradigmes géométriques et de la théorie des niveaux de van Hiele. La géométrie à l'école primaire est essentiellement une géométrie spatio-graphique (G1) où les objets sont les représentants d'objets physiques et les validations perceptives. Le niveau de van Hiele que l'élève doit maîtriser à la fin du CM2 est celui de l'identification-visualisation (N1). La géométrie au collège vise à être une géométrie proto-axiomatique (G2) où les objets sont théoriques et les validations de type hypothético-déductif. L'élève doit alors maîtriser le niveau de déduction informelle de van Hiele (N3). <br />Le cadre théorique mis à l'épreuve dans cette étude, propose que le niveau d'analyse (N2) de van Hiele soit une « zone de tuilage » entre les paradigmes géométriques G1 et G2.<br />Des élèves de CM2 et de 6ème ont répondu aux mêmes questions à propos des triangles particuliers, des quadrilatères particuliers, du cercle. <br />L'analyse des réponses a permis de montrer qu'un élève de CM2 ou de 6ème ne pouvait être caractérisé par un mode de fonctionnement dans un paradigme unique ou un seul niveau de van Hiele. Selon l'activité il peut fonctionner dans un paradigme ou dans un autre et témoigner de différents niveaux de van Hiele. Le niveau N2 d'analyse de la théorie de van Hiele se confirme comme la « zone de tuilage » entre les deux paradigmes géométriques. Des activités mettant en évidence ce niveau de van Hiele dans l'un ou l'autre des deux paradigmes permette d'instaurer une continuité dans l'enseignement de la géométrie au passage de l'école primaire vers le collège.

Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006.

This study aimed to determine the effects of drama based learning on seventh grade students&rsquo / achievement (angles and polygons, circle and cylinder), attitudes and thinking levels in geometry compared to the cooperative learning. The study was conducted on four seventh grade classes from two public elementary schools in the same district in the 2006-2007 academic year, lasting seven and a half week (30 lesson hours). The data were collected through angles and polygons (APA) / and circle and cylinder achievement (CCA) tests, the van Hiele geometric thinking level test (POSTVHL), geometry attitude scale (PRE-POSTGAS). The quantitative analyses were carried out by using Multivariate Analysis of Variance (MANOVA). The results showed that drama based learning had a significant effect on students&rsquo / angles and polygons achievement, circle and cylinder achievement, van Hiele geometric thinking level compared to the cooperative learning. However, attitude findings regarding the attitudes revealed that there is not a significant difference according to the geometry attitudes of drama group and cooperative group after treatment. Both the two instructional methods supported active participation, created cooperative working environment, included daily life examples and gave the chance to classroom communication. On the other hand, drama group students&rsquo / significantly better performance was attributable to the make belief plays and improvisations of daily life examples included in drama activities.

This study aimed to investigate the effects of using dynamic geometry software while teaching by guided discovery compared to paper-and-pencil based guided discovery and traditional teaching method on sixth grade students&rsquo / van Hiele geometric thinking levels and geometry achievement. The study was conducted in one of the private schools in Ankara and lasted six weeks. The sample of the study consisted 47 sixth grade students in the school. The present study was designed as pretest-posttest control group quasi-experimental study.In order to gather data, Geometry Achievement Test (GAT) and Van Hiele Geometric Thinking Level Test (VHL) were used. At the end of the research, the data were analyzed by means of analysis of covariance. The results of the study indicated that there was a significant effect of methods of teaching on means of the collective dependent variables of the sixth grade students&rsquo / scores on the POSTVHL after controlling their PREVHL scores, and there was a significant effect of methods of teaching on means of the collective dependent variables of the sixth grade students&rsquo / scores on the POSTGAT after controlling their PREGAT scores.

Traditionally, geometry at school starts on a formal level, largely ignoring prerequisite skills needed for formal spatial reasoning. Ignoring that geometry conceptualisation has a sequential and hierarchical nature, causes ineffective teaching and learning with a long lasting inhibiting influence on spatial development and learning. One of the current reform movements in mathematics education is the appropriate use of dynamic computer technology in the teaching and learning of mathematics. Concerning mathematics education, the lecturers may involve the introduction of both dynamic computer technology and mathematics in meaningful contexts that will enable interplay between the two. Pre-service mathematics teachers (PMTs) can be encouraged to become actively involved in their learning and, therefore, less frustrated in their study orientation in mathematics. Therefore, such learning environments may be essential to enhance the conceptual understanding of PMTs. To be able to reach their eventual learners, PMTs' own conceptual understanding of geometry should be well developed. When PMTs have conceptual understanding of a mathematical procedure, they will perceive this procedure as a mathematical model of a problem situation, rather than just an algorithm. This study aimed at investigating the effect of a technologically enhanced learning environment on PMTs' understanding of geometry concepts and their study orientation in mathematics, as prerequisite for deep conceptualisation. A combined quantitative and qualitative research approach was used. The quantitative investigation employed a pre-experimental one-group pre-test post-test design. A Mayberry-type test was used to collect data with regard to PMTs' conceptualisation of geometry concepts, while the Study Orientation in Mathematics (SOM) questionnaire was used to collect data with regard their study orientation in mathematics. The qualitative investigation employed phenomenological interviews to collect supplementary information about the participating PMTs' experiences and assessment of the influence of the use of the dynamic software Geometer's Sketchpad (GSP) on their learning and conceptualisation of geometry concepts. During post-testing the participating group of PMTs achieved practically significantly higher scores in the Mayberry-type test, as well as in all fields of the SOM questionnaire. Results seem to indicate that PMTs gained significantly in the expected high levels of conceptualisation, as well as high degrees of acquisition of those levels during the intervention programme. The main conclusion of the study is that a technologically enhanced learning environment (such as GSP) can be successfully utilised to significantly enhance PMTs' conceptualisation and study orientation, as prerequisite for deep conceptualisation, in geometry. / Thesis (M.Ed.)--North-West University, Potchefstroom Campus, 2006

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.