The Students’ Perspective of Geometry Teaching and Learning in High School

The purpose of this article is to present the results obtained from a questionnaire applied to Costa Rican high school students, in order to know their perspectives about geometry teaching and learning. The results show that geometry classes in high school education have been based on a traditional system of teaching, where the teacher presents the theory; he presents examples and exercises that should be solved by students, which emphasize in the application and memorization of formulas. As a consequence, visualization processes, argumentation and justification don’t have a preponderant role. Geometry is presented to students like a group of definitions, formulas, and theorems completely far from their reality and, where the examples and exercises don’t possess any relationship with their context. As a result, it is considered not important, because it is not applicable to real life situations. Also, the students consider that, to be successful in geometry, it is necessary to know how to use the calculator, to carry out calculations, to have capacity to memorize definitions, formulas and theorems, to possess capacity to understand the geometric drawings and to carry out clever exercises to develop a practical ability.

A dinâmica cibercultural na ressignificação do conhecimento geométrico: uma proposta metodológica para o ensino da geometria espacial

O estudo que apresento está assentado em questões, cujo aprofundamento pretende trazer contribuição à ressignificação dos processos de ensino-aprendizagem, especialmente no âmbito da geometria espacial. Dentre as questões destaco: (1) a relação entre cibercultura e processos de ensinar-aprender, especialmente no que se refere ao conteúdo da geometria espacial, (2) os modos de sentir, de expressar-se e de aprender que a mediação da cultura digital traz contemporaneamente para os jovens; (3) a pesquisa entendida como acontecimento/experiência, cuja dimensão de intervenção permite a pesquisador e pesquisados relacionarem-se dialogicamente, reconhecendo-se como co-autores do processo de investigação. O principal interesse da pesquisa foi investigar se a dinâmica do uso das tecnologias em redes, própria da cibercultura, pode ressignificar o aprendizado do conhecimento de geometria espacial de jovens alunos do Ensino Médio. A abordagem teórico-metodológica está fundamentada nos princípios bakhtinianos da dialogia e da alteridade e no conceito vigotskiano de mediação. Sob a orientação da abordagem histórico-cultural, outros interlocutores teóricos contribuiram de modo significativo para a compreensão das questões que envolvem a relação entre educação e processos comunicacionais pós-massivos, tendo sido indispensáveis à construção e interpretação dos dados Dentre eles, cito Lucia Santaella, Maria Teresa Freitas, Pierre Lévy, Marília Amorim, Maria Helena Bonilla, Nelson Pretto, Edmea Santos, Guaracira Gouvêa, Maria Luiza Oswald, entre outros. O estudo foi realizado numa escola da rede estadual na cidade de Cabo Frio/RJ, sendo sujeitos da pesquisa 78 alunos/as do 2 e 3 ano do Ensino Médio. Para colher as informações de caráter objetivo, foi aplicado um questionário através do aplicativo Google Docs. Os dados qualitativos foram construídos por intermédio da dinâmica de convergência de mídias que engloba a metodologia Webquest, a interface wiki e o software Geogebra. Tendo em vista os pressupostos do estudo que relacionam propostas autorais, posturas alteritárias e práticas cotidianas procurei construir uma estratégia metodológica em que a apropriação das dinâmicas ciberculturais e das interfaces digitais fosse capaz de me auxiliar a identificar como usar estes dispositivos no processo de ressignificação da construção do conhecimento geométrico, bem como descobrir os limites de sua aplicação. Os resultados alcançados, ainda que provisórios dado o inacabamento dos acontecimentos que fazem da pesquisa uma experiência inacabada, apontam para a necessidade de reconhecer os jovens como produtores de saberes que deveriam ser legitimados para que a prática de ensinar-aprender geometria resultasse em conhecimento que articula ciência e vida cotidiana. Essa foi a valiosa lição que a pesquisa trouxe à minha própria prática de professora de matemática, lição que, espero, possa ecoar para outros professores.

问题之间共性关系的意识水平对平面几何解题迁移的影响

Transfer of learning is one of the major concepts in educational psychology. As cognitive psychology develops, many researchers have found that transfer plays an important part in problem solving, and the awareness of the similarity of related problems is important in transfer. So they become more interested in researching the problem of transfer. But in the literature of transfer research, it has been found that many researchers do not hold identical conclusions about the influence of awareness of related problems during problem solving transfer. This dissertation is written on the basic of much of sub-research work, such as looking up literature concerning transfer of problem solving research, comparing the results of research work done recently and experimental researches. The author of this dissertation takes middle school students as subjects, geometry as materials, and adopts factorial design in his experiments. The influence of awareness of related problems on problem solving transfer is examined from three dimensions which are the degree of difficulty of transfer problems, the level of awareness of related problems and the characteristics of subjects themselves. Five conclusions have been made after the experimental research: (1) During the process of geometry problem solving, the level of awareness of related problems is one of the major factors that influence the effect of problem solving transfer. (2) Either more difficult or more easy of the transfer problems will hinder the influence of awareness of related problems during problem solving transfer, and the degree of difficulty of the transfer problems have interactions with the level of awareness of related problems in affecting transfer. (3) During geometry problems solving transfer, the level of awareness of related problems has interactions with the degree of student achievement. Compared with the students who have lower achievement, the influence of the level of the awareness is bigger in the students who have higher achievement. (4) There is positive correlation between geometry achievement and reasoning ability of the middle school students. The student who has higher reasoning ability has higher geometry achievement, while the level of awareness is raised, the transfer achievement of both can be raised significantly. (5) There is positive correlation between geometry achievement and cognitive style of the middle school students. The student who has independent field tendency of cognitive style has higher geometry achievement, while the level of awareness is raised, the transfer achievement of both can be raised significantly. At the end of the dissertation, the researcher offers two proposals concerning Geometry teaching on the basis of the research findings.

Um estudo exploratório sobre a formação conceitual em geometria de alunos do ensino médio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Criando novos tabuleiros para o jogo Tri-Hex e sua validação didático-pedagógica na formação continuada de professores de matemática: uma contribuição para a geometria das séries finais do ensino fundamental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A Utilização do computador e do programa LOGO como ferramentas de ensino de conceitos de geometria plana

Pós-graduação em Educação Matemática - IGCE

Geometria esférica por meio de materiais manipuláveis

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Projetos em geometria analítica usando software de geometria dinâmica: repensando a formação inicial docente em matemática

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relação espaço-plano: uma intervenção pedagógica para o desenvolvimento do pensamento geométrico

Pós-graduação em Educação - FCT

Simetria no ensino fundamental através da resolução de problemas: possibilidades para um trabalho em sala de aula

This paper presents an alternative way of working with the theme of symmetry in the elementary school classroom. The proposal is based on qualitative research developed in the Professional Masters degree program in Science and Mathematics Teaching. We conducted field-work consisting of applying a sequence of activities for students in the seventh grade. The sequence was developed from the perspective of mathematics teaching using problem solving, taking into consideration aspects relevant to the study of geometry, such as intuition and visualization. In carrying out the activities, the dialogues between students and teacher were recorded and later transcribed. For data analysis we used the procedures of phenomenology. When interpreting the data, we observed that the teaching of symmetry using problem-solving enhances learning. We also found that, in an investigative environment, students are able to identify properties, argue about the geometric characteristics, and justify their opinions.

Aprendendo por meio de experiências com situações problema

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

ARTGEO: ensino interdisciplinar

The ARTGEO Project aimed at integrating science, art, and technology, emphasizing geometric elements which must be explored within the teaching process. Geometry, present in the most primitive civilizations, assists man in settling relationships and organizing his space. It has been clearly identified in human constructions, consisting of an important instrument of knowledge and domain of nature. The art, in its turn, can mediate the elaboration of knowledge, whether it is scientific, technical, or philosophical. Science and art are products that express the imaginary representations from distinct cultures. The Brazilian Concretism, for its relations with the geometry, is the period in art history chosen as reference. Technology was represented by the computational environments, as a didactic support and an instrument for the accomplishment of practical activities. Microsoft Word is one of the basic softwares for this proposal because of its easy access in most public schools.

Connecting visual and analytic reasoning to improve students' spatial visualization abilities: A constructivist approach

Current reform initiatives recommend that school geometry teaching and learning include the study of three-dimensional geometric objects and provide students with opportunities to use spatial abilities in mathematical tasks. Two ways of using Geometer's Sketchpad (GSP), a dynamic and interactive computer program, in conjunction with manipulatives enable students to investigate and explore geometric concepts, especially when used in a constructivist setting. Research on spatial abilities has focused on visual reasoning to improve visualization skills. This dissertation investigated the hypothesis that connecting visual and analytic reasoning may better improve students' spatial visualization abilities as compared to instruction that makes little or no use of the connection of the two. Data were collected using the Purdue Spatial Visualization Tests (PSVT) administered as a pretest and posttest to a control and two experimental groups. Sixty-four 10th grade students in three geometry classrooms participated in the study during 6 weeks. Research questions were answered using statistical procedures. An analysis of covariance was used for a quantitative analysis, whereas a description of students' visual-analytic processing strategies was presented using qualitative methods. The quantitative results indicated that there were significant differences in gender, but not in the group factor. However, when analyzing a sub sample of 33 participants with pretest scores below the 50th percentile, males in one of the experimental groups significantly benefited from the treatment. A review of previous research also indicated that students with low visualization skills benefited more than those with higher visualization skills. The qualitative results showed that girls were more sophisticated in their visual-analytic processing strategies to solve three-dimensional tasks. It is recommended that the teaching and learning of spatial visualization start in the middle school, prior to students' more rigorous mathematics exposure in high school. A duration longer than 6 weeks for treatments in similar future research studies is also recommended.

Pavimentações do plano : uma exploração com materiais manipulativos no 4º ano de escolaridade

Relatório de Estágio apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré- Escolar e 1º Ciclo do Ensino Básico.

Facilitating growth in prospective teachers’ knowledge : teaching geometry in primary schools

This paper reports on a study that focused on growth of understanding about teaching geometry by a group of prospective teachers engaged in lesson plan study within a computer-supported collaborative learning (CSCL) environment. Participation in the activity was found to facilitate considerable growth in the participants’ pedagogical-content knowledge (PCK). Factors that influenced growth in PCK included the nature of the lesson planning task, the cognitive scaffolds inserted into the CSCL virtual space, the meta-language scaffolds provided to the participants, and the provision of both private and public discourse spaces. The paper concludes with recommendations for enhancing effective knowledge-building discourse about mathematics PCK within prospective teacher education CSCL environments.