No ensino da Geometria Espacial é notável a dificuldade de nossos alunos em atividades que necessitam a mobilização de habilidades espaciais e nas quais é exigida a compreensão da representação bidimensional de objetos tridimensionais. Este estudo apresenta uma sequência didática que explora conceitos da Geometria Espacial através da utilização do software de geometria dinâmica GeoGebra. A proposta tem como objetivo provocar o desenvolvimento do pensamento geométrico espacial, nisso tirando-se proveito dos recursos de representação que se tem no software, especialmente aquele que diz respeito a interação dinâmica entre as representações do objeto tridimensional e diferentes planos de corte. São dez atividades, em crescente nível de dificuldade e envolvendo diferentes conceitos da Geometria Espacial. A análise da produção dos alunos é feita a luz das teorias de Van Hiele, Duval e Gutiérrez. A metodologia de pesquisa é inspirada na Engenharia Didática e foi possível sinalizar, a partir do confronto entre análises a priori e a posteriori, o progresso dos alunos quanto ao desenvolvimento de habilidades para visualização espacial. / In teaching the Spatial Geometry is remarkable the students difficulty in activities that require spatial skills and the understand of the two-dimensional representation of three-dimensional objects. This study presents a didactic sequence that explores concepts of Spatial Geometry using the software GeoGebra. The aim is to provoke the development of spatial geometric thinking, taking advantage of dynamic representations available in the software, especially the one concerning the interaction between the representations of three-dimensional object and intersecting planes. Ten activities in increasing level of difficulty and involving different concepts of spatial geometry were applied in the experiment. The analysis of the students’ production is based on Van Hiele, Duval and Gutiérrez theories and the research methodology takes as reference the Didactic Engineering. From confrontation between the priori and posteriori analysis, it was possible to observe the progress of students and especially the development of skills related to spatial visualization.

Many authors have expressed concern regarding the extent of underachievement in mathematics. The role of language proficiency as a causal factor in this underachievement has been neglected. Researchers found sufficient evidence to conclude that language proficiency is related to mathematics achievement. In mathematics, symbolic language fills a dual role: It serves as an instrument of communication and as an instrument of thought by making the representation of mathematical concepts, structures and relationships possible (Esty & Teppo, 1996:45). According to Van Hiele (1988:5), language structure is a critical factor in the progression through the Van Hiele levels from the visual, concrete structures to the abstract structures. In this study, the influence of language proficiency on geometric thinking is investigated. 152 grade 8 and 9 learners completed two tests each. One test measured language proficiency in the learners' mother tongue. The second is a geometric test based on a Mayberry-type Van Hiele test for assessing learners' geometric thinking levels. Language proficiency was taken as the independent variable, and geometric thinking as the dependent variable. In the analysis of the results, the top 25 % and bottom 25% performers in the language proficiency test were chosen. Cohen's (1988) d-value was used to determine if there was a practical significant difference in the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels. Results showed a practical significant difference between the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels, but also with respect to the geometry test as a whole. In particular, two aspects of language proficiency, namely reading comprehension and vocabulary, appeared to be very strong predictors for geometric thinking on the first three Van Hiele levels (d ≥ 0,8). Key terms for indexing: geometry, geometry learning, mathematics learning, geometric thinking, language, language proficiency, geometry and language, mathematics and language. / Thesis (M.Sc. (Education)--North-West University, Potchefstroom Campus, 2004.

Many authors have expressed concern regarding the extent of underachievement in mathematics. The role of language proficiency as a causal factor in this underachievement has been neglected. Researchers found sufficient evidence to conclude that language proficiency is related to mathematics achievement. In mathematics, symbolic language fills a dual role: It serves as an instrument of communication and as an instrument of thought by making the representation of mathematical concepts, structures and relationships possible (Esty & Teppo, 1996:45). According to Van Hiele (1988:5), language structure is a critical factor in the progression through the Van Hiele levels from the visual, concrete structures to the abstract structures. In this study, the influence of language proficiency on geometric thinking is investigated. 152 grade 8 and 9 learners completed two tests each. One test measured language proficiency in the learners' mother tongue. The second is a geometric test based on a Mayberry-type Van Hiele test for assessing learners' geometric thinking levels. Language proficiency was taken as the independent variable, and geometric thinking as the dependent variable. In the analysis of the results, the top 25 % and bottom 25% performers in the language proficiency test were chosen. Cohen's (1988) d-value was used to determine if there was a practical significant difference in the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels. Results showed a practical significant difference between the performance of the more proficient language learners and the less proficient language learners with respect to each of the first three Van Hiele levels, but also with respect to the geometry test as a whole. In particular, two aspects of language proficiency, namely reading comprehension and vocabulary, appeared to be very strong predictors for geometric thinking on the first three Van Hiele levels (d ≥ 0,8). Key terms for indexing: geometry, geometry learning, mathematics learning, geometric thinking, language, language proficiency, geometry and language, mathematics and language. / Thesis (M.Sc. (Education)--North-West University, Potchefstroom Campus, 2004.

No ensino da Geometria Espacial é notável a dificuldade de nossos alunos em atividades que necessitam a mobilização de habilidades espaciais e nas quais é exigida a compreensão da representação bidimensional de objetos tridimensionais. Este estudo apresenta uma sequência didática que explora conceitos da Geometria Espacial através da utilização do software de geometria dinâmica GeoGebra. A proposta tem como objetivo provocar o desenvolvimento do pensamento geométrico espacial, nisso tirando-se proveito dos recursos de representação que se tem no software, especialmente aquele que diz respeito a interação dinâmica entre as representações do objeto tridimensional e diferentes planos de corte. São dez atividades, em crescente nível de dificuldade e envolvendo diferentes conceitos da Geometria Espacial. A análise da produção dos alunos é feita a luz das teorias de Van Hiele, Duval e Gutiérrez. A metodologia de pesquisa é inspirada na Engenharia Didática e foi possível sinalizar, a partir do confronto entre análises a priori e a posteriori, o progresso dos alunos quanto ao desenvolvimento de habilidades para visualização espacial. / In teaching the Spatial Geometry is remarkable the students difficulty in activities that require spatial skills and the understand of the two-dimensional representation of three-dimensional objects. This study presents a didactic sequence that explores concepts of Spatial Geometry using the software GeoGebra. The aim is to provoke the development of spatial geometric thinking, taking advantage of dynamic representations available in the software, especially the one concerning the interaction between the representations of three-dimensional object and intersecting planes. Ten activities in increasing level of difficulty and involving different concepts of spatial geometry were applied in the experiment. The analysis of the students’ production is based on Van Hiele, Duval and Gutiérrez theories and the research methodology takes as reference the Didactic Engineering. From confrontation between the priori and posteriori analysis, it was possible to observe the progress of students and especially the development of skills related to spatial visualization.

No ensino da Geometria Espacial é notável a dificuldade de nossos alunos em atividades que necessitam a mobilização de habilidades espaciais e nas quais é exigida a compreensão da representação bidimensional de objetos tridimensionais. Este estudo apresenta uma sequência didática que explora conceitos da Geometria Espacial através da utilização do software de geometria dinâmica GeoGebra. A proposta tem como objetivo provocar o desenvolvimento do pensamento geométrico espacial, nisso tirando-se proveito dos recursos de representação que se tem no software, especialmente aquele que diz respeito a interação dinâmica entre as representações do objeto tridimensional e diferentes planos de corte. São dez atividades, em crescente nível de dificuldade e envolvendo diferentes conceitos da Geometria Espacial. A análise da produção dos alunos é feita a luz das teorias de Van Hiele, Duval e Gutiérrez. A metodologia de pesquisa é inspirada na Engenharia Didática e foi possível sinalizar, a partir do confronto entre análises a priori e a posteriori, o progresso dos alunos quanto ao desenvolvimento de habilidades para visualização espacial. / In teaching the Spatial Geometry is remarkable the students difficulty in activities that require spatial skills and the understand of the two-dimensional representation of three-dimensional objects. This study presents a didactic sequence that explores concepts of Spatial Geometry using the software GeoGebra. The aim is to provoke the development of spatial geometric thinking, taking advantage of dynamic representations available in the software, especially the one concerning the interaction between the representations of three-dimensional object and intersecting planes. Ten activities in increasing level of difficulty and involving different concepts of spatial geometry were applied in the experiment. The analysis of the students’ production is based on Van Hiele, Duval and Gutiérrez theories and the research methodology takes as reference the Didactic Engineering. From confrontation between the priori and posteriori analysis, it was possible to observe the progress of students and especially the development of skills related to spatial visualization.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This paper refers to an research that sought to develop geometric thinking students in the sixth grade of elementary school from practices. The school activities in which it was held that job belongs to the Municipal network of Júlio de Castilhos Education, it is located on the outskirts of this city. The activities were proposed in order to provide the student with the construction of some basic, concepts and definitions of geometry from the geometric objects classification. The classification user as a basic criterion the predominant characteristics of each geometric object, which is the geometric figures or not they belong to the same class in adition, students to develop the proposed activities worked in groups, following the criteria proposed by the joint assimilation. / O presente trabalho refere-se a uma pesquisa que buscou desenvolver o pensamento geométrico em alunos do 6º ano do Ensino Fundamental a partir de atividades práticas. A escola em que foi realizado esse trabalho pertence à Rede Municipal de Ensino de Júlio de Castilhos, localizada na periferia desta cidade. As atividades foram propostas com o objetivo de proporcionar ao aluno a construção de alguns conceitos e definições básicas da Geometria, a partir da classificação de objetos geométricos. Para realizar as atividades, os alunos utilizavam como critério básico as características predominantes de cada objeto geométrico, do qual faz as figuras geométricas pertencerem ou não a uma mesma classe. Além disso, os alunos, ao desenvolverem as atividades propostas, trabalharam em grupo, seguindo os critérios propostos pela assimilação solidária.

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.

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.

Submitted by Patricia Priscilla Ferraz Da Costa Souza (pattyprisouza@hotmail.com) on 2018-04-27T00:22:20Z No. of bitstreams: 1 dissertacao final 26.4 pdf.pdf: 2417567 bytes, checksum: 1abe0bb8e0c6321f6bb465a52d816ef5 (MD5) / Approved for entry into archive by Maria Marlene Zaniboni null (zaniboni@bauru.unesp.br) on 2018-04-27T14:55:07Z (GMT) No. of bitstreams: 1 souza_ppfc_me_bauru.pdf: 2417567 bytes, checksum: 1abe0bb8e0c6321f6bb465a52d816ef5 (MD5) / Made available in DSpace on 2018-04-27T14:55:07Z (GMT). No. of bitstreams: 1 souza_ppfc_me_bauru.pdf: 2417567 bytes, checksum: 1abe0bb8e0c6321f6bb465a52d816ef5 (MD5) Previous issue date: 2018-02-22 / Esta pesquisa teve por meta investigar os seguintes problemas: Alunos do 5º ano do EF da rede pública possuem conhecimentos adequados sobre os conteúdos de geometria? “O recurso didático de uma HQ poderá possibilitar o desenvolvimento do pensamento geométrico de alunos dos AIEF?”. O ensino da Geometria nos Anos Iniciais do Ensino Fundamental enfrenta, atualmente, dificuldades em vários níveis, seja no tocante à aprendizagem e desenvolvimento do pensamento, seja na formação de professores. Sendo assim, surgiu a necessidade desta pesquisa de caráter qualitativo, tendo como objetivo geral compreender a situação atual do ensino da Geometria nos anos iniciais do Ensino Fundamental, refletindo sobre o desenvolvimento do pensamento geométrico e apresentando uma nova proposta de recurso didático. O instrumento utilizado para a produção de dados foi um questionário com perguntas de conhecimento geométrico destinado a 24 alunos do 5º ano do Ensino Fundamental. Esse questionário foi fundamentado nos objetivos de aprendizagens dos PCN de 1997 e nos objetivos de conhecimentos descritos na 3ª versão da BNCC de 2017, dos anos iniciais do Ensino Fundamental, com foco nos conteúdos de figuras planas e tridimensionais. Em um primeiro momento, os alunos teriam que identificar o nome das figuras e, logo após, em uma etapa mais avançada, teriam que reconhecer as figuras por suas propriedades e utilizar seus atributos na resolução de problemas. Para análise dos dados, foram utilizados os níveis de pensamento geométrico descritos na Teoria Van Hiele. O resultado observado com a pesquisa mostrou que apenas 16,66% dos alunos investigados conseguiram chegar ao nível 1 da teoria Van Hiele, e a grande maioria ficou classificada no nível 0, ou seja, não reconhecem a figura geométrica com base em sua aparência global e, consequentemente, não utilizam o vocabulário geométrico correto e tão pouco, possuíam condições de realizar situações problemas que explorem atributos e propriedades das figuras. Com os dados desta pesquisa, foi produzida uma HQ, tendo como objetivo possibilitar avanços no desenvolvimento do pensamento geométrico. / This research the objective was to investigate the following research problem: Students of the 5th year of public network EF have adequate knowledge about the contents of geometry? The teaching of Geometry in the Early Years of Elementary School currently faces difficulties at various levels, whether in terms of learning and development of thought or in teacher training. Thus, the need arose for this qualitative research, which seeks to understand the current situation of Geometry teaching in the initial years of Elementary School, allowing reflection on the development of geometric thinking and presenting a new proposal of didactic resource. The instrument used for the production of data was a questionnaire with questions of geometric knowledge destined to 24 students of the 5th year of Elementary School. This questionnaire was based on the learning objectives of the 1997 NCPs and on the knowledge objectives described in the 3rd version of the BNCC in 2017, from the initial years of Elementary School, focusing on the contents of flat and three - dimensional figures. At first, students would have to identify the names of the figures, and soon afterwards, at a later stage, they would have to recognize the figures by their properties and use their attributes in problem solving. For data analysis, the levels of geometric thinking described in Van Hiele Theory were used. The results showed that only 16.66% of the investigated students were able to reach level 1 of the Van Hiele theory, and the great majority was classified at level 0, that is, they do not recognize the geometric figure based on their overall appearance and consequently do not use the correct geometric vocabulary and so few, were able to realize situations problems that explore attributes and properties of the figures. With the data of this research, a comic was produced with the objective of enabling advances in the development of geometric thinking.