Skolverket (2013) skriver att läroplanen för gymnasieskolan ska överföra värden, förmedla kunskaper och förbereda eleverna att arbeta och medverka i samhället. Då tekniken ständigt utvecklas, förändras samhället och skolan följer även med i förändringen. Vidare skriver Skolverket (2013) att eleverna också ska kunna orientera sig och agera i en komplex verklighet med stort informationsflöde, ökad digitalisering och snabb förändringstakt. Arbetet har inspirerats av våra egna personliga erfarenheter från både vår skolgång och verksamhets förlagda utbildning. Syftet är att undersöka hur lärare integrerar digitala verktyg inom området geometri med avsikt att inspirera studenter eller redan verksamma lärare. Det teoretiska ramverket som används i studien kommer från forskarparet Dina och Pierre van Hieles nivåer om elevers geometriförståelse. Forskarparet van Hiele är i nuläget ledande inom forskning gällande elevers förståelse för geometri, den är uppdelade i fem nivåer där högre nivåer innebär djupare förståelse. För att elever ska stiga från en så kallad van Hiele-nivå till en högre krävs det att eleven tillsammans med läraren genomgår fem av van Hieles inlärningsfaser. I studien har semistrukturerade intervjuer förts med frågor av öppen art. I dataanalysen användes tematisering som redskap, det är för att lyfta datan till en högre analytisk nivå samtidigt som den sammanfattas på ett effektivt sätt. Resultatet visar att samtliga lärare använder digitala verktyg som medel främst för visualisering, de är alla positivt inställda gentemot digitala verktyg som medel och uppnår även höga van Hiele-nivåer samt inläsningsfaser i undervisningen med digitala verktyg. Det som saknas för att uppfylla alla van Hiele-nivåer och inlärningsfaser är ämnesdiskussioner med elever på ett individuellt plan.

No description available.

Studiens syfte är att undersöka kunskaperna i plangeometri hos elever på samhällsvetenskapliga och naturvetenskapliga programmen.  Elevernas kunskaper kartläggs med ett kunskapstest, och detta kunskapstest genomförs även i två gymnasieklasser i Finland. De finska eleverna inkluderas för att bidra med ett internationellt perspektiv på de svenska elevernas resultat. Elevsvaren bedöms med hjälp av van Hieles teori om kunskapsutveckling. Resultaten visar att eleverna klarar av att utföra de beräkningarna som krävs, men att det saknas en djupare förståelse för geometri, speciellt inom området area. Jämförelsen mellan de finska och de svenska eleverna visar att det inte finns någon större skillnad mellan eleverna.

Detta är en studie som har sin utgångspunkt i Pierre M. van Hieles teori om lärande i geometri, som presenterades 1986 i boken Structure and Insight. Van Hiele har i boken vidareutvecklat sin och Dina van Hiele-Geldofs ursprungliga lärandeteori från 1955. Vår studie har som syfte att se om van Hieles teori går att tillämpa i en individuell, skriftlig diagnos för att nivåbestämma elever i årskurs 1 på gymnasiet.

Spatial sense is an important ability in mathematics. Formula application is very different from spatial concept acquisition. But it is often observed that in schools students learn spatial concepts by memorizing instead of understanding. In the past academic year we had tried out and developed a series of learning activities based on van Hiele’s model for guiding learners to explore the cube and its cut sections. The ideas in origami, and mathematical modelling by manipulative as well as mathematical software are integrated into our study. This paper gives a brief account on our works. We start by presenting a sequence of math-rich learning tasks, followed by some related folding ideas and mathematical background analysis. Finally we round up our paper with a concise discussion on some major elements of our design based on the van Hiele learning phases.

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-06-20T17:52:33Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_AndréPereira.pdf: 4946213 bytes, checksum: 7c107c2e3c7fc4a9983f95790958afb9 (MD5) / Made available in DSpace on 2016-06-20T17:52:33Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_AndréPereira.pdf: 4946213 bytes, checksum: 7c107c2e3c7fc4a9983f95790958afb9 (MD5) Previous issue date: 2016-02-15 / Capes / A presente dissertação teve por objetivo analisar os efeitos de uma sequência didática para a construção do conceito de quadriláteros notáveis, utilizando o software de Geometria Dinâmica GeoGebra como recurso didático. O estudo, que compreendeu uma replicação de pesquisa do trabalho de Câmara dos Santos (2001), foi desenvolvido com 30 estudantes de uma turma do sexto ano do ensino fundamental de uma escola da rede pública da cidade de Recife, capital do Estado de Pernambuco, Brasil. Nesse sentido, utilizamos como sustentação teórica a teoria de Van-Hiele (1957) para o desenvolvimento do pensamento geométrico, por apresentar uma articulação adequada com o nosso objeto de estudo, ou seja, com o conceito de quadriláteros notáveis. Considerando o objetivo que se buscou alcançar, analisamos os dados obtidos, isto é, as produções dos alunos, que compreendeu as atividades propostas na sequência didática, os documentos escritos (as fichas de atividades), as gravações realizadas no GeoGebra e os resultados da pré e póstestagem. Além disso, estes testes se efetuaram em dois momentos: no primeiro, antes da aplicação da sequência didática, e no segundo, após o término do trabalho com a sequência. Dessa forma, no que se refere ao desenvolvimento dos níveis de pensamento geométrico, considerando a teoria de Van-Hiele (1957), verificamos um progresso importante nesse processo, pois parte considerável dos estudantes participantes avançou entre os níveis iniciais, por meio da sequência didática (sendo verificado entre 17% do total de alunos). Observamos, também, que alguns alunos não alcançaram a passagem do primeiro para o segundo nível, mas, esses alunos progrediram significativamente dentro do próprio nível, deixando-os bem próximos do nível seguinte (43% dos estudantes). Além disso, nos foi possível identificar alunos trabalhando nos dois níveis ao mesmo tempo (40% dos alunos), tal fato é um indício de que podem existir faixas de transição entre os níveis vanhielianos, como foi verificado por Câmara dos Santos (2001). Nessa pesquisa, o GeoGebra mostrouse um importante recurso didático aos processos de ensino e de aprendizagem da Geometria, sobretudo, para o desenvolvimento dos níveis de pensamento geométrico no 6º ano do ensino fundamental, tendo a teoria vanhieliana como sustentação. / This present dissertation aimed to investigate the effects of a didactic sequence for notable quadrilaterals concept construction, using the GeoGebra Dynamic Geometry software as a didactical resource. The study, that is a replication of Câmara dos Santos (2001) research and it was developed in a class with 30 students of sixth grade class of elementary public school in Recife city, capital of Pernambuco State, Brazil. In this sense, we used as theoretical support the Van-Hiele (1957) theory for the development of geometric thinking by presenting appropriate links with our object of study, this is, with the concept of notable quadrilaterals. By considering the objective that we sought to achieve, we analyzed the obtained data, that is, the productions of the students, which included the activities proposed in the didactic sequence, written documents (worksheets), GeoGebra recordings and the results of pre and post-testing. Besides, these tests were performed in two stages: first, before didactic sequence application of, and, secondly, after the final work with the sequence. In this way, which regard to the development of levels of geometric thinking, considering Van-Hiele (1957) theory, we verified an important progress in this process, because a considerable part of the participating students had advanced among initial levels, through didactic sequence (being checked around 17% of the total of students). We also observed some students did not reach the passage from first to second level, but, these students had a significantly progress inside their own level, what made them being close to the next level (43% of students). Futhermore, was possible to identify students working on two levels at the same time (40% of students), this fact indicates that may exist transition zones between vanhielians’ levels, as Câmara dos Santos (2001) verified. In this research, GeoGebra was an important didactical resource for geometry teaching and learning process, mostly, for the development of levels of geometric thinking in the 6th grade of elementary school, having the Van-Hiele theory as support.

Submitted by Celso Magalhaes (celsomagalhaes@ufrrj.br) on 2017-06-08T12:58:44Z No. of bitstreams: 1 2016 - Alan Jorge Ciqueira Gon?alves.pdf: 2968550 bytes, checksum: c41aeac563a3e880f387fa38231d62f7 (MD5) / Made available in DSpace on 2017-06-08T12:58:44Z (GMT). No. of bitstreams: 1 2016 - Alan Jorge Ciqueira Gon?alves.pdf: 2968550 bytes, checksum: c41aeac563a3e880f387fa38231d62f7 (MD5) Previous issue date: 2015-08-31 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / This study aims to improve understanding of studies of conics. For this, we will use as theoretical foundation in the construction of the proposed activities, the geometric constructivist theory of Van Hiele. Moreover, in line with the new teaching, and learning tools, we use a dynamic geometry software, the GeoGebra / Este trabalho tem por objetivo melhorar a compreens?o do estudo de c?nicas. Para isto, usaremos como fundamenta??o te?rica na constru??o das atividades propostas a teoria construtivista geom?trica de Van Hiele. Al?m disso, em conson?ncia com as novas ferramentas de ensino e aprendizagem, utilizaremos um software de geometria din?mica, GeoGebra.

Thesis (M.Ed. (Education)) - Rhodes University, 2009. / Submitted in partial fulfilment of the requirements for the degree of Master in Education (Mathematics Education)

Magister en Educación Mención Informática Educativa / Autor No autoriza la publicación de su tesis a texto completo en el Portal de Tesis Electrónicas. / Esta investigación tiene como objetivo entregar a los docentes de matemática una propuesta de trabajo para la enseñanza de la geometría, integrando un modelo de razonamiento con el uso de las tecnologías de información y comunicación. Para esto se diseñaron guías de aprendizaje, según los niveles de razonamiento geométrico de Van Hiele, para la enseñanza del objeto geométrico Simetrías, a través del software Geogebra. El trabajo con estos talleres permite a los estudiantes pasar de lo más simple a lo más complejo en el estudio de las simetrías, visualizar, manipular y resolver los problemas planteados a través de applets construidos con Geogebra. Es importante señalar que la puesta a prueba de estos recursos permite verificar si el aprendizaje de las simetrías es más significativo al usar el modelo de Van Hiele, o integrando este modelo con el uso de Geogebra, o utilizando la metodología tradicional del establecimiento. Para validar y probar esta propuesta se implementó con un grupo de alumnos de la comuna de Maipú

This study investigates the effect of using Van Hiele’s instructional model in the teaching of congruent triangles in grade 10 in Gauteng high schools. Three randomly selected high schools in Gauteng formed the research fields, while intact groups of grade 10 learners in these schools formed the study participants (136 learners) for the study. A mixed method approach which was adopted for the study, using pre-test/post-test matching control group design and classroom observation. The pre-test/post-test was used to collect quantitative data, while classroom observation was used to glean qualitative data. Some of the findings from the quantitative data analysis suggested that the intervention improve the achievement scores in the experimental groups while the qualitative data was revealed that the intervention facilitated the learning of the concepts of congruent. It was recommended that Van Hiele learning and instructional model be adopted and applied in the teaching of other areas of mathematics / Mathematics Education / M. Sc. (Mathematics Education)