Problem Solving in Geometry: From Microworlds to Intelligent Computer Environments

Laborde, Colette; Laborde, Jean-Marie

doi:10.1007/978-3-642-58142-7_13

Cited by 15 publications

(7 citation statements)

References 6 publications

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“…Those findings are consistent with the claim of Laborde and Laborde (1992) that perceptual control in geometry learning had been facilitative for finding out solution paths and for validation of those paths.…”

Section: Resultssupporting

confidence: 90%

Effects of imagery representations and question aids in comprehension of geometry texts by elementary school children, junior-highschool and college students

Mitsuda

1993

Jpn. Psychol. Res

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In a series of causal modeling analyses, imagery rotation and several other measures of geometry skill were used as predictors of comprehension-monitoring activities of young students when they read word problems of axis-and point symmetry. In Experiment I, close causal relationship was obtained for younger students, as compared to the cases of older ones, between their abilities to rotate imagery representations and efficiency in monitoring their own problem solving activities. In Experiment 2, similar results were obtained for sixth, but not for fourth graders. The results were discussed in terms of growth of perceptual and metacognitive control in geometry tasks.

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Section: Resultssupporting

confidence: 90%

Effects of imagery representations and question aids in comprehension of geometry texts by elementary school children, junior-highschool and college students

Mitsuda

1993

Jpn. Psychol. Res

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“…These DG attributes raise questions concerning the teaching/ learning of geometry in general and create a dilemma concerning the role of proof in particular. On the one hand, mathematics educators point out that one of the dangers of DG software is that the student may naturally conceive theoretical objects or relations only through perception (Laborde & Laborde, 1992). On the other hand, research, including the present research, suggests that DG environments open opportunities for learning meaningful geometry (see de Villiers, 1990de Villiers, , 1999Dreyfus & Hadas, 1996;Laborde, 1995).…”

Section: The Dg Environmentsmentioning

confidence: 85%

Analyses of activity design in geometry in the light of student actions

Hadas

Hershkowitz

Schwarz

2002

Canadian Journal of Science, Mathematics and Technology Educati

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The goal of this study is to show that inquiry activities in a dynamic geometry environment, intentionally designed to confront students with contradictions and uncertainties, push them towards explanations that include deductive elements. Three different but dependent aspects of the activities are characterized and analysed: The epistemological, which includes all possible inquiry paths; the didactic, which involves only those paths that reflect the intention of the designer; and the cognitive, which accounts for actual student actions (conjectures and explanations) and their analyses. The research conclusions are based on the interplay among these three aspects. The analysis of students' investigations and the analysis of their explanations fulfil, to a broad extent, the design goals.Sommaire exécutif :Le but de cette recherche est de montrer que des activités d'investigation conçues pour créer des contradictions entre des conjectures, prédictions ou doutes émis par des élèves poussent ces derniers à formuler des explications à caractère déductif. Trois activités d ' investigation ont été élaborées afin d'amener les élèves à émettre des conjectures, à explorer les situations à l'étude grâce au rôle médiatisant d'un logiciel de géométrie dynamique, à tirer des conclusions et à les expliquer. Les activités ont été mises au point selon un processus de conception-recherche-conception.Les élèves qui participaient à chacune de ces activités étaient regroupés deux par deux. Les activités se sont d'abord déroulées dans le cadre d'entrevues semi-structurées, puis en classe. Les entrevues nous ont permis d'observer l'évolution des conjectures émises par les élèves ainsi que le processus suivant lequel ces derniers produisent des explications dans des situations où ils font face à des contradictions ou à des incertitudes. Les transcriptions des entrevues et des rapports portant sur les activités réalisées en classe par chaque paire d'élèves ont fourni à la fois une perspective quantitative et des exemples qualitatifs. Ces données nous ont permis d'établir dans quelle mesure les élèves ont dû résoudre des contradictions ou des incertitudes, et d'obtenir une grande variété d'explications que nous avons regroupées en catégories.Les activités ont été analysées selon trois aspects différents quoique interdépendants. Tout d'abord, nous nous sommes intéressés à la structure épistémologique des activités : nous avons répertorié toutes les façons possibles d'aborder la tâche, sans en privilégier une en particulier. Deuxièmement, nous nous sommes penchés sur les caractéristiques didactiques des activités, y compris le rôle de l'outil que constitue le logiciel de géométrie dynamique, et ce en tenant compte des intentions du concepteur, qui favorisent certaines possibilités sur le plan épistémologique. Un examen plus attentif de ces intentions a orienté le troisième volet de notre analyse, qui portait sur l'aspect cognitif sous-tendant les actions des élèves (conjectures ou explications) et leurs analyses. Les résultats obtenus ont m...

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“…Vários sistemas computacionais dedicados ao ensino da geometria têm sido desenvolvidos e aperfeiçoados nestes últimos anos. Além do Geogebra, outros ambientes bastante utilizados tem sido o Tabulae [25], o Cabri Geometre [6] e o Geometer's Sketchpad [24]. Outro importante fator tem sido a forma de como representações externas podem corroborar no desenvolvimento desses sistemas computacionais, notadamente para facilitar a compreensão de conhecimentos complexos ( [33], [34], [37]).…”

Section: Figura 2: O Triangulo Isósceles Abc E As Conjecturas Preservadasunclassified

Aprimoramento Conceitual e Uso de Demonstrações Matemáticas: Um Estudo de Caso Sobre a Geometria Dinâmica e as Pesquisas de Campo com Ambientes Computacionais de Ensino

Ferreira¹,

Soares

Lima

2012

RBIE

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Resumo Esta publicação mostra uma pesquisa original sobre implicações conceituais decorrentes de pesquisas de campo que usam ambientes computacionais de ensino. Os resultados de um estudo de caso confirmaram a hipótese de que a participação de professores em pesquisas de campo desta natureza pode servir de auto-estímulo para: i) dar continuidade à formação; ii) aprimorar as conceitualizações e os futuros processos de ensino e aprendizagem. O uso de demonstrações matemáticas foi particularmente analisado e essa abordagem embasou os propósitos sedimentais de identificar, compreender e codificar as conceitualizações, dadas as habilidades docentes em fazer demonstrações. Os resultados também mostraram que as conceitualizações adquiridas em pesquisas de campos são conservadas e se traduzem posteriormente numa docência mais segura, ladeada por uma maior habilidade e um uso mais consciente de ambientes computacionais de ensino.

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Problem Solving in Geometry: From Microworlds to Intelligent Computer Environments

Cited by 15 publications

References 6 publications

Effects of imagery representations and question aids in comprehension of geometry texts by elementary school children, junior-highschool and college students

Effects of imagery representations and question aids in comprehension of geometry texts by elementary school children, junior-highschool and college students

Analyses of activity design in geometry in the light of student actions

Aprimoramento Conceitual e Uso de Demonstrações Matemáticas: Um Estudo de Caso Sobre a Geometria Dinâmica e as Pesquisas de Campo com Ambientes Computacionais de Ensino

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