From static to dynamic mathematics: historical and representational perspectives

Moreno–Armella, Luis; Hegedus, Stephen; Kaput, James J.

doi:10.1007/s10649-008-9116-6

Cited by 105 publications

(41 citation statements)

References 15 publications

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“…Authors Luis Moreno-Armella, Stephen J. Hegedus, and James J. Kaput provide in [4], p. 103 an historical overview of symbolization, which can be considered as a kind of the evolution of cognitive tools. They identify five stages of the evolution of symbolization "from static, inert inscriptions to dynamic objects or diagrams that are constructible, able to be manipulated and interactive".…”

mentioning

confidence: 99%

Interactive Maths with GeoGebra

Velichová¹

2011

Int. J. Emerg. Technol. Learn.

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Abstract-This paper brings information on dynamic multiplatform mathematical software GeoGebra produced by Markus Hohenwarter in 2002 for learning and teaching mathematics, available free on web in 45 languages. GeoGebra enables production of self-standing dynamic worksheets as interactive java applets embedded in html pages presenting dynamic constructions and interactive calculations on Internet. Thus it is enhancing available powerful electronic tools suitable for production of instructional materials in on-line maths education. Several possibilities are presented on how this useful utility might be used in e-learning solutions as a dynamic interactive platform for calculations and drawings.Index Terms-dynamic mathematical software, cognitive tools, cognitive connections, symbolization in mathematics.

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confidence: 99%

Interactive Maths with GeoGebra

Velichová¹

2011

Int. J. Emerg. Technol. Learn.

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“…L'utilisation des technologies aurait, selon certains d'entre eux, aidé à améliorer leurs compé-tences dans certains domaines, dont celui des apprentissages autorégulés, ainsi que le suggèrent Depover, Karsenti et Komis (2008). Le logiciel semble être perçu par certains élèves comme une aide dans la résolution du problème, tout en étant utilisé à des stades dynamiques, tels que définis par Moreno-Armella, Hegedus et Kaput (2008).…”

Section: Resultsunclassified

Perceptions des élèves du secondaire par rapport à la résolution de problèmes en algèbre à l’aide d’un logiciel dynamique et la stratégie Prédire – investiguer – expliquer

Gauthier

2014

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Dans le cadre d’un projet d’innovation en apprentissage mis en oeuvre par le ministère de l’Éducation du Nouveau-Brunswick, nous avons créé et expérimenté quatre scénarios d’enseignement-apprentissage de l’algèbre en 12e année du secondaire, touchant particulièrement le concept de paramètres de fonctions introduit à l’aide d’une stratégie Prédire-Investiguer-Expliquer et d’un logiciel dynamique, dans un contexte de résolution de problèmes. Cette recherche exploratoire de type développement adopte une approche de design d’un produit éducatif ou, encore, de création d’activités d’apprentissage particulières (Loiselle, 2001). Les données qualitatives ont été recueillies auprès des élèves, à l’aide d’un questionnaire et d’entrevues semi-dirigées.D’une part, le contexte de vie réelle et l’aspect visuel d’une investigation dynamique et interactive à l’aide d’un logiciel semblent avoir rendu l’apprentissage des fonctions plus signifiant pour l’élève. Ils ont permis à l’élève de voir des liens entre différentes représentations mathématiques, le rendant plus autonome dans les démarches de résolution de problèmes. D’autre part, ce changement de pratique conduit possiblement à une rupture du contrat didactique, ce qui a déstabilisé certains élèves qui cherchaient, alors, plus de clarté et d’encadrement de la part de l’enseignant. Cette complexification du processus de résolution de problèmes appelle donc une étude plus approfondie de cette pratique innovante afin de déterminer son impact réel sur les apprentissages des élèves et la dynamique de la salle de classe.As part of a learning innovation project initiated by the New Brunswick Ministry of Education, we created and tested four algebra teaching-learning scenarios at the grade 12 level, which touched particularly on the concept of function parameters introduced using a Predict-Observe-Explain strategy and dynamic software a problem solving context. This development-type exploratory research adopts a design approach for an educational product, or the creation of specific learning activities (Loiselle, 2001). Qualitative data were collected from students through a questionnaire and semi-structured interviews.On one hand, the real-life context and the visual aspect of a dynamic and interactive investigation using software seems to have made the learning of functions more significant for the student, and provided a chance to see connections between different mathematical representations, making the students more independent in the problem solving process. On the other hand, this change in practice may have led to a breakdown in the didactic contract, which destabilized some of the students, who were looking for more clarification and supervision from the teacher. This innovative practice of complexifying the problem-solving process deserves further study to determine its real impact on student learning and classroom dynamics.En el cuadro de un proyecto de innovación en aprendizaje iniciado por el Ministerio de Educación de Nueva-Brunswick, creamos y experimentamos cuatro es...

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“…Research has often put forward the fact that dynamic software allows students to create their own dynamic mathematical objects as references to the task at hand (Moreno-Armella, Hegedus & Kaput, 2008). That is, instead of referring to static objects created by pen and paper or presented by teachers or textbooks, students can create and manipulate mathematical objects tailored to provide exactly the information they think they need to have in order for them to proceed with solving the task at hand (Mariotti, 2000;Moreno-Armella et al, 2008). Furthermore, the creation of mathematical objects in an environment of dynamic software such as GeoGebra and Cabri can be carried out stepwise.…”

Section: Dynamic Software Supporting Problem-solving and Reasoningmentioning

confidence: 99%

“…That means that every step is associated with an activity resulting in a response from the software, which in turn may guide the next step in task solving. Working with dynamic software means both guiding the software and being guided by the software (Moreno-Armella et al, 2008).…”

Section: Dynamic Software Supporting Problem-solving and Reasoningmentioning

confidence: 99%

The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems

Olsson

2017

Int J of Sci and Math Educ

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This study investigates how students' reasoning contributes to their utilization of computer-generated feedback. Sixteen 16-year-old students solved a linear function task designed to present a challenge to them using dynamic software, GeoGebra, for assistance. The data were analysed with respect both to character of reasoning and to the use of feedback generated through activities in GeoGebra. The results showed that students who successfully solved the task were engaged in creative reasoning and used feedback extensively.

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From static to dynamic mathematics: historical and representational perspectives

Cited by 105 publications

References 15 publications

Interactive Maths with GeoGebra

Interactive Maths with GeoGebra

Perceptions des élèves du secondaire par rapport à la résolution de problèmes en algèbre à l’aide d’un logiciel dynamique et la stratégie Prédire – investiguer – expliquer

The Contribution of Reasoning to the Utilization of Feedback from Software When Solving Mathematical Problems

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