Research bibliography: dynamic geometry software

This bibliography lists research that has investigated the use of dynamic geometry software (DGS) in the teaching and learning of mathematics. The bibliography is not intended to be exhaustive; rather it includes the major studies across the range of research that has been published

Formación inicial de profesores de matemáticas de secundaria: actividades basadas en la utilización de software de geometría dinámica

En este artículo presentamos actividades de enseñanza para la formación inicial de profesores de matemáticas de secundaria. El objetivo es proporcionar al futuro profesor aspectos específicos de conocimiento profesional relacionados con el uso de software de geometría dinámica. Para ello, hacemos una propuesta metodológica que pretende combinar la experiencia del futuro docente en el uso de Cabri- Géomètre con algunas aportaciones teóricas más generales que sustentan la utilidad de adquirir conocimiento profesional asociado al empleo de estas tecnologías

Overcoming the Technical Nature in Learning Translation: Cabri Geometry, a Tool to Sustain Conceptual Comprehension?

This article presents the results of a didactic experimentation conducted with two elementary pupils (11-12 years of age) in a Quebec school in the of learning geometric translation with a mathematical software, called Cabri Geometry. The teaching-learning sequence experimented with Barth’s (2001) process of conceptualization. The working strategies of pupils were analyzed in relationship to this process. Their comprehension of the concept of translation was considered before and after the teaching-learning sequence using the Herscovics and Bergeron (1988) model of comprehension of conceptual schemata. Results indicated that by following the teachinglearning sequence, the logical mathematical comprehension of the concept of translation evolved in the pupils, while the logical- physical comprehension of this concept remained inaccurate. Moreover, the results revealed different utilization procedures of Cabri Geometry software. These utilization procedures likely affected the process of conceptualization and, consequently, the comprehension of pupils

Problem Solving and Problem Posing in a Dynamic Geometry Environment

In this study, we considered dynamic geometry software (DGS) as the tool that mediates students’ strategies in solving and posing problems. The purpose of the present study was twofold. First, to understand the way in which students can solve problems in the setting of a dynamic geometry environment, and second, to investigate how DGS provides opportunities for posing new problems. Two mathematical problems were presented to six pre-service teachers with prior experience in dynamic geometry. Each student participated in two interview sessions which were video recorded. The results of the study showed that DGS, as a mediation tool, encouraged students to use in problem solving and posing the processes of modeling, conjecturing, experimenting and generalizing. Furthermore, we found that DGS can play a significant role in engendering problem solving and posing by bringing about surprise and cognitive conflict as students use the dragging and measuring facilities of the software

On the Learning of geometric concepts using Dynamic Geometry Software

Many results on computer mediated geometry learning conclude about different heuristic approaches to problem solving with Dynamic Geometry Software (DGS). However, little is described concerning conceptualization process. We used a theoretical framework built upon constructivist foundations for analyzing mediated learning of specific geometrical concepts. Our point is illustrated in a case study in which we analyzed studentsí interaction with a DGS. Our results points to a clear mapping of potential conceptualization of geometry in software using.Many results on computer mediated geometry learning conclude about different heuristic approaches to problem solving with Dynamic Geometry Software (DGS). However, little is described concerning conceptualization process. We used a theoretical framework built upon constructivist foundations for analyzing mediated learning of specific geometrical concepts. Our point is illustrated in a case study in which we analyzed studentsí interaction with a DGS. Our results points to a clear mapping of potential conceptualization of geometry in software using

Theorem Justification and Acquisition in Dynamic Geometry: A Case of Proof by Contradiction

Theorem acquisition and deductive proof have always been core elements in the study and teaching of Euclidean geometry. The introduction of dynamic geometry environments,DGE (e.g., Cabri-Géomètre, Geometer's Sketchpad), into classrooms in the past decade has posed a challenge to this praxis. Student scan experiment through different dragging modalities on geometrical objects that they construct, and consequently infer properties(generalities, theorems) about the geometrical artefacts. Because of the inductive nature of the DGE, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical and epistemological concern. In this paper, we will describe and study a ‘Cabri proof by contradiction’ of a theorem on cyclic quadrilaterals given by a pair of 16 year-old students in a Hong Kong secondary school. We will discuss how their construction motivates a visual-cognitive scheme on `seeing' proof in DGE, and how this scheme could fit into the theoretical construct of cognitive unity of theorems proposed by Boero, Garuti and Mariotti(1996). The issue of a cognitive duality and its relation to visualization will be raised and discussed. Finally, we propose a possible perspective to bridge the experimental-theoretical gap in DGE by introducing the idea of a dynamic template as a visualizer to geometrical theorem justification and acquisition.postprin

Software tools for geometrical problem solving: potentials and pitfalls

Dynamic geometry software provides tools for students to construct and experiment with geometrical objects and relationships. On the basis of their experimentation, students make conjectures that can be tested with the tools available. In this paper, we explore the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, we show how dynamic software tools can not only scaffold the solution process but also help students move from argumentation to logical deduction. However, by reference to the work of less successful students, we illustrate how software tools that cannot be programmed to fit the goals of the students may prevent them from expressing their (correct) mathematical ideas and thus impede their problem solution

Dificultades en las demostraciones en geometría

La geometría enseñada trata de objetos teóricos pero pone también en juego representaciones gráficas, cuyo papel en el aprendizaje de la geometría es destacable. El dibujo puede ser considerado como un significante de un referente teórico, es decir, podemos pensar en un emparejamiento de un referente dado con todos sus dibujos. Al escoger un dibujo determinado, de todos los dibujos posibles del referente, se establece una relación entre un objeto geométrico y sus posibles representaciones. Las relaciones entre un dibujo y su referente construidas por un sujeto constituyen el significado, para este sujeto, de la figura geométrica asociada. Es allí donde radica la importancia de una representación geométrica correcta, centrando la atención sobre elementos pertinentes al objeto geométrico en cuestión. Es interesante analizar cómo las representaciones gráficas de objetos y conceptos geométricos producen muchas veces dificultades durante la resolución de problemas y en la demostración en Geometría. Pero no se puede ignorar que el proceso de trabajar con una representación clarifica, aporta detalles, provee un material sobre el cual es posible elaborar ideas y hacer correcciones y se convierte en un marco de referencia importante para la percepción. Así el software Cabri-Géometre; que permite una vez hecho el dibujo, moverlo, agrandarlo, cambiar los puntos de lugar... contribuyendo de manera notoria al desarrollo de la percepción, intuición y sentido estético; es un soporte para las actividades que requieran el planteo de conjeturas

111 propuestas en ambientes dinámicos que ponen en jaque imágenes conceptuales

Se presentan tareas centradas particularmente en el concepto de regularidad de polígonos y poliedros. Son diseñadas para un curso con estudiantes universitarios desarrollado en dos encuentros y planteado en un entorno dinámico. Del análisis de sus resoluciones vislumbramos que sus imágenes conceptuales no se ajustan a las definiciones de los conceptos de polígono regular y poliedro regular. Por ejemplo, concluyen que es suficiente que un polígono tenga todos sus lados iguales para afirmar que es regular o que un tetraedro con caras iguales es siempre regular. Se considera provechoso plantear en las tareas imágenes de lo extra matemático y a partir de ello focalizar en el concepto a estudiar. Las tareas se plantean de modo de abordar el contexto físico, a partir de plegado y modelos reales, y el contexto informático a través de un software de geometría dinámica