scholarly journals On the Learning of geometric concepts using Dynamic Geometry Software

RENOTE ◽  
2004 ◽  
Vol 2 (1) ◽  
Author(s):  
Alex Sandro Gomes ◽  
Gerard Vergnaud
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Theoretical Framework ◽  
Dynamic Geometry Software ◽  
Mediated Learning ◽  
Computer Mediated ◽  
Geometric Concepts ◽  
Geometrical Concepts ◽  
Geometry Learning

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.

scholarly journals Nature of metacognition in a dynamic geometry environment

2015 ◽  
Vol 3 (5) ◽  
pp. 627-646
Author(s):  
Ana Kuzle
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Dynamic Geometry Environment ◽  
Mathematics Problem Solving ◽  
Managerial Decisions ◽  
Metacognitive Processes ◽  
Geometry Problem ◽  
Mathematics Problem

This case study examined the metacognitive processes of a preservice teacher when solving a nonroutine geometry problem in a dynamic geometry environment. The main purpose of the study was to uncover and investigate patterns of metacognitive processes and to understand what circumstances, situations, and interactions in a dynamic geometry environment promoted metacognitive behaviors. An adaptation of Schoenfeld’s (1981) model of episodes and executive decisions in mathematics problem solving, and the theory of instrumentation (Rabardel, 2001) was used to identify patterns of metacognitive processes in a dynamic geometry environment. During different phases of problem solving the participant engaged in different metacognitive behaviors whereas the dynamic geometry software supported strategies that are available and/or not available on paper and pen. The effectiveness of solution paths was dependent on the presence of managerial decisions, and well-orchestrated usage of different resources, both knowledge and technology. However, the results of the study call to question to which extent engagement in metacognitive behaviors is necessarily desirable or productive.

scholarly journals Investigation of pre-service elementary mathematics teachers’ problem posing situations in dynamic geometry environment

2018 ◽  
Vol 9 (1) ◽  
pp. 125-148
Author(s):  
Birnaz Kanbur Tekerek ◽  
Ziya Argün
Keyword(s):  
Mathematics Teachers ◽  
Elementary Mathematics ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Problem Posing ◽  
Dynamic Geometry Environment ◽  
Spring Semester ◽  
Geometric Concepts ◽  
Multiple Case

This study examined problem posing situations of pre-service elementary mathematics teachers in dynamic geometry environment by using problem posing strategies. The qualitative method of multiple case study was applied and geometric concepts that participants used for each type of problem posing are examined. Eight participants from 3rd grade pre-service mathematics teachers voluntarily participated in the study in 2015-2016 fall semester had previously received Computer Aided Mathematics course in the 2014-2015 spring semester. During six weeks’ data collection period, participants tried to pose new problems via dynamic geometry software by using given problem posing situations and their studies were recorded by screen saving program. The relationship between the problems that given to them and the concepts in the new problems were examined through screen recordings. Findings show new problems are established in parallel with the shape or problem statement in the problem posing situations given to them. Compared with other types of problem posing situations, it is seen the concepts are more diversified in the free problem posing. Participants develop their problem posing skills during the process so it is suggested these topics should be included in mathematics education undergraduate program in order for future students to gain these skills.

“Click, Drag, Think!”

2013 ◽  
pp. 37-69
Author(s):  
Thomas Gawlick
Keyword(s):  
Conceptual Framework ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Advanced Case ◽  
Teaching Unit

The author points out that to fully exploit the heuristic potential of Dynamic Geometry Software (DGS) and to increase the heuristic literacy of students, extant DGS teaching units have to be ameliorated in several ways. Thus the author develops a twofold conceptual framework: heuristic reconstruction and heuristic instrumentation of problems. Its origin is rooted in the literature, its use is demonstrated by various examples, and its value is made plausible by an introductory teaching unit an advanced case study.

Online Interaction Styles

2010 ◽  
pp. 138-149
Author(s):  
Dazhi Yang ◽  
Jennifer C. Richardson
Keyword(s):  
Learning Environments ◽  
Online Courses ◽  
Mediated Learning ◽  
Online Interaction ◽  
Interaction Style ◽  
Interaction Styles ◽  
Computer Mediated ◽  
Vicarious Interaction ◽  
Active Interaction

Past studies indicate that students demonstrate different online interaction styles, which consist of the ways or habits students acquire knowledge from computer-mediated discussions (Sutton, 2001). Such interaction styles include the active interaction style (Beaudion, 2002), the vicarious interaction style (Sutton, 2001), and the mixed or balanced-interaction style. The purposes of this chapter are to: (1) examine relative studies on students’ online interaction styles; (2) propose a hypothesis that students’ online interaction styles can change during the course of computer-mediated discussion; (3) conduct a case study on students’ online interaction styles to test the hypothesis. This chapter reviews current issues related to students’ online interaction styles. It offers practical suggestions on the design of online learning environments, instructor’s role in online courses, and educational tools to facilitate students in adapting to more active interaction styles in computer-mediated learning environments.

Evaluating the Learning Effectiveness of Collaborative Problem Solving in Computer-Mediated Settings

2009 ◽  
pp. 151-167
Author(s):  
Ourania Petropoulou ◽  
Georgia Lazakidou ◽  
Symeon Retalis ◽  
Charalambos Vrasidas
Keyword(s):  
Problem Solving ◽  
Learning Environments ◽  
Evaluation Process ◽  
Collaborative Problem Solving ◽  
Learning Effectiveness ◽  
Computer Supported Collaborative Learning ◽  
Collaborative Problem ◽  
Problem Solving Environments ◽  
Computer Mediated

here is a growing need for systematic evaluations of computer-supported collaborative learning environments. The present chapter focuses on the evaluation of the learning effectiveness of the interactions that take place in computer-supported problem solving environments. This chapter emphasizes the need for supporting evaluators of such environments with holistic evaluation conceptual frameworks and tools that can facilitate the analysis of data gathered during the evaluation process. We discuss in detail such a holistic framework which has been tested through a primary education case-study.

scholarly journals A dynamic approach to quadrilateral definitions

Pythagoras ◽  
2004 ◽  
Vol 0 (59) ◽  
Author(s):  
Rajendran Govender ◽  
Michael De Villiers
Keyword(s):  
Mathematics Teachers ◽  
Sufficient Conditions ◽  
Dynamic Geometry ◽  
Secondary Mathematics ◽  
Necessary And Sufficient Conditions ◽  
Dynamic Geometry Software ◽  
Dynamic Approach ◽  
Secondary Mathematics Teachers ◽  
Geometric Concepts ◽  
Necessary And Sufficient

This study examined 18 prospective secondary mathematics teachers' understanding of the nature of definitions, and their use of the dynamic geometry software Sketchpad to improve not only their understanding of definitions but also their ability to define geometric concepts themselves. Results indicated that the evaluation of definitions by accurate construction and measurement enabled students to achieve a better understanding of necessary and sufficient conditions, as well as the ability to more readily find counter-examples, and to recognise and improve on uneconomical definitions.

From the Editorial Panel: Teaching Geometry

2011 ◽  
Vol 105 (4) ◽  
pp. 244
Keyword(s):  
Problem Solving ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Sense Making ◽  
Geometric Constructions ◽  
Natural Area ◽  
Teaching Geometry ◽  
Hands On

Geometry is a natural area for developing students' reasoning, visualization, and sense-making skills. Through the use of dynamic geometry software, students engage in hands-on explorations: They create and manipulate geometric constructions, they make and test conjectures, and they develop proofs. Geometry is found everywhere in our world, thus providing students with opportunities to connect geometric ideas with algebra through modeling and problem solving.

scholarly journals Análisis del aprendizaje de geometría espacial en un entorno de geometría dinámica 3-dimensional

2015 ◽  
Vol 9 (2) ◽  
pp. 53-83
Author(s):  
Ángel Gutiérrez ◽  
Adela Jaime
Keyword(s):  
Mathematics Education ◽  
Secondary School ◽  
Dynamic Geometry ◽  
Teaching Experiment ◽  
Dynamic Geometry Software ◽  
3 Dimensional ◽  
School Based ◽  
Space Geometry ◽  
Straight Lines ◽  
Geometry Learning

El creciente uso de software de geometría dinámica 3-dimensional plantea nuevas cuestiones a los investigadores en Educación Matemática. Para aportar información sobre el aprendizaje de geometría espacial en esta disciplina mediante entornos de geometría dinámica 3-dimensional, y sobre posibles fortalezas y debilidades de tales entornos, presentamos resultados de una investigación experimental en la que se analiza cómo un estudiante de altas capacidades matemáticas aprende conceptos relativos a paralelismo entre rectas y/o planos en el espacio mediante la resolución de actividades en un entorno de Cabri 3D.Analysis of space geometry learning in a 3-dimensional dynamic geometry environmentThe increasing use of 3-dimensional dynamic geometry software raises new questions to researchers in mathematics education. To contribute information about the learning of space geometry in Secondary School based on 3-dimensional dynamic geometry software environments, and about possible strengths and weaknesses of such environments, we present results from a teaching experiment designed to analyze a gifted student’s learning of concepts relative to parallelism between straight lines and/or planes in the space based on solving activities in a Cabri 3D environment.Handle: http://hdl.handle.net/10481/34155WOS-ESCINº de citas en WOS (2017): 1 (Citas de 2º orden, 0)Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 0)

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