scholarly journals Exploring Properties of Quadrilaterals in the Poincaré Disk Model of Hyperbolic Geometry Using the Dynamic Geometry Software

2018 ◽  
Vol 13 (3) ◽  
Keyword(s):  
Hyperbolic Geometry ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Disk Model ◽  
Poincaré Disk

The Nature of Arguments Provided by College Geometry Students With Access to Technology While Solving Problems

2010 ◽  
Vol 41 (4) ◽  
pp. 324-350 ◽  
Author(s):  
Karen F. Hollebrands ◽  
AnnaMarie Conner ◽  
Ryan C. Smith
Keyword(s):  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Dynamic Geometry ◽  
Disk Model ◽  
Geometric Objects ◽  
Access To Technology ◽  
Poincaré Disk ◽  
Support Students

Prior research on students' uses of technology in the context of Euclidean geometry has suggested it can be used to support students' development of formal justifications and proofs. This study examined the ways in which students used a dynamic geometry tool, NonEuclid, as they constructed arguments about geometric objects and relationships in hyperbolic geometry. Eight students enrolled in a college geometry course participated in a task-based interview that was focused on examining properties of quadrilaterals in the Poincaré disk model. Toulmin's argumentation model was used to analyze the nature of the arguments students provided when they had access to technology while solving the problems. Three themes related to the structure of students' arguments were identified. These involved the explicitness of warrants provided, uses of technology, and types of tasks.

scholarly journals KONSISTENSI AKSIOMA-AKSIOMA TERHADAP ISTILAH-ISTILAH TAKTERDEFINISI GEOMETRI HIPERBOLIK PADA MODEL PIRINGAN POINCARE

EDUPEDIA ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 161
Author(s):  
Febriyana Putra Pratama ◽  
Julan Hernadi
Keyword(s):  
Half Plane ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Cross Ratio ◽  
Literature Study ◽  
Disk Model ◽  
Non Euclidean Geometry ◽  
The Cross ◽  
Definition Of ◽  
Poincaré Disk

This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012), Euclidean and Non Euclidean Geometry (Development and History)  by Greenberg (1994), Geometry : Euclid and Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle . Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two types. The first type is any open diameters of   . The second type is any open arcs of circle. Half-plane in Poincare disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by the cross-ratio as follows. The definition of distance from  to  is , where  is cross-ratio defined by  . Finally the study also is able to show that axioms of Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms.

scholarly journals MENINGKATKAN KEMAMPUAN SPASIAL SISWA MELALUI PEMBELAJARAN GEOMETRI BERBANTUAN CABRI 3D

2017 ◽  
Vol 2 (2) ◽  
pp. 179-194
Author(s):  
Eline Yanty Putri Nasution
Keyword(s):  
High School Students ◽  
Spatial Ability ◽  
Direct Instruction ◽  
Junior High School ◽  
Teaching And Learning ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Control Group ◽  
School Students ◽  
Ability Test

The purpose of this study are to investigate and to describe the gain of students‘ spatial ability through Geometry teaching and learning by using a dynamic geometry software, Cabri 3D. This study was a quasi experimental research with not equivalent control group design. Direct instruction was implemented in control group otherwise Geometry teaching and learning with using Cabri 3D was implemented in experimental group. The population of this study are all of the eight grade of junior high school students in one of the SMP Negeri in Padangsidimpuan City. The sample of this study were two groups of eighth grade. The sample has been choosed with using purposif sample technique. The instruments of this study were spatial ability test, quationere, observation sheet and interview. The test was analysed quantitatively and non test was analyzed qualitatively in order to answer the  the hypotesa, the gain of students’ spatial ability who has studied and lerant with using Cabri 3D is better than direct instruction.

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.

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