scholarly journals Visualization of Functional Dependences in Dynamic Geometry Systems

2020 ◽  
pp. 93-112
Author(s):  
Vladimir Dubrovskii ◽  
Keyword(s):  
Teaching And Learning ◽  
Dynamic Geometry ◽  
Computer Models ◽  
School Mathematics ◽  
Geometer's Sketchpad ◽  
Geometric Transformations ◽  
Learning Functions ◽  
Dynamic Geometry Systems

We describe various methods of visualization of functions and geometric transformations encountered in school mathematics by means of the dynamic geometry systems such as MathKit, The Geometer’s Sketchpad, and GeoGebra and their usage scenarios in the spirit of modern trends in education. Novel opportunities for teaching and learning functions and their properties based on computer models are discussed. The focus is on specifically computerized interpretations of functions, in particular, the so-called dynagraphs, in which parallel axes of arguments and values are used, and the correspondence given by the function is found when the argument-point moves along its axis.

Developing Pre-service Secondary Teachers' Skills of Using the Geometer's Sketchpad to Teach Mathematics through Lesson Study

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Chew Cheng Meng ◽  
Lim Chap Sam ◽  
Wun Thiam Yew ◽  
Lim Hooi Lian
Keyword(s):  
Secondary Teachers ◽  
Lesson Study ◽  
Teaching And Learning ◽  
Dynamic Geometry ◽  
Two Dimensions ◽  
Dynamic Geometry Software ◽  
Methods Course ◽  
Geometer's Sketchpad ◽  
Set Up ◽  
Mathematics Teaching Methods

The purpose of this study was to develop pre-service secondary teachers’ skills of using The Geometer’s Sketchpad (GSP) to teach mathematics through Lesson Study (LS). GSP is a dynamic geometry software program for constructing and investigating mathematical objects that adds a powerful dimension to the teaching and learning of geometry and many other areas of mathematics. Lesson Study is a Japanese model of teacher professional development in which small groups of teachers collaboratively plan, teach and revise a lesson to improve the quality of their teaching as well as to enrich students’ learning experiences. Twenty-three LS groups comprising 2 pre-service secondary teachers who attended a mathematics teaching methods course in a local public university were set up in four tutorial groups each consisting of five or six LS groups. This paper discusses how LS has helped to develop pre-service secondary teachers’ skills of using GSP to teach the topic of ‘Loci in Two Dimensions’ in one of the LS groups. Analysis of their GSP sketches in the first, second and third lessons indicates that the participants of this LS group showed positive changes in their skills of using GSP to teach the topic.

Towards Digital Competencies in Mathematics Education

2012 ◽  
Vol 3 (2) ◽  
pp. 1-19 ◽  
Author(s):  
Egle Jasute ◽  
Valentina Dagiene
Keyword(s):  
Digital Technology ◽  
Teaching And Learning ◽  
Dynamic Geometry ◽  
Dynamic Geometry Software ◽  
Digital Music ◽  
Geometer's Sketchpad ◽  
Digital Resources ◽  
Video Cameras ◽  
Digital Competencies ◽  
Digital Equipment

Technological innovation has influenced learning, and teachers have suggested different ways of use for digital equipment, to improve learning and to achieve better outcomes from their students. Today’s youth has grown up with digital technology and has lived immersed in environments populated by computers, video games, digital music players, video cameras, cell phones, and thousands of other toys and tools of the digital age. It is for this reason that the authors are persuaded that education in the 21st century should be directed to use digital resources as well as digital ways of teaching in all subjects. Mathematics needs digitization and the paper deals with the development of dynamic sketches for geometry teaching and learning. The concept of dynamic geometry is introduced and discussed together with problems and examples of application of dynamic geometry software. The model for interactive geometry visualization is described and the implementation of this model is reported. Together with former topics an experimental research is presented, which is based on the use of the interactive pre-constructed sketches by the dynamic geometry software Geometer’s Sketchpad. At last the didactical approach of the experiment is analyzed, the results of the experience are described and conclusions and discussions are proposed.

Technology Tips: Multiple Representations Using Dynamic Geometry

2009 ◽  
Vol 103 (2) ◽  
pp. 146-150
Author(s):  
Michael A. Tamblyn
Keyword(s):  
Teaching And Learning ◽  
Regular Polygon ◽  
Multiple Representations ◽  
Dynamic Geometry ◽  
Geometric Object ◽  
Geometer's Sketchpad ◽  
Geometric Concepts ◽  
Relationship Of ◽  
The Relationship

The power of The Geometer's Sketchpad® (GSP) for teaching and learning lies in its potential for enabling students to explore geometric concepts and recognize relationships among these concepts as illustrated through the use of multiple representations. This article explores two problems and examines how the use of tables along with GSP sketches may assist students in understanding these concepts. The first activity investigates the relationship of the length of a trapezoid's median (or midsegment) to that of its bases. The second involves showing how the area of a regular polygon approaches that of a circle when the number of sides increases. In both activities, we will start with the geometric object, look at the measurements, tabulate these, and make a graph to illuminate the situation.

scholarly journals The Effect of Geogebra on Students’ Conceptual and Procedural Knowledge: The Case of Applications of Derivative

2017 ◽  
Vol 7 (2) ◽  
pp. 67 ◽  
Author(s):  
Mehmet Fatih Ocal
Keyword(s):  
Conceptual Knowledge ◽  
Teaching And Learning ◽  
Procedural Knowledge ◽  
Dynamic Geometry ◽  
The Other ◽  
Control Group ◽  
Other Hand ◽  
Significant Difference ◽  
Before And After ◽  
Post Test

Integrating the properties of computer algebra systems and dynamic geometry environments, Geogebra became an effective and powerful tool for teaching and learning mathematics. One of the reasons that teachers use Geogebra in mathematics classrooms is to make students learn mathematics meaningfully and conceptually. From this perspective, the purpose of this study was to investigate whether instruction with Geogebra has effect on students’ achievements regarding their conceptual and procedural knowledge on the applications of derivative subject. This study adopted the quantitative approach with pre-test post-test control group true experimental design. The participants were composed of two calculus classrooms involving 31 and 24 students, respectively. The experimental group with 31 students received instruction with Geogebra while the control group received traditional instruction in learning the applications of derivative. Independent samples t-test was used in the analysis of the data gathered from students’ responses to Applications of Derivative Test which was subjected to them before and after teaching processes. The findings indicated that instruction with Geogebra had positive effect on students’ scores regarding conceptual knowledge and their overall scores. On the other hand, there was no significant difference between experimental and control group students’ scores regarding procedural knowledge. It could be concluded that students in both groups were focused on procedural knowledge to be successful in learning calculus subjects including applications of derivative in both groups. On the other hand, instruction with Geogebra supported students’ learning these subjects meaningfully and conceptually.

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 Preparing In-Service Teacher Using Dynamic Geometry Software

2018 ◽  
Vol 7 (4.30) ◽  
pp. 367
Author(s):  
Fariz Setyawan ◽  
Yosep Dwi Kristanto ◽  
Naufal Ishartono
Keyword(s):  
Professional Development ◽  
Learning Process ◽  
Teaching And Learning ◽  
Dynamic Geometry ◽  
Development Program ◽  
Dynamic Geometry Software ◽  
Professional Development Program ◽  
Skills Transfer ◽  
Teachers Perceptions ◽  
Use Of Technology

The use of technology is essential in teaching and learning process. Many researchers have already been implemented Dynamic Geometry Software (DGS) in teaching and learning process. Given the importance of DGS, it is necessary for in-service teachers to use the software in their teaching and learning. Hence, it is important to prepare in-service teacher in utilizing DGS through the professional development program. This is a qualitative research which describes a professional development program to facilitate in-service teachers in utilizing DGS. Both questionnaire and review measured in-service teachers’ perceptions, knowledge and skills transfer, and impact for their practice. From the findings, four of five in-service teachers recognized that they can interact with geometric figures to move on to the next level by using DGS. The teachers felt that DGS has helped them to understand the mathematics concept and demonstrate their understanding in front of the class. Besides, DGS does not only offer opportunities for teachers and students to use them both at home and in the classroom, but they also provide a means for developing support and user communities reaching across borders especially in understanding of geometrical transformation. It has contributed that the teachers easily recognize the geometrical shapes interpretations dynamically on DGS.

scholarly journals Reasoning by contradiction in dynamic geometry

2013 ◽  
Vol 7 (2) ◽  
pp. 63-73
Author(s):  
Anna Baccaglini-Frank ◽  
Samuele Antonini ◽  
Allen Leung ◽  
Maria Alessandra Mariotti
Keyword(s):  
Dynamic Geometry ◽  
Proof By Contradiction ◽  
Dynamic Geometry Systems ◽  
Indirect Argument

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students’ work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we support the claim that a DGS can offer guidance in the solver’s development of an indirect argument thanks to the potential it offers of both constructing certain properties robustly, and of helping the solver perceive pseudo objects.Razonamiento por contradicción en geometría dinámicaEste artículo aborda las contribuciones que los sistemas de geometría dinámica (DGSs) pueden dar al razonamiento por contradicción en geometría. Presentamos un análisis de tres extractos del trabajo de estudiantes y el uso de la noción de pseudo-objeto, elaborado a partir de investigaciones anteriores, para mostrar algunas especificidades del DGS en la construcción de pruebas por contradicción. En particular, afirmamos que un DGS puede orientar en el desarrollo de un argumento indirecto gracias a las posibilidades que ofrece tanto para construir sólidamente algunas propiedades como para ayudar a percibir los pseudoobjetos.Handle: http://hdl.handle.net/10481/22368Nº de citas en WOS (2017): 2 (Citas de 2º orden, 4)Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 5)

Bringing Dynamic Geometry to Three Dimensions

2015 ◽  
pp. 68-99
Author(s):  
Nicholas H. Wasserman
Keyword(s):  
Teaching And Learning ◽  
Spatial Reasoning ◽  
Mathematics Classroom ◽  
Three Dimensional ◽  
Dynamic Geometry ◽  
State Standards ◽  
Three Dimensions ◽  
Two Dimensional ◽  
The Common ◽  
K 12

Contemporary technologies have impacted the teaching and learning of mathematics in significant ways, particularly through the incorporation of dynamic software and applets. Interactive geometry software such as Geometers Sketchpad (GSP) and GeoGebra has transformed students' ability to interact with the geometry of plane figures, helping visualize and verify conjectures. Similar to what GSP and GeoGebra have done for two-dimensional geometry in mathematics education, SketchUp™ has the potential to do for aspects of three-dimensional geometry. This chapter provides example cases, aligned with the Common Core State Standards in mathematics, for how the dynamic and unique features of SketchUp™ can be integrated into the K-12 mathematics classroom to support and aid students' spatial reasoning and knowledge of three-dimensional figures.

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