A Brief Review of Dynamic Mathematics Software GeoGebra in Local and Global Context.

                                                                          GeoGebra

Abstract

This review presents new trends in technology and learning through Geogebra, which could be especially important for the future development of e-learning for school and College mathematics. GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level.  Dynamic geometry software is computer programs which allow one to visualize abstract concepts as figures and dynamic representations on a computer screen.  Traditional methods of teaching and learning are still dominant in Nepal. Normally, teachers distribute knowledge and skills to their students who in turn memorize facts, definitions, and algorithms. The paper- pencil method has a dominant role as a mathematical tool. Technology has a minimal to nonexistent role at schools in Nepal. The open source software GeoGebra provides an easy way to create interactive and dynamic web pages. In this article we explain how this is done and present first experiences of the use of this new tool for teaching mathematics at the college level. Geogebra is rapidly gaining popularity in the teaching and learning of mathematics around the world.

Key Words: Dynamic Geometry Software, GeoGebra, local and global, Mathematics.

Table of Contents

Introduction. 1

Background of the study. 1

Objectives of the study. 3

Methods of study. 3

Use of GeoGebra software in Nepalese Context. 3

Use of GeoGebra Software in Global Context. 4

GeoGebra Main Features. 5

Discussion. 6

Conclusion. 8

References. 9

Introduction

Background of the study

The software GeoGebra originated in the master’s thesis project of Markus Hohenwarter at the University of Salzburg in 2002. It was designed to combine features of interactive geometry software (e.g. Cabri Geometry, Geometer’s Sketchpad) and computer algebra system (e.g. Derive, Maple) in a single, integrated, and easy to use system for teaching and learning mathematics (Hohenwarter & Preiner, 2007a). During the past years, GeoGebra has developed into an open-source project with a group of 15 developers and over 100 translators all over the world.

The current version, GeoGebra 6.0.4, offers dynamically linked multiple representations for mathematical objects through its graphical, algebraic, and spreadsheet views. The software, which is currently available in 52 languages, has received several educational software awards in Europe and the USA (e.g. EASA 2002, digita 204, Comenius 2004, eTwinning 2006, AECT 2008, BETT 2009 Finalist, eureleA 2009 Finalist, Tech Awards 2009, NTLC 2010, MERLOT Award 2013, Archimedes 2016). Apart from the standalone application, GeoGebra also allows the creation of interactive web pages with embedded applets (Hohenwarter & preiner, 2007b). These targeted learning and demonstration environments are freely shared by mathematics educators on collaborative online platforms like the GeoGebraWiki (www.geogebra.org/wiki). Since 2004, the number of visitors to GeoGebra’s Website has increased from 7,000 per month to currently over 100 million per month coming from 190 countries.

GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level.

GeoGebra is available on multiple platforms with its desktop applications for Windows, macOS and Linux, with its tablet apps for Android, iPad and Windows, and with its web application based on HTML5 technology. Its creator, Markus Hohenwarter, started the project in 2001 (as part of his master's thesis) at the University of Salzburg, continuing it at Florida Atlantic University (2006–2008), Florida State University (2008–2009), and now at the University of Linz together with the help of open-source developers and translators all over the world. After a successful Kickstarter campaign, GeoGebra expanded their offerings to include an iPad, an Android and a Windows Store app version. In 2013, Bernard Parisse's Giac was integrated into GeoGebra's CAS view. GeoGebra includes both commercial and not-for-profit entities that work together from the head office in Linz, Austria, to expand the software and cloud services available to its user community (Wikipedia, 2018).

According to ( Key & Mainali, 2013)Traditional methods of teaching and learning are still dominant in Nepal, so professional development in more modern pedagogical practice is an area deserving close attention. As it is, teachers ‘distribute’ knowledge and skills to their students who in turn memorize facts, definitions, and algorithms, but who have little or no practice in thinking for themselves. In an effort to begin some small change in the present situation, in 2008 the first author began a professional development initiative targeting Nepalese mathematics teachers to introduce them to the Dynamic Geometry Software (DGS) package, GeoGebra. Over a three year period some small trainings were provided on an ad hoc basis to teachers hearing about them by word-of-mouth. This initiative culminated in a training package supported by the National Teachers Association. To enable teachers in this, basic skills and knowledge of computer use are essential in order to work with dynamic software like GeoGebra successfully. Nepal to provide an overview of GeoGebra and its possible integration in the teaching/learning of secondary school mathematics there. Teachers’ impressions and beliefs concerning both the training and the software were researched in the context of applicability in Nepalese schools.

Objectives of the study

            This study was intended to accomplish the following objectives.

·         To identify about dynamic mathematics software GeoGebra in local and international Context.

·         To find out brief review of GeoGebra.

·         To explore students and teacher attitudes towards the use of GeoGebra Software in mathematics teaching and learning.

Methods of study

Use of GeoGebra software in Nepalese Context

Nepalese education is strongly influenced by content and by examination-driven practices, with little or no attention paid to encourage students to use their knowledge and skills to solve practical problems, or to try to access their own, already acquired knowledge and construct new ideas. Currently, Information and Communication Technology (ICT) has a minimal to nonexistent role at secondary school level in Nepal. There is no clear vision regarding the use of ICT in the classroom by either teachers or students. Although the government of Nepal has initiated a school reform project in which ICT-assisted and “child-friendly” teaching/learning are encouraged in all schools. GeoGebra is freeware, written in Java, and easily downloadable software from the internet for the purpose of the study of geometry, algebra, calculus at the different level.

The potential for using GeoGebra to teach and learn mathematics in Nepal is very large. In an effort to begin some small change in the present situation, in 2008 the first author began a professional development initiative targeting Nepalese mathematics teachers to introduce them to the Dynamic Geometry Software (DGS) package, GeoGebra. Over a three year period some small trainings were provided on an ad hoc basis to teachers hearing about them by word-of-mouth. This initiative culminated in a training package supported by the National Teachers Association. Two overarching concerns were as follows. Teachers in this study showed positive impressions and were motivated to learn to use GeoGebra, but most were not ready to integrate it in their mathematics teaching.

Use of GeoGebra Software in Global Context

GeoGebra is an interactive mathematics software program for learning and teaching mathematics and science from primary school up to university level. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards. Elements can be entered and modified directly via mouse and touch, or through the Input Bar. GeoGebra has the ability to use variables for numbers, vectors and points, find derivatives and integrals of functions and has a full complement of commands like Root or Extremum. Teachers and students can use GeoGebra to make conjectures and to understand how to prove geometric theorems.

Dynamic GeoGebra applets can be directly uploaded to the GeoGebra Materials platform, the official cloud service and repository of GeoGebra related and interactive learning and teaching resources. GeoGebra Materials was initially launched under the name GeoGebraTube in June 2011 and renamed in 2016. With recent improvement and extended functionality the service now hosts more than 1 million resources (April 2016), 400,000+ of which are shared publicly as searchable materials  such as interactive worksheets, simulations, games, and e-books created using the GeoGebraBook feature. The International GeoGebra Institute (IGI) is the not-for-profit entity of The GeoGebra Group, coordinating deployment and research efforts across a global network of user groups at universities and non-profit organizations. IGI joins teachers, students, software developers and researchers to support, develop, translate and organise the GeoGebra related tasks and projects. The local user groups support students and teachers in their region.

GeoGebra Main Features

GeoGebra is dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easy-to-use package. GeoGebra is a rapidly expanding community of millions of users located in just about every country. GeoGebra has become the leading provider of dynamic mathematics software, supporting science, technology, engineering and mathematics (STEM) education and innovations in teaching and learning worldwide. The main feature are

ü  Interactive geometry environment (2D and 3D)

ü  Built-in CAS and spreadsheet

ü  Built-in statistics and calculus tools

ü  Allows scripting

ü  Large number of interactive learning and teaching resources at GeoGebra Materials

ü  Graphics, algebra and tables are connected and fully dynamic

ü  Easy-to-use interface, yet many powerful features

ü  Authoring tool to create interactive learning materials as web pages

ü  Available in many languages for our millions of users around the world

ü  Free and open source software Geometry, Algebra and Spreadsheet are connected and fully dynamic

ü  Easy-to-use interface, yet many powerful features

ü  Authoring tool to create interactive learning materials as web pages

ü  Available in many languages for our millions of users around the world .

Discussion

Nepal is still at an early stage of developing countries. Nepal teacher association do not collaboration of international GeoGebra institute. It research and collaborations may be provide a real opportunity for teachers to rethink fundamental pedagogical issues in teaching and learning of Mathematics along with the approaches to learning that students need to apply in classrooms. There is a need to integrate GeoGebra use in Mathematics curriculum in Nepal so that learners can access a better way of learning Mathematics especially Geometry and geometrical connections of other concepts, and teachers can have a stronger sense of the technology’s utility and connection to learning outcomes. In this digital era, Nepal mathematics society collaboration in future mathematics content knowledge, pedagogical content knowledge include to technology.

Geogebra is rapidly gaining popularity in the teaching and learning of mathematics around the world. According to ( Yüksel & Çıldır, 2015)  Hohenwarter (2006) defined GeoGebra, known as dynamic geometry software, as “a computer based tool which provides active, experimental and exploratory instruction with the help of symbolic links and which offers many opportunities in this respect”. Beyond defining it as dynamic geometry software, described GeoGebra as a bridge between computer algebra systems and dynamic geometry software. The main aims of IGI

ü  Training and Support: To coordinate and provide professional development opportunities and support for both pre-service and in-service teachers.

ü  Development and Sharing: To develop and share workshop resources and classroom materials, and to continually improve and extend the dynamic mathematics software GeoGebra.

ü  Research and Collaboration: To conduct and support GeoGebra-related research which focuses on the teaching and learning of mathematics in order to inform and improve training and development activities, and to promote collaboration between IGI and local GeoGebra Institutes and between international colleagues.

GeoGebra is an easy-to-use and versatile tool that seems especially useful for undergraduate college level courses like geometry or calculus. As a multi-platform open source software it is available for everyone everywhere which makes it easy to use this tool for homework assignments too. The export of html pages for creating interactive teaching materials can both support classroom demonstration for dynamic visualizations and active student participation through dynamic worksheets ( Hohenwarter & yi, 2007).

Conclusion

Positive impressions and attitudes are simply not sufficient for teachers to be able to integrate a digital learning environment like GeoGebra in a mathematics classroom. Improving teachers’ pedagogical content knowledge to include technical skill and knowledge, and doing this through professional development combined with some local support, appears to be the way forward, particularly in the context of countries like Nepal. The use of GeoGebra in mathematics provides an ample opportunity to each individual for unlocking creativity step by step through active participation. And it up-rises students’ curiosity because GeoGebra helps students to reconstruct their existing state of knowledge and enforces them to engage in inquiry based activities such as searching application of construction.

I highlighted some opportunities and examples on how GeoGebra can be used in classrooms to explore some basic concepts in linear algebra and calculus. It was showed that GeoGebra has many possibilities to help students to get an intuitive feeling and to visualize adequate math process. The use of this software’s tools allows students to explore a wider range of function types, and provides students to make the connections between symbolic and visual representations.

References

Hohenwarter, M., & yi, T. (2007). Incorporating GeoGebra into teaching mathematics at the college level.

Key, M. B., & Mainali, B. R. (2013). Using dynamic geometry software GeoGebra in developing countries:A case study of impressions of mathematics teachers in Nepal.

Yüksel, N. S., & Çıldır, S. (2015). The Impacts of Dynamic Geometry Software on Graphing Abilities.

Hohenwarter, M., & Preiner, J. (2007a). Creating mathlets with open source tool. journal of online mathematics and its applications, 7.

Hohenwarter, M., & preiner, J. (2007b). dynamic mathematics with GeoGebra. journal of online mathematics and its applications, 7.

Wikipedia. (2018, august 09). Wikipedia. Retrieved from www.eikipedia.org: https://en.wikipedia.org/wiki/GeoGebra