# Educational Impact GeoGebra

## Introduction

GeoGebra refers to a free and interactive geometry, statistics, algebra and calculus application software intended for making the process of learning and teaching mathematics and science easier on all levels of education. It was developed by Markus Hohenwarter in 2018. According to Microsoft (2019) the application can easily graph functions and find special points of functions as well as solve equations, save and share the results to any individual with the application over the internet. Given the wide range of the global population using the application spanning millions the application presents a platform for learning as well as teaching mathematics that is easily accessible despite the geographical location of an individual around the globe.

## Usage of Geogebra software

Geogebra.Org (2019) points out among the applications functions and capabilities to include: Plotting functions of both polar and parametric curves, experiencing transformation with sliders, identification of special points of functions such as roots, intersections, min, max…, solving equations, finding derivatives an integrals as well as developing regressions with best fit lines. The applications logarithm basically provides the basis of teaching and solving functions. The conceptualization of the software was based on making easier the process of learning functions, as such the software was designed specifically for educational purposes and can be of assistance to enable students grasp experimental, research oriented as well as problem oriented learning of mathematics both in the classroom as well as outside of it.

The integration of the software into teaching of functions was fundamentally due to the development of the software with similar concepts and principles base lining functions algebra and calculus. According to Dikovic (2009), GeoGebra supports constriction of geometry with points, lines as well as conic sections. The basic idea of the applications interface includes the presentation of each mathematical object in its algebraic and geometric representation in two different windows. As such the student can be able to trace the relationship and construction process of determining the solution. Altering an object in one representation automatically adjusts the presentation in the other window which expresses the effect of altering different parts of the functions enhancing the students understanding of linear functions.

While a wide variety of computer software exist for developing solutions to functions and other mathematical problems, for instance Algebra software such as Mathematica and Maple as well as dynamic geometry software such as Cabri Geometry and Geometers sketchpad, Ruthven and Hennessey (2004) highlight that the major problem has always been developing technology that enables the integration of technology into teaching. GeoGebra was integrated into the teaching process of functions and Algebra in a number of different ways.

It has a more user friendly interface which offers easier to use and understand multi lingual menus and commands, it also enables students to engage in different projects in mathematics as well as multiple presentations and experimental and guided discovery learning, further students can personalize their own creation into the most understandable format that impacts on their easier understanding of different concepts being taught through adjusting the quality of graphics, the color of the graphics, font size, language, line style coordinates, line thickness and a wide range of other features. Agyei and Benning (2015) point out that student can manipulate variables easily through simply dragging objects across the plane of the drawing or by using sliders, this enables students to get a better understanding of mathematics through graphs and diagrams. Through the investigation of the dynamic relations between mathematical objects, for example through generating changes using the technique of manipulating objects to determine the effects of the dependent objects, a student can easily develop solutions to problems of linear functions using intercepts.

According to Dubinsky and Schwingendorf (2004), the process of lecturing mathematics is ineffective and should be effectively replaced with a more interactive, task oriented classroom. They highlight that the primary role of teaching mathematics is not to transfer mathematical knowledge, lecture or explain mathematical content but rather to foster the ability to solve problems within the students themselves through the creation of situations enable them to make necessary mental constructions. GeoGebra provides cooperative learning as well as cooperative problem solving in big as well as small groups. Further GeoGebra stimulates teachers to assess and use technology on visualization of mathematics, investigation in mathematics as well as interactive mathematics classes that enables a more efficient outcome of the teaching process.

## Advantage of using the software

GeoGebra allows easier plotting of mathematical and scientific functions to enable the investigation of the relationship of different variables and be able to solve linear equations. The simplicity of use and control of the software enables it to be used by individuals in different education levels from the primary to the tertiary level as such its integration is viable throughout the learning process (Majerik, 2014). He further highlights that other than the basic capabilities of GeoGebra such as drawing, lines, figures and functions, the software can also be used to calculate or measure angles, points of interceptions, circumferences, lengths, fields and many others, making it a one stop efficient point for learning functions and all the concepts related to the functions themselves.

However, while the software has been developed in a light way and thus easier for students to comprehend its functionality, the role of the teachers in enabling proper teaching cannot be overlooked especially considering the integration of GeoGebra into teaching functions is facilitated by them. Agyei and Bennings (2015) point out that teachers play a particularly essential role in the learning of the students and as such the teachers professional development highlighted as the most effective strategy to enhance teaching, involving comprehensive, intensive and effective approaches in raising a teachers familiarity with the requisite skills and the content they are teaching is key in enhancing students understanding. In mathematics and science GeoGebra plays an important part in the teachers’ professional development especially with the teaching o functions, algebra and calculus.

In summation, current trends in the teaching of science and mathematics call for interactive and visualization techniques to which GeoGebra fits in perfectly highlighting its benefits and need for utilization by all students and teachers in learning functions.

## References

• Agyei D. D. and Benning I. (2015). Pre-service eachers' use and perceptions of GeoGebra software as an instructional tool in teaching mathematics. Journal of Educational Development and Practice (JED-P), 5 (1), pp. 14-30
• Dikovic, L. (2009). Applications GeoGebra into teaching some topics of mathematics at the college level. Computer Science and Information Systems, 6(2), pp.191-203.
• GeoGebra.Org (2019). GeoGebra | Free Math Apps - used by over 100 Million Students & Teachers Worldwide. [online] GeoGebra. Available at[Accessed 22 Jan. 2019].
• Majerek, D. (2014). APPLICATION OF GEOGEBRA FOR TEACHING MATHEMATICS. Advances in Science and Technology Research Journal, 8, pp.51-54.
• Microsoft (2019). Get GeoGebra Graphing Calculator - Microsoft Store. [online] Microsoft Store. Available at:
• Ruthven K. and Hennessy S. (2004). Teacher Representations of the successful use of computer based tools and resources in secondary schools, English, Mathematics and Sciences, Teaching and Teacher Education, 20(3), pp 259-275

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