University of Oslo
Open source, open collaboration and innovation
Benefits of FOSS in Education
with focus on GeoGebra
Authors:
Anastasia Parramore anastapa@ifi.uio.no
Amund Stramrud amundstr@sfe.uio.no
Mehdi Noroozi mehdin@ifi.uio.no
November 15, 2015
Abstract
In our initial research for this project we came across some interesting statistics, showing the awareness and usage of an open source software called GeoGebra.
According to these statistics only a few of the teachers had heard about GeoGebra,
and only around 10% of those said to have used it in the classroom [1]. The purpose
of this paper is therefore to explore open source software in an educational setting,
and why this can benefit both students and teachers. We will be looking into how
open source software can contribute to more engaged students and increased understanding of difficult problems, with the use of freely available software solutions.
More specifically we will be studying the mathematics software GeoGebra and its
usage in several countries and specifically Norway.
1
Introduction
Technology is becoming an increasingly big part of education in today’s society, and in
Norway the use of technology in education is common and in some cases even required
by the government [2]. As early as in the 1980s it was predicted that computer would
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become more and more integrated into mathematics teaching and learning, due to the
increasing accessibility of affordable technology in this era. Even though the development
wasn’t as rapid as predicted, the use of technology and the choices within this area is
wide.
Some of these choices are free and open-source software (FOSS). These computer programs have licenses that allow users to run the program, study, modify it and distribute
copies of the original version as well as their own modified version [3].
1.1
How can schools benefit from FOSS?
It’s believed that computers are beneficial in schools; for a long time now they have
been used to teach English, Math and some other subjects [4]. It’s difficult to collect all
the data on how students succeeded in the process of learning without using a computer.
FOSS is great in education first of all because it has lower costs than proprietary software
and therefore it can reduce the obstacles to the access of Information and Communication
Technologies. It’s very important because educational Institutions often have financial
restrictions.
The argument that FOSS has lower costs than proprietary software will differ depending on what kind of software it is. For instance the open source systems (like Moodle
or Linux), will require maintenance and have an elaborate installation process. Another
example is standalone softwares, like GeoGebra, which doesn’t require the user to do
anything other than installing and applying updates to the program. This of course,
doesn’t require as many resources.
Other than cost advantages there are a lot of other benefits in using FOSS in education,
one of them being pedagogical benefits. There are many ongoing projects through which
courses taught in universities become available online and teachers, students and selflearners anywhere in the world can have access to this material. The availability of this
data can encourage collaborative efforts and innovations in teaching. Students can use
it as an additional material to their program and teachers can built a more advanced
curriculum.
Other advantage is that large number of stakeholders are involved in FOSS development, so bugs are being very early discovered and rapidly fixed therefore software is more
reliable. In addition FOSS is considered to have better security and performance [5].
FOSS is also good for education because of the availability of source code, it’s open
not just for reading but also for modification, which might be very useful in computer
education. Students who learn programming can use FOSS projects as a virtual “laboratory”. This way instead of being taught specific tools students are taught how to learn
any tool [6].
Unfortunately in many school systems the software in use on computers is closed,
students are by implication forced to use illegal copies of the software [5]. Of course it
hinders process of learning and decreases level of motivation.
2
Case study: GeoGebra
GeoGebra is a community-supported open source mathematics program for educational
environments that joins geometry, algebra and calculus. From one point of view, Ge2
oGebra is an interactive geometry system. It gives opportunity to do constructions with
vectors, segments, points, lines, polygons and conic sections as well as functions while
modifying them dynamically afterwards. From another point of view, equations and coordinates can be entered directly. GeoGebra has the capability to work with variables
for numbers, vectors and points. It offers such commands as Vertex or Root and discovers derivatives and integrals of functions [7]. Thus GeoGebra was designed to combine
features of geometry programs and computer algebra systems in a single and easy touse software for learning and teaching mathematics from elementary through university
level [8]. Geogebra has familiarisations modules that allow students to learn how to use
the software [9].
The open-source nature of the project plays an important role for both pedagogues
and students. Learners are not obliged to use the software only in schools or universities
allowed by site licenses, like with commercial systems, they have a possibility to download
and install GeoGebra on their own personal computers. GeoGebra also gives the powerful
opportunity for teachers to create interactive online learning environments and many
teachers already shared free materials on the Internet [8].
Since May 2008 more than forty local GeoGebra institutes have been established
around the world by help of International GeoGebra Institute in order to provide help
and support to their local needs by gathering mathematicians and mathematics educators
to develop educational and professional materials. For example, the Norwegian GeoGebra
Institute in Trondheim consists of more than 50 people in a nation-wide network which
includes GeoGebra trainers, mathematicians, and mathematics educators who provide
help and support for teachers and collaborate on research projects in relation to the use
of free educational resources in Norway. There are also some projects ongoing regarding
the use of laptops and netbooks, like in Argentina in which the government by help of The
GeoGebra Institute in Buenos Aires has given out three million laptops with GeoGebra
pre-installed to students to use in the classroom. Similar projects are in progress in
Australia and Spain [10].
2.1
History
The system GeoGebra was originated at the University of Salzburg in 2002. During the
past years, software has evolved into an open-source project with a group of 15 developers
and more than 100 translators worldwide.
Version 3.2 of GeoGebra offers a lot of different dynamically linked representations for
mathematical objects through its graphical and algebraic views. Geogebra is translated
to 52 languages and it has received few educational software awards in Europe and the
USA. Beside main functions the system also gives possibility to create interactive web
pages with embedded applets. These demonstration environments are widely shared by
mathematics pedagogues on collaborative websites like the GeoGebraWiki. Number of
visitors of GeoGebra website is increasing rapidly, currently it is over 600.000 visitors per
month coming from 190 countries [11].
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2.2
Licensing
GeoGebra is licensed under the "GeoGebra Non-Commercial License Agreement" for noncommercial use, but for using the software commercially another license and collaboration
agreement must be agreed upon by contacting the GeoGebra Group.
The GeoGebra source code is licensed under the terms of the GNU General Public
License (version 3 or later) and is openly available to everyone. The GeoGebra language
files (including all user interface "translation" files in the GeoGebra application and applets), all GeoGebra documentation (including "GeoGebra Help", "GeoGebra Quickstart"
and all other documentation files found on the GeoGebra web servers) and all GeoGebra
user interface image and style files (including logos, icons and style sheets) are licensed
under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike licence (version 3.0 or later) [12]. GeoGebra includes open source libraries licensed under
the GNU General Public License (GPL), the LGPL, the Apache license and others [13].
Although the software is licensed under the GPU agreement but according to the
definition of the Free Software Foundation it can not be considered as free because some
elements of the software can not be used for free for commercial purposes [12].
3
Learning mathematics using GeoGebra
When learning mathematics using Geogebra students have more possibilities to examine,
test and analyze their knowledge. Users can connect formulas with their graphics thanks
to very valuable feature of the Geogebra package that allows mathematical formula and
corresponding graphic be seen together on the screen. Figure 1 picturizes the possibilities
of the GeoGebra package in investigating functions.
Figure 1: Graphs of the function and its derivatives [14].
This empowers the visualization of every step of the calculation and the visualization
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supports analyzing the properties of a function. Students have a possibility to make their
own conclusions on the basis of specific examples, therefore they improve their theoretical
knowledge.
The procedures of investigating functions without use of Geogebra are almost identical: student examine functions estimating their domain, monotonicity, extremes, etc.,
after that they show what they learned about the function by designing its graph. However work with GeoGebra empowers much more possibilities to investigate function. Students are enabled to arrange their learning in many different ways depending on their
knowledge and creativity.
Using GeoGebra students can see whether their knowledge is correct. They can have
an immediate feedback of the correctness of any information about the function and its
graph at any time, they can compare their own design with picture on the screen. This
empowers students to think more over the properties of the function.
From the discussing above it becomes clear that GeoGebra helps its users to create
complex knowledge about functions and their properties. This proves that GeoGebra
enables creating efficient learning environment for investigating functions and designing
their graphs [14].
3.1
Experiences of using GeoGebra in Calculus
Dynamic GeoGebra constructions and interactive figures were united into interactive
learning environments in a project for Australian high schools. Students had to discover
the concepts of derivatives and/or integrals by using several kinds of educational materials
as ‘traditional’ worksheets on paper, quizzes, applets. Several hundred students took part
when these learning environments were tested. In general participating student found the
dynamic and interactive material helpful to visualize and understand basic mathematical
concepts. Students described learning through GeoGebra with following statements: “It
is helpful when you see what is changing when you change something else”, “If you move
point B towards point A, you realize that the secant becomes the tangent line. With
a drawing on paper I never was able to visualize what this would look like.”, “You can
experiment a lot and try out a lot of things to find your own solution to problems.”
GeoGebra is widely used by students in middle and high school, mostly in Europe, but
its use in universities also arises. Some educators in the USA have published interactive
university-level calculus material on the Internet and they have stated that creating these
materials in GeoGebra was easier and faster than with other systems [8].
3.2
The effect of Geogebra on student achievement in teaching
of parameters
The results of the pedagogical experiment in Russia has shown that the use of GeoGebra
software has led to significant improvements in the performance of the assignment with
the parameters during the state exam 2012.
There was not only the increase of students’ understanding of graphics, but also
an increase of information knowledge, development of skills to effectively carry out the
processing, effective use of information in the educational activity, the development of
thinking, cognitive abilities, spatial imagination of students.
5
Students that have experience with using software GeoGebra are better prepared for
different parts of state exam. Also these students build the willingness to self-development
and continuing education as well as motivation to work and cooperation. Students gain
the ability to carry out project activities, ability to simulate real life situations, investigate
the constructed models and to interpret the outcoming result.
Students learn to work independently using this software and it allows to change
structure and organization of educational process, and that can improve the efficiency of
teaching. Usage of software Geogebra in schools improves quality of mathematics education, increases effectiveness of learning process and improves students’ perception [15].
3.3
The deficiencies of using GeoGebra
There might be some deficiencies/difficulties about using the software though, like for
example If students don’t have any previous programming experience it might be hard for
them to enter algebraic commands in the input box. Even though the primary commands
are not hard to learn, students might not know what to do and feel embarrassed. Also
some methodological approaches might not be suitable for all the students, for example,
not all the students can explore material and experiment independently [16].
4
GeoGebra from teachers’ perspective
Understanding the factors that influence the teachers’ use of technology for teaching and
educational purposes has a vital importance [17]. The usage of computers and technology
by teachers in the classroom depends on their knowledge and experience about technology.
They might use technology in several different ways from using it just for presentation
purposes to letting students to use a full range of technology resources [17]. Computer
Algebra Systems (CAS) helps students’ to improve their conceptual understanding as well
as their abilities to solve mathematical problems [18]. Dynamic mathematics software
offers the opportunity to both use the computer algebra system and dynamic geometry
software [19] [20]. In order to use Information and Communication Technologies (ICT)
in the classrooms teachers might need to improve their technological skills [21].
The main reason for using mathematical software including dynamic geometry systems
(DGA) like GeoGebra in mathematics classrooms is the creation of an experimental,
interactive and dynamic environment to enhance active learning [22]. Some teachers
have used GeoGebra to bring real life examples to the math classroom by means of
using example from the real world which are relevant to the field they are teaching.
Figure 2 shows an example in which the teacher has used the interesting case of Pisa
tower in Italy to teach her students about the usage of mathematics in real life [21].
GeoGebra also gives users the ability of web-publishing which could be used for building
interactive web pages in which students could play with complex mathematical concepts,
like fractals, without getting bored and learn new things every time they visit the web
site [21]. By using GeoGebra teachers can also actively involve students in the learning
process and it is specially useful in developing good learning environment. This is because
of the fact that students render the idea to reality more easier and more accurately
as a result of being exposed to simulation [23]. The utilization of GeoGebra can help
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students visualize abstract concepts and know the relationship in mathematics. The
ability to solve mathematical problems by means of using software tools can increase
cognitive abilities; for example GeoGebra can be used simultaneously to describe a linear
or quadratic function and its inversive, planning the mobile phones’ cycle, and sketching
of triangle prism [24].
Figure 2: Use of Pisa tower as a real life example [21].
There are four aspects that GeoGebra can contribute to the process of mathematics
teaching and learning:
1. Multiple display options: mathematical contents can be displayed in different
formats like from symbolic to graphic. For understanding mathematical ideas it is always
important to have good demonstration and visualization and clarity in the process of
learning and problem solving. Dynamic and visual tools allow mathematics to be explored
in the way that is actually used in the real life.
2. Experimental work: the possibility for students to use experimentation to gain
ideas, new knowledge and new ways of solving problems.
3. Elementarisation of mathematical methods: some elementary methods have been
abandoned due to complex calculations, while with GeoGebra as a construction tool
which has all the abilities demanded by a drawing software we can use those elementary
methods that are very important for teaching constructive geometry.
4. Connectivity: GeoGebra can be used by teachers as a cooperation, communication
and presentation tool by preparing teaching materials which opens new opportunities for
shared knowledge construction [25].
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There have been several studies about the usage of GeoGebra around the world which
have tried to see how is the reaction of teachers after using GeoGebra for the first time or
after using it for a while and what is their expectations from using the GeoGebra in their
mathematics classrooms. Generally the respondents has found GeoGebra pretty simple
and straightforward, both regarding the language and the ways symbols are used in the
software. The information is also displayed in a simple and understandable way. The instructions provided in GeoGebra are clear and don’t cause frustration and confusion from
the teachers’ point of view. They also believe that GeoGebra provides innovative ways
for teaching mathematical concepts like presenting the concept of circle in an entertaining way. The technique of presenting information by GeoGebra is very clear and concise
and well structured. GeoGebra is also helpful for meaningful learning and enhances long
term recalling of mathematical concepts by actually understanding the concepts by the
pupils rather than memorizing them. The following table shows some of the respondents’
responses in one of the studies in Malaysia [26] [27].
Figure 3: Some of the teachers’ opinions about GeoGebra [23].
5
Geogebra in Norway
For several years GeoGebra has been popular in Norway, and it has many norwegian
users. There are several reasons for this, but the most compelling reason might be the
fact that it has been available in norwegian since 2006, the same year as “digital literacy”
became labeled as a basic skill in the norwegian schools national curriculum [28]. In
addition to this, several norwegian textbooks and online platforms encourages the use of
GeoGebra in their examples.
Because of the increased popularity and use of GeoGebra the Norwegian GeoGebra
Institute (NGI) was established in 2008 [28]. NGI is part of the International GeoGebra
Institute, with several main goals; e.g.:
• Develop freely available GeoGebra resources.
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• Offer courses and workshops for teachers.
• Contribute to national and international cooperation and further research of GeoGebra and other digital tools for educational purposes.
In Norway the use of GeoGebra is by teachers, mainly for demonstration and illustration of various mathematical problems, in addition to being a tool for which students
can solve traditional mathematical problems. Teachers can also use GeoGebra to give
assignments to students, or for the students personal exploration and experimentation
within the world of mathematics [28]. The end goal of this is to further increase the
interest and motivation for mathematics at an early age.
GeoGebra is also mentioned as one of the main softwares to use for written digital
exams in mathematics, and starting from the spring semester of 2015 GeoGebra is part
of the examination in years 10-13 in the norwegian school system [29].
Figure 4: Example from an exam using GeoGebra [28].
In 2010 the Nordic GeoGebra Network (NGGN) was established, to build a stronger
community around the use of GeoGebra. This is a nordic/baltic cooperation project, with
7 partners, getting financial backing from Nordplus Horizontal to hold conferences and
seminars. The most recent conference focused on screencasting and flipped classrooms.
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They are currently increasing their network to also include schools [28].
6
Conclusion
During the whole history, humanity has fought for knowledge and it is so incredible
how just a few centuries ago people discovered new things without any universities or
laboratories. Then humanity had to fight for asses to knowledge as not all segments of
the the population was able to get access to even secondary education, let alone higher
education.
Nowadays it has become much easier to gain knowledge, especially with the appearance of FOSS educative programs. In this article we gave an overview of how FOSS
systems contribute to the education. FOSS has no or lower costs compared to proprietary software which makes it available in poor countries where teachers’ salaries are
relatively low and parents of most students cannot afford paying for expensive softwares.
As an example of educative FOSS program we looked into mathematical system called
GeoGebra.
GeoGebra has a dramatic effect on teaching of mathematics. Several studies show
that teachers get lots of benefits from using the software in their classrooms, though
there might be a challenging task for the teachers who are not that much familiar with
ICT and do not have enough knowledge about the computers. These teachers must
first or simultaneously improve their technological skills to take the most benefit of the
software.
Generally the main reason for using mathematical software including dynamic geometry systems (DGA) like GeoGebra in mathematics classrooms is the creation of an
experimental, interactive and dynamic environment in which students can learn mathematics by experimenting and sometimes even by using the real life examples which are
more tangible for them. In this way the students will learn deeply and the process of recalling the knowledge in the future will be easier for them, and at the same time this will
solve one of the most important problems of the teachers which is the students distraction
and lack of focus in mathematics classes.
There are also some aspects that GeoGebra can contribute to the process of mathematics teaching and learning like displaying the content in different formats, giving the
experimentation opportunities to students, elementarisation of mathematical methods,
and the connectivity and sharing ability for teachers.
In Norway there has been an increased focus on motivating students in the classroom
for the last 10 years, and GeoGebra is contributing a great deal to this. It’s been established a network for the sole purpose of making GeoGebra better, and it has already
seen use in mathematical examination on high school level. There is still a long way to
go, but we are happy to see the adaption of both technology and FOSS to help form the
next generations.
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