Received June 2017.
Volume 10, Number 3, 2017
PRE-SERVICE MATHEMATICS TEACHERS’ VIEWS
ABOUT GEOGEBRA AND ITS USE
Tuğba Horzum, Melihan Ünlü
Abstract: The purpose of this study was to determine the views of pre-service Mathematics
teachers’ (PMTs) about GeoGebra and its use after being exposed to GeoGebra activities
designing processes. This is a case study which was conducted with 36 PMTs. Three open-ended
questions were used, after the completion of the 14-week process of GeoGebra training and
designing of GeoGebra activities. The content analysis of the open-ended questions indicated that
all of the PMTs think that GeoGebra has positive effects on their professional development. They
also stressed that GeoGebra can contribute to students’ academic achievement. In addition all the
PMTs stated that they would like to use GeoGebra in their professional career. However, while
more than half of the teachers stated that their use of GeoGebra in their professional lives depends
on some conditions and the rest of them stated that they would use GeoGebra and expressed their
reasons for using it.
Key words: pre-service mathematics teachers, Computer assisted teaching, Geogebra,
Mathematics education
1. Introduction
As mathematics is a universal language which consists of figure, number and symbols that enable us
to understand the world and to improve the environment we live in (Baykul, 2009), it is an important
discipline that affects human life. In changing world, if it is taken into consideration that people who
understand the mathematics and who are good at mathematics will be more successful in the future
(National Council of Teachers of Mathematics [NCTM], 2000), the importance of mathematics
education is understood better. Although it is an important field, it has been reported that students are
not successful at mathematics sufficiently (PISA, 2015; TIMSS, 2016). On the other hand there are
studies that indicate usage of technology in mathematics lessons improves success of mathematics by
making positive contribution for learning of students (Dikovic, 2009; Seloraji & Kwan-Eu, 2017). In
consideration of the opportunities that technology presented for learning, the use of technology is a
necessity and beyond preference anymore (López, 2011; NCTM, 2000) and technology should be used
as a learning instrument for improving learning opportunities of the students by including them in
mathematics lessons (Van De Walle, Karp & Bay-Williams, 2012/2010). In the light of this
information, it is stated that information and communication technologies should be used for learning
and teaching mathematics effectively in current elementary school mathematics curriculum in Turkey
(Ministry of National Education, [MoNE], 2013) as well and the use of technology is encouraged,
especially in geometry lessons. In fact, technology enriches mathematical learning and presentation of
content with giving permission to be increased explorations and it enables students to solve problem,
make reasoning and focus on mathematical ideas and examine them (Van De Walle et al., 2012/2010).
However, the integration of technology into class environment depends on teacher (NCTM, 2000),
moreover, it is hard to achieve this integration for teacher (Cuban, Kilpatrick, & Peck, 2001). By the
reason of obstacles in educational environment and classroom management as the availability of
computers and software, the restriction of curriculum and time, the lack of support of colleagues and
school management, it is known that the integration of technology into mathematics lessons gets
difficult (Hohenwarter, Hohenwarter, & Lavicza, 2008). These causes that obstruct the integration of
78 Tuğba Horzum, Melihan Ünlü
Acta Didactica Napocensia, ISSN 2065-1430
technology have been classified in literature in two steps: First order (external) and second order
(internal) factors (Ertmer, Addison, Lane, Ross, & Woods, 1999). As the deficiencies of software and
hardware apart from proficiency of teacher, the inadequateness of trainings that are provided for pre-
service teachers-teachers-academicians, the deficiencies of managers about the support for using
technology, the inadequateness of physical conditions of classes and school, crowded classes, the lack
of experts who should provide technical support, the lack of economic resources, the lack of time that
is necessary for making arrangements to integrate technology into class are classified as first order
factors; the factors that stem from teachers as lack of knowledge about use of technology, low level of
self-efficacy, negative attitudes, lack of motivation, the problem that they are not technology literate
are the second order factors. Despite these difficulties about integration of technology into class
environment, technology is considered as a means of improving quality and accessibility of education
by researchers and many teachers (Van De Walle et al., 2012/2010).
With the use of technology and computers in the classroom environment, the concept of computer-
assisted teaching emerged. In recent years, for computer-assisted mathematics teaching, computer
algebra systems and dynamic geometry software (DGS) programs have been developed (Davenport,
1994; Sträßer, 2001, 2002). One of the DGS programs is GeoGebra showing the multiple
representations of objects (Aktümen, Yıldız, Horzum & Ceylan, 2011). Developed by Markus
Hohenwarter, this software program includes both the features of computer algebra systems and DGS
programs (Hohenwarter & Jones, 2007); thus offers many opportunities for its users (Dikovic, 2009;
Hohenwarter & Preiner, 2007).
GeoGebra can be used as a tool in the training of PMTs. Because it is strongly believed that the use of
this program in the classroom environment by PMTs will contribute them to teach mathematics. In
fact, research has revealed that mathematics teachers should possess a profound grasp of mathematics,
should understand how students learn mathematics by considering their individual differences and
should select instructional tasks and strategies that can promote learning in order to increase the
quality of mathematics education (Shulman, 1986; Van De Walle et al. 2012/2010). In addition,
research also indicates that teachers did not use the technology in their class because of not having
enough knowledge about the technology integration (Karagiorgi & Charalambous, 2004; Niess, 2005).
Thus, teachers need to acquire knowledge, skills, attitudes and habits in order to adapt to technology,
to understand technology, and to take advantage of opportunities offered by technology (Mishra &
Koehler, 2006). It is thought that it is important to change attitudes, skills and habits at the desired
level (Ertmer & Ottenbreit-Leftwich, 2010) and to acquire the necessary knowledge for mathematics
teachers before starting their professional career. Thus, the content of undergraduate teacher training
programs can be organized to achieve these objectives. As a matter of fact, as what can be done by
students through DGSs particularly while learning the subjects related to geometrical figures is
considerably different from what can be done without computer, the mathematics education to be
conducted by using DGS programs will be both changeable and improvable (Van De Walle et al.,
2012/2010, p.117). Hence, PMTs should be able to use GeoGebra activities in their lessons, and be
able to design and to have the skills to use GeoGebra activities. On the other hand, research states that
teachers' beliefs and views influence the learning environments they create in their classrooms (Ball,
1998). Therefore, it is believed to be of great importance to investigate the views of PMTs about
GeoGebra after they have learned how to design GeoGebra activities to be used in their classrooms.
When the literature was reviewed, studies investigating PMTs’ (Agyei & Benning, 2015; Baltacı,
Yıldız, & Kösa, 2015; Kutluca & Zengin, 2011; Zengin, Kağızmanlı, Tatar, & İşleyen, 2013) and
mathematics teachers’ (Aktümen, et al., 2011; Kaleli-Yılmaz, 2015; Zakaria & Lee, 2012) views about
the use of GeoGebra in math classes were found. In their study, Zengin et al. (2013) indicated that the
PMTs think that the use of GeoGebra can lead to positive outcomes such as facilitating understanding,
increasing retention and concretization. Baltacı et al. (2015) reported that elementary mathematics
teachers are of the opinion that GeoGebra facilitates thinking by encouraging reasoning and
interpretation. In addition, there are some studies exploring the learning processes regarding subjects
such as calculus (Dikovic, 2009; Majerek, 2014), probability (Radakovic & Aizikovitsh-Udi, 2012),
translation and rotation transformations (Baltacı & Baki, 2016), analytic geometry (Baltacı & Yıldız,
2015), geometrical reflection (Seloraji & Kwan-Eu, 2017). These researches found that GeoGebra is
effective in teaching of such subjects. In the current study; on the other hand, the purpose is to
Pre-service mathematics teachers’ views about geogebra and its use 79
Volume 10 Number 3, 2017
investigate the views of the PMTs about GeoGebra and its use after being exposed to GeoGebra
activities designing processes. To this end, the answers to the following questions will be investigated:
1. What are PMTs’ views about the effect of GeoGebra activities designing processes on their
professional development (PD)?
2. What are the PMTs’ views about the effect of the mathematics education using GeoGebra on
students’ academic development?
3. What are the PMTs’ views about their using GeoGebra in their classes when they become teachers?
2. Method
2.1. Research model
This qualitative research is a case study to investigate the PMTs’ views about the GeoGebra and its
use. In the case study, environments, individuals or processes are evaluated as a whole and the focus is
on the roles and relationships in the process and it allows an in-depth investigation of a particular
group and the analysis of the data obtained through the data collection tools without having any
concern about the generalization of the data (Yıldırım & Şimşek, 2008).
2.2. Participants
This investigation was realized with 36 PMTs (11 males and 25 females) studying in mathematics
teaching department in Turkey. The participants of the study were given names such as S1, S2, S3, …,
S36. First, it was determined that the PMTs have no information about GeoGebra and its use. The
participants were volunteers to participate and had taken the lessons of Mathematics Teaching
Methods I-II, Basic Concepts of Mathematics and Instructional Technologies and Materials Design.
So that the PMTs could have the required pedagogical content knowledge to design GeoGebra
activities. It was a desired condition for the participating PMTs to have acquired the knowledge about
how to teach mathematics to elementary school students and to have discussed this in the class.
2.3. Procedure
The current research was carried out within a 14-week period (three class-hours per-week). Firstly,
GeoGebra training was given to the PMTs by the first author within the context of “Computer-assisted
Geometry Teaching”. Then, the PMTs were shown how to develop activities to be used in teaching of
different subjects of mathematics and geometry lessons by means of GeoGebra. At the end of this
process, the PMTs were asked to randomly select from among the acquisitions determined considering
the content of the mathematics curriculum in Turkey and then to design activities to contribute to the
accomplishment of the selected acquisition by using GeoGebra and then to submit this as an
assignment. A total of 36 activities were designed by the PMTs working individually by using
GeoGebra for five weeks. Finally, the views of the PMTs having been subjected to a 14-week
GeoGebra training program about three questions were elicited. The first question is about the effect
of GeoGebra and the activities they prepared through GeoGebra on their PD; the second one is about
the effect of mathematics teaching to be conducted through GeoGebra on students’ academic
development and the third one is about the possibility of their using GeoGebra in their classes when
they become teachers. For this purpose, a form was given to the PMTs to write their views about the
questions. Below is given the Computer-assisted Geometry Teaching lesson.
1st week: Introduction, educational basis of GeoGebra, GeoGebra and multiple-representations, user
interface of GeoGebra.
2nd week: Presentation called “Basic concepts”, Algebra view, and Graphic view (drawing board).
3rd week: Terms and explanations concerning the use of computer in education, spreadsheet view,
input bar, menu bar.
4th week: Objectives, advantages, limitations of computer-assisted teaching, toolbar buttons-2D,
GeoGebra activities.
80 Tuğba Horzum, Melihan Ünlü
Acta Didactica Napocensia, ISSN 2065-1430
5th week: Teaching mathematics and computer, basis of interactive geometry, toolbar buttons-2D,
GeoGebra activities.
6th week: Presentation called “DGS in the curriculum”, toolbar button-2D, GeoGebra activities.
7th week: Toolbar buttons-3D, GeoGebra activities.
8th week: Toolbar buttons-3D, GeoGebra activities.
9th week: Activity sharing, GeoGebra activities.
10th-14th weeks: Designing activities.
2.4. Data collection and analysis
In order to determine the views of the PMTs about GeoGebra and its use, three open-ended questions
were used in the study after the completion of the 14-week process of GeoGebra training and
designing of GeoGebra activities. These three questions were submitted to the scrutiny of an expert
holding a PhD degree in the field of mathematics education and then the required corrections were
made in line with the expert opinions. The PMTs were asked to write their views in the form given to
them. Moreover, no time limit was set for the students to answer these questions.
Content analysis was used to analyze the PMTs’ responses. In the content analysis, it is intended to
create certain frameworks by making sense of the raw data and then to arrive at some certain codes
and themes to classify the data (Patton, 2002). Thus, for these questions, separate data analyses were
conducted. Before the analysis of the collected data, numbers were assigned to the participants and
then the responses were coded separately for each individual participant. After that, the themes derived
from the responses of one PMT were compared with the responses of the other PMTs. In this way, the
themes were determined and then it was checked whether the consistency was attained within each
theme itself. Then each theme was compared with the other themes and the participants’ responses.
Thus, common themes were obtained. While conducting data analysis, it was seen that some
participants gave responses including more than one theme. As each of these responses refers to a
different meaning, such responses of the participants were included in different themes.
3. Findings
In this section, the views of the PMTs about GeoGebra and its use will be addressed under three
headings: the effects of GeoGebra on the PD of the PMTs; the effect of mathematics teaching by using
GeoGebra on the students’ academic development, the possibility of the PMTs to use GeoGebra in
their professional life.
3.1. The Effect of GeoGebra on the PD of the PMTs
The findings derived from the analysis of the PMTs’ responses to the question “What do you think
about GeoGebra activities and GeoGebra on your PD?” are presented in Table 1.
Table 1. Positive effects of GeoGebra on the PMTs’ PD
Main Categories
f (%)
Related effects
f
Pedagogical dimension
30 (83.3%)
Tool to
16
9
5
5
1
The dimension of enhancing
teaching process
22 (61.1%)
Tool to
17
7
4
2
The dimension of
contribution to the
conceptual understanding of
students
16 (44.4%)
Tool to
7
4
4
3
Pre-service mathematics teachers’ views about geogebra and its use 81
Volume 10 Number 3, 2017
2
1
Affective dimension
13 (%36,1)
Tool to
5
5
3
3
Others
10 (%27,8)
Tool to
5
4
1
As can be seen in Table 1, all of the PMTs stated that GeoGebra has positive effects on their PD.
These positive effects are classified under five dimensions, which are pedagogical dimension, the
dimension of enhancing teaching process, the dimension of contribution to the conceptual
understanding of students, affective dimension and others. High majority of the PMTs (83.3%) stated
that within the pedagogical dimension, GeoGebra could be used to facilitate learning, to make
teaching more effective, to produce better drawings, to make learning more permanent and to facilitate
classroom management. In this regard, Ö5 expressed his opinion as follows “Even I had difficulties in
trigonometry, after conducting activities with GeoGebra I understood how to teach it better”. Ö19
mentioned how GeoGebra makes teaching more effective by stating that “GeoGebra will provide us
with more applicable and effective instructional environments”. The effect of GeoGebra on the PD of
the PMTs by providing them with a tool to produce better drawings is mentioned by Ö6 with the
statement of “When we use GeoGebra program, we can produce more scientific and accurate
drawings”. Ö34 thinks that GeoGebra is a good material to make learning more permanent with the
expression of “We may not always find time to develop materials for our students. This program can
serve the function of supplementary materials by creating more permanent and visual image in the
mind of the student”. With the statements of “I think I will be able to make good use of time and
planning in terms of both exams and presentations”, Ö15 emphasizes the time management and
planning, two important components of classroom management.
More than half of the PMTs (61.1%) stated that GeoGebra could make contributions to the
enhancement of teaching process. In this dimension, it is mentioned that GeoGebra can be used in
mathematics lessons as a tool to visualize subjects, to increase the choices of instruction, to concretize
and to increase exemplification and thus contribute to the teachers in teaching process. In this regard,
Ö35 indicated that GeoGebra could be used as a means of visualization in teaching mathematics by
stating that “It is quite difficult to teach abstract concepts, topics of analytic geometry, rotating and
reflexive shapes. It is necessary to visualize to make them more comprehensible”. Ö19 mentioned the
idea that GeoGebra can be used as a tool for concretization by saying “We can use it to concretize
abstract mathematical operations”. The idea that GeoGebra can be used to increase exemplification
and choices of instruction which are in the dimension of enhancing teaching process was expressed by
Ö31 in the following way: “We, as teachers, frequently avoid drawing some shapes in mathematics
and geometry classes as we think that they are difficult to draw or that if I draw them, students can
experience great difficulties in imagining them; yet, such shapes can be easily drawn in computer
environment. Thus, we can have broader presentation alternatives. We can show more examples to our
students”.
The PMTs (44.4%) stating that GeoGebra contributes to students’ conceptual understanding focused
on its effects as a tool to be used for concept teaching, elimination/prevention of misconceptions,
seeing the details, thinking development, understanding the logic of a subject, prevention of rote
learning. The effect of GeoGebra on PD such as concept teaching and development of thinking was
mentioned by Ö21 saying “I need to give information to my students about shapes and concepts and
demonstrate this information in an applied manner. In this regard, GeoGebra broadened my horizon”.
On the other hand, the expressions of Ö29 “As it can show live demonstrations of theorems and can
proceed one step forward and backward, students can understand the demonstrations of theorems
better” shows that GeoGebra has a contribution to the PD as a means of understanding the logic of a
subject and seeing details. The effect of GeoGebra on the elimination of misconceptions is mentioned
by Ö12 as “Through GeoGebra, some misconceptions of students can be eliminated”. Finally, Ö36
82 Tuğba Horzum, Melihan Ünlü
Acta Didactica Napocensia, ISSN 2065-1430
emphasized that GeoGebra can prevent rote learning by stating that “Our teachers got us to memorize
formulas without properly knowing geometric figures. Therefore, when I saw this computer-assisted
program, I thought that I could teach students better”.
Some PMTs (36.1%) stated that the use of GeoGebra has some effects on affective dimension. In this
regard, the PMTs are of the opinion that GeoGebra can be used as a tool to draw interest/attention, to
motivate or increase motivation, to make learning environment more enjoyable and to endear
mathematics. Emphasizing that GeoGebra can contribute to PD as a tool to draw students’ attention
and increase their motivation, Ö22 stated that “It draws students’ attention and increases their
motivation. Thus, students’ motivation to participate in lesson increases and their curiosity arises”.
The effect of GeoGebra on PD by creating an enjoyable learning environment and increasing
motivation was mentioned by Ö2 as “As the instruction will be more enjoyable by doing exercises on
GeoGebra, it will be easier to motivate students”. On the other hand by stating that “It can be useful to
endear geometry to students”, Ö7 indicated that GeoGebra is a tool to endear the lesson by his
expression as “GeoGebra can be an effective tool to endear geometry to students”.
Finally, more than one fourth of the PMTs (27.8%) stated that GeoGebra contributes to their PD as a
tool that can help them to keep up with the age, prepare exam questions and enhance the academic
achievement. The potential effect of GeoGebra to contribute to PD by helping to keep up with the age
was mentioned by Ö3 with the statement of “As a result of developing technology and contemporary
conception of education, it seems to be not possible to teach everything on the blackboard”. Ö32
indicated how GeoGebra could contribute to their PD by helping them to prepare exam questions as
“While preparing my exam questions, instead of drawing geometrical figures in the questions by hand,
I can use this program to draw these figures in the future”. By stating that “Students’ achievement can
promote our success as teachers” Ö31 shows that she thinks that GeoGebra not only enhances
students’ achievement but also teachers’ performance.
3.2. The Effect of the Mathematics Teaching by Using GeoGebra on Students’ Academic
Development
The findings obtained from the analysis of the PMTs’ responses to the question “What do you think
that mathematics teaching by using GeoGebra can affect students’ academic development?” are
presented in Table 2.
Table 2. The effect of GeoGebra on students’ academic development
Theme
f (%)
Sub-theme
f
Promoting learning
24 (66.7%)
Meaningful learning
11
Permanent learning
7
Learning through concretization
7
Individual learning
7
Effective learning
6
Internalized learning
1
Providing functionality
24 (66.7%)
Increasing academic achievement
14
Broadening the horizon
4
Preventing misconceptions
3
Keeping up with technology
3
Promoting reinforcement
3
Encouraging participation in class
3
Providing guidance
1
Overcoming information deficiency
1
Imparting skills
16 (44.4%)
Higher level thinking skills
11
Creativity skill
7
Mental visualization skill
5
Developing positive
attitudes
13 (36.1%)
Increasing interest in the lesson
7
Finding the lesson enjoyable
6
Overcoming the fear of mathematics
3
Loving the lesson
2
Changing the perspective of the lesson
2
Pre-service mathematics teachers’ views about geogebra and its use 83
Volume 10 Number 3, 2017
Increasing motivation
1
Increasing desire to research
1
Facilitating
12 (33.3%)
Learning
6
Understanding
3
Thinking
2
Visualization in mind
1
Seeing details
1
Internalization
1
Recalling
1
As can be seen in Table 2, majority of the PMTs are of the opinion that GeoGebra can contribute to
students’ academic achievement in terms of promoting learning and providing functionality. Of the
PMTs, 44.4% stated that GeoGebra could impart some skills to students, 36.1% stated that it would
help students develop positive attitudes and 33.3% stated that it would facilitate the learning process.
The PMTs stated that GeoGebra could promote learning by improving meaningful learning,
permanent learning, concretization, individual learning, effective learning and internalization. For
example, indicating the positive effects of GeoGebra on effective, permanent and meaningful learning,
Ö34 stated that: “It allows students to learn mathematics efficiently. Instead of memorizing formulas,
student can achieve more permanent learning by understanding the logic of the figures. It might be
easier for students to understand abstract things”. On the other hand, Ö9 mentioned students’
meaningful learning by means of concretization stated that “It allows students to see how events are
taking place; thus, they can make sense of them”. Claiming that GeoGebra could provide many
opportunities for individual learning, Ö14 expressed her opinions as follows “For example, let’s take
the subject of triangles in geometry; if a student himself/herself draws a triangle, with the help of
feedbacks he/she can better understand what comes from where and how it happens”.
The PMTs arguing that GeoGebra provides functionality (66.7%) mostly focused on its cognitive
effects on students’ academic lives such as increasing academic achievement, broadening the horizon,
preventing misconceptions, keeping up with technology, helping to reinforce, encouraging
participation in class, providing guidance and overcoming information deficiency. For instance, with
this statement “Such different ways of instruction can certainly broaden students’ horizon. They
increase students’ achievement. They can provide guidance for students”, Ö23 indicates that
GeoGebra can broaden students’ horizon, increase their academic achievement and provide guidance
for them. On the other hand, Ö36 emphasized that GeoGebra could prevent misconceptions and help
to overcome information deficiencies by stating that “The frequency of observing misconceptions and
information deficiencies in students will considerably decrease”. Ö3 argued that GeoGebra could help
students keep up with technology with this statement “As children are growing up in a developing and
changing world in a close interaction with technology, they find such applications more enjoyable and
interesting”. Ö9 pointed to its effect on class participation “It can increase active participation in
class”. Finally, Ö5 pointed out that GeoGebra could contribute to the reinforcement of learning by
stating that “In my opinion, GeoGebra should be used as an activity; that is, to visualize what has been
taught in the traditional style of lecturing”.
The PMTs stating that GeoGebra could impart some skills to students mentioned three skills that are
higher level thinking skills, creativity skills and mental visualization skills. In this regard, the
explanation of PMTs such as considering an issue from different perspectives, seeing the cause-result
relation, interpreting concepts and analytic thinking are interpreted as high level skills. On the other
hand, statements related to new designs, originality, viewing the life in different respects and
improving imagination were addressed under the heading of creative skills. For instance, Ö20
mentioned these three skills by stating that “As it enables students to think multi-dimensionally and
visually, it can promote students’ academic thinking. Through this program, new designs and new
mathematical methods can be discovered; thus, it can contribute to their academic development”.
Some PMTs stated that GeoGebra would develop students’ affective characteristics. Here affective
characteristics manly refer to developing positive attitudes and the positive attitudes to be developed in
students were mentioned to be increasing interest in the lesson, finding the lesson
enjoyable/interesting, overcoming the fear of mathematics, loving the lesson, changing students’
84 Tuğba Horzum, Melihan Ünlü
Acta Didactica Napocensia, ISSN 2065-1430
perspective of the lesson, increasing motivation and increasing desire to research. For instance, with
her statements “As students will find GeoGebra more interesting and a different way of learning the
lesson, their view of the lesson may change a bit. They will enjoy the lesson”, Ö19 indicated that
GeoGebra would increase students’ interest in the lesson, make the lesson more enjoyable for students
and change the perspective of the lesson. Ö24 argued that students could overcome their fear of
mathematics and increase their motivation through GeoGebra by stating that “Students’ motivation
and interest in the lesson increase. Today, mathematics has become students’ most feared school
subject. In my opinion, students will be able to overcome this fear by using GeoGebra”.
PMTs also maintained that GeoGebra would provide some opportunities for students to facilitate their
cognitive activities. These are facilitating learning, facilitating understanding, facilitating thinking,
facilitating visualization in mind, facilitating seeing details, facilitating internalization and facilitating
recalling. One of the PMTs thinking that GeoGebra will facilitate learning, Ö22 expressed her opinion
“Student can see and understand a mathematics subject; which he/she could not understand previously
as it was abstract, in its three-dimensional form”. On the other hand, Ö32 mentioned that GeoGebra
would facilitate understanding by stating that “I think that students will be able to understand
operations related to geometrical figures in this way more easily as they are visual”. While Ö35
maintained that GeoGebra would facilitate thinking by stating that “As it directs students to thinking,
particularly to analytic thinking, students’ academic achievement will be positively affected by this”,
Ö8 argued that GeoGebra would facilitate recalling by stating that “Mathematics has always been
taught us on the board. This has resulted in weak recall or prevention of our learning”. Finally, with
her following statement, Ö31 indicated that GeoGebra would enable students to see details and
visualize in mind “By means of GeoGebra, students can see the most complex figures more easily and
visualize them in their minds”. Ö33 expressed his opinions about the effect of GeoGebra on students’
internalization of knowledge with this statement “As it is difficult to internalize abstract concepts, this
program reifies them. Thus, students can more easily internalize them”.
3.3. PMTs’ Possibility of Using GeoGebra in their Professional Life
The PMTs were asked the question “What do you think about using GeoGebra in your classes when
you become a teacher?” and the findings obtained from their responses are presented in Table 3.
Table 3. PMTs’ views about using GeoGebra
Views
f (%)
Reasons / Conditions for Using
f
I will use
14 (38,9%)
For
geometry subjects
5
visualization
3
retention
3
keeping up with the technology age
2
teaching concepts
2
establishing links with the daily life
1
making better use of time
1
concretizing abstract concepts
1
making the lesson more interesting
1
I will use but
22 (61,1%)
When
the conditions are suitable
11
I use the program effectively
3
For
(some) geometry subjects
8
teaching abstract concepts
6
visualization
6
designing activities
2
establishing links between concepts
1
After
the presentation of the subject
1
When Table 3 is examined, it is seen that all of the PMTs are willing to use GeoGebra. However,
while some of the PMTs expressed their reasons for using the program (38.9%), the majority of them
(61.1%) stated that their use of the programs depends on some conditions. Of the PMTs stating that
they want to use GeoGebra in their future professional lives, five of them pointed out that they want to
use it particularly for teaching geometry subjects. One of these five teachers is Ö31 and she expressed
her opinions as follows: “Instead trying to draw a figure on the board in a geometry lesson, I can draw
Pre-service mathematics teachers’ views about geogebra and its use 85
Volume 10 Number 3, 2017
this figure more accurately with my students by using GeoGebra in the computer environment”. Some
PMTs stated that they want to use GeoGebra in their professional lives as it enhances visualization and
retention. In this regard, while Ö20 expressed his opinions as follows “By producing three-
dimensional drawings, I will try to develop students’ thinking capacity”, Ö11 stated that “There is no
need to ponder with GeoGebra, it is practical and increase retention; we can also solve the problem at
the same time. It is very convenient”. Other reasons mentioned by PMTs for using GeoGebra are to
keep up with the technology age, to facilitate concept teaching, to make better use of time and to
concretize abstract concepts. In this regard following explanations were provided by Ö12 “In order to
be successful, teachers need to be open to innovations in their fields and to actualize themselves. Our
age is a technology age. Therefore, we need to use technology while teaching our subjects” and by
Ö15 “I will use it to make better use of time and to teach concepts to students more effectively”.
The PMTs stating that their use of GeoGebra in their professional lives depends on some conditions
most frequently mentioned the existence of a smart board and a computer lab and characteristics of the
subject and students suitable for the use of program. For instance, Ö15 emphasized that “Depending
on the characteristics of the subject and also those of students, environment and school, I think I will
be able to use it”. Ö24 also pointed out the varying conditions of schools in different geographical
regions “It will be difficult to use this program if I am appointed to the eastern regions of the country
because there are no smart boards or computer labs in schools in these regions”. Some PMTs stated
that GeoGebra should only be used while teaching three-dimensional geometry subjects requiring
analytic thinking. In this connection, Ö2 stated that “When I become a teacher, I am certainly thinking
of using this program while teaching three-dimensional objects, not every subjects, because it is really
difficult to teach and learn three-dimensional objects; yet, they can be very clearly demonstrated in
GeoGebra”. Some PMTs stated that they would use GeoGebra to teach and visualize abstract
concepts. This is pointed out by Ö36 as follows “I want to preset abstract concepts to students by
concretizing them” and is explained by Ö9 “It should be preferred for teaching subjects for which
students experience difficulties in visualizing in their minds”. Some PMTs stated that they cannot use
this program effectively and if they manage to use it effectively then they will prefer to use it. In this
regard, Ö33 stated that “For now, I cannot use it; otherwise, it would be a waste of time because I am
not qualified enough to use this program. When I can use this program effectively, I will use in my
classes”. Finally, PMTs stated that they want to use GeoGebra to design activities, to establish links
between concepts and after presenting the subject. For instance, Ö25 stated that “If I use it, it will be
easier to develop activities”, Ö9 “I will enhance my classes with related visuals and activities” and
Ö26 “After the presentation of a subject, I am thinking of using it for students to see figures and to
understand the subject better”.
4. Results and Discussion
The purpose of this study is to investigate the views of PMTs who had no experience of DGS program
before the completion of GeoGebra activities designing process about GeoGebra and its use. In this
respect, it was intended to determine the PMTs’ views about the effects of GeoGebra on their PD, on
the academic development of their students and using the program when they become a teacher.
Though this study, was conducted with 36 PMTs, the findings are not enough to make generalizations.
Despite this limitation of the study, on the basis of the findings, it can be argued that PMTs have
positive views about GeoGebra and its use in general. Similarly, in many studies, PMTs and teachers
stated positive views about GeoGebra (Aktümen et al., 2011; Baltacı et al. 2015; Baltacı & Yıldız,
2015; Mwingirwa & Miheso-O’Connor, 2016; Tatar, 2013). On the other hand, in the study of Kaleli-
Yılmaz (2015), it was also found that there are some teachers having negative feelings about the use of
technology in mathematics classes.
All of the PMTs participating in this study stated that GeoGebra activities designing processes had
positive effects on their PD. This can be interpreted as the PMTs’ considering GeoGebra as an
effective tool to be used in teacher education for their PD. As a matter of fact, GeoGebra can provide
many opportunities for them to concretize and visualize subjects so that students can learn better and
solve problems by dynamically researching mathematical relationships and to create interactive on-
86 Tuğba Horzum, Melihan Ünlü
Acta Didactica Napocensia, ISSN 2065-1430
line learning environments (Dikovic, 2009; Hohenwarter et al., 2008). Therefore, it is an expected
situation that the PMTs think that GeoGebra will have positive effects on their PD. Similarly, it is
known that GeoGebra can make important contributions to mathematics teacher education (Baltacı &
Baki, 2016) and learning environments generated by using GeoGebra positively affect PMTs (Zengin
et al., 2013). When the PMTs’ views about the effect of GeoGebra on their PD were examined, it was
found that they think that this process has positive effects on their pedagogical knowledge, on
enhancing the learning environment, on students’ conceptual understanding and affective dimensions.
Within the pedagogical dimension, the PMTs most frequently emphasized the effect of GeoGebra on
facilitating learning and classroom management, making teaching more effective, producing better
drawings and permanent learning. On the other hand, they think that GeoGebra can contribute to their
PD by enhancing the teaching process. Within this dimension, they mentioned that GeoGebra could be
used as a tool to visualize, to increase choices of presentation and exemplification in mathematics
lessons and to concretize. The PMTs stating that GeoGebra can promote students’ conceptual
understanding mostly focused on concept teaching, elimination/prevention of misconceptions, seeing
details, promoting the development of thinking, understanding the logic of a subject and prevention of
rote learning. In fact, technological learning environments allow teachers to select learning methods
tailored to the needs of students and to apply them in their classes (NCTM, 2000). The findings of the
current study are parallel to the findings reported by Zengin et al. (2013), who argued that the use of
GeoGebra could improve visualization, facilitating comprehension, retention and concretization.
Given that mathematics deals with abstract subjects (Baykul, 2009), the PMTs’ thinking that by using
GeoGebra, they can improve their students’ achievement by concretizing and visualizing subjects and
promote permanent learning can be interpreted as a sign that they will use technology in their classes
to teach mathematics. Thus, it can be concluded that the use of GeoGebra can help PMTs to teach
mathematics more effectively and integrate technology into their classes.
Moreover, within the affective dimension, the PMTs mentioned the effects of GeoGebra in terms of
drawing students’ interest/attention, increasing their motivation and endearing mathematics lesson by
creating more enjoyable learning environments. This views of the PMTs is considered as a sign that
they will be able to provide effective teaching by integrating technology and pedagogy and thus
rendering classes more enjoyable for students. These findings concur with the findings reported by
Aktümen et al. (2011) concluding that mathematics teachers believe that with GeoGebra, important
contributions can be made to students’ learning process and lesson preparation and students’ attitudes
towards mathematics classes can be changed.
Some of the PMTs stated that GeoGebra has positive effects on their PD as a tool that can be used to
keep up with the age, to prepare exam questions and to promote achievement. Therefore, these PMTs
are of the opinion that GeoGebra can improve them and help them to keep up with the age thus they
will not fall behind the age. Moreover, they think that they can save time by producing drawings in
computer environment. Hohenwarter and Preiner (2007) pointed out that due to its features such as
affordances it offers and saving time GeoGebra is preferred in mathematics teaching and learning.
The PMTs also stated that GeoGebra would contribute to the academic life of their students as well as
their PD. They mentioned that GeoGebra can have many other positive effects such as promoting
students’ learning and providing functionality, imparting skills to students, helping them develop
positive attitudes and facilitating learning, understanding, thinking, visualization in the mind, seeing
details, internalization and recall. Similar findings were found in the study by Dikovic (2009)
reporting that GeoGebra helps students to understand mathematics better and to solve problems by
dynamically researching mathematical relationships. This is also supported by Van De Walle et al.
(2012/2010) arguing that by integrating technology into classes, it can be turned into a tool that can
promote students’ learning. In here, the PMTs stating that GeoGebra provides functionality mostly
focused on its cognitive effects on students’ academic lives. These effects are increasing academic
achievement, broadening horizon, preventing misconceptions, keeping up with technology, helping
reinforcement, encouraging students to participate in class and overcoming information deficiencies. It
is particularly important that the PMTs consider GeoGebra as a tool to impart higher level skills to
students such as thinking from different perspectives, recognizing cause-effect relationships,
interpreting concepts and analytic thinking and also creativity and visualization skills. In fact, in the
Pre-service mathematics teachers’ views about geogebra and its use 87
Volume 10 Number 3, 2017
renewed mathematics curriculum in Turkey, a great emphasis is put on the inculcation of these higher
level skills (MoNE, 2013). Moreover, these findings concur with the findings reported by Baltacı et al.
(2015) stating that the PMTs think that GeoGebra facilitates mathematical thinking by allowing
reasoning and interpretation.
PMTs think that GeoGebra also improves students’ affective characteristics. These affective
characteristics are centered on developing positive attitudes. The positive attitudes to be developed by
students; according to the PMTs, are increasing interest in the lesson, finding the lesson
enjoyable/interesting, overcoming the fear of mathematics, loving the lesson, changing the perspective
of the lesson, increasing motivation and promoting the desire to research. These findings can be
interpreted as GeoGebra can help to establish a convenient and interesting learning environment in
mathematics classes, has a potential for students to discover themselves and thus can increase interest
in the lesson (Baltacı et al., 2015). In fact, during the activity designing process, the PMTs lived the
experiences to be lived by students.
PMTs also mentioned that GeoGebra can also provide some opportunities for students’ cognitive
development. These are facilitating and promoting learning, understanding, thinking, visualization in
the mind, seeing details, internalization and recall. Given that visualization can play an important role
in today’s mathematics education (Majerek, 2014), these findings seem to be remarkable. In this
connection, Dikovic (2009) stressed that GeoGebra can provide many opportunities for students to
visualize the mathematical process and acquire an intuitional viewpoint. Furthermore, these views of
the PMTs concur with the statements of high school students found in the study conducted by Kutluca
and Zengin (2011) using activities and applications developed through GeoGebra. The high school
students stated that they use GeoGebra willingly and enthusiastically, the information they learned
previously by memorizing can be retained more easily when visualized by using GeoGebra, the
program enhances visualization and provides a discovery-based learning environment enabling them
to recognize the relationships between mathematical concepts.
Moreover, it is a remarkable finding that all the PMTs stated that they would like to use GeoGebra in
their professional career. However, while more than half of the teachers stated that their use of
GeoGebra in their professional lives depends on some conditions and the rest of them stated that they
would use GeoGebra and expressed their reasons for using it. Here the reasons presented by the PMTs
are mostly pedagogical such as learning is permanent, instruction is related to the daily life and
making better use of time. Other reasons presented by the PMTs are associated with enhancing
learning environment such as visualization and concretization to improve students’ conceptual
understanding while teaching geometry subjects and concepts.
While some of the teachers stating that their use of GeoGebra depends on some conditions aside from
their own competencies, some other associated it with reasons arising from only their own
competencies. For instance, factors such as presence of computer labs and smart boards, curriculum,
structure and content of the subject were considered to be factors aside from teacher competencies;
yet, factors such as effective use of the program was considered to be related to teacher competencies.
These show similarities with the theoretical framework of obstacles in front of the technological
integration proposed by Ertmer et al. (1999). These results; as stated by Hohenwarter et al. (2008),
pinpoint the fact that teachers may experience difficulties in technology use due to obstacles such as
instructional environments and classroom management. The PMTs stating that they would not use
GeoGebra due to internal factors are believed to see themselves incompetent in terms of using
technology (Karagiorgi & Charalambous, 2004; Niess, 2005). In fact, in some studies, it was
concluded that PMTs and teachers think that the training they received in their undergraduate
education is not enough to integrate technology into their mathematics classes (Kaleli-Yılmaz-2015)
and that they see themselves inadequate for using GeoGebra (Aktümen et al., 2011; Tatar, 2013).
Therefore, it would be useful to provide students with environments where they could practice the use
of GeoGebra throughout their undergraduate education.
88 Tuğba Horzum, Melihan Ünlü
Acta Didactica Napocensia, ISSN 2065-1430
References
[1] Agyei, D.D. & Benning, I. (2015). Pre-service teachers’ use and perceptions of GeoGebra
software as an instructional tool in teaching mathematics. Journal of Educational Development
and Practice, 5(1), 14-30.
[2] Aktümen, M., Yıldız, A., Horzum, T. & Ceylan, T. (2011). İlköğretim matematik öğretmenlerinin
GeoGebra yazılımının derslerde uygulanabilirliği hakkındaki görüşleri. Turkish Journal of
Computer and Mathematics Education, 2(2), 103-120.
[3] Ball, D. (1998). Research on teacher learning: Studying how teachers’ knowledge changes.
Action in Teacher Education, 10(2), 7-24.
[4] Baltacı, S. & Baki, A. (2016). Dinamik matematik yazılımının öteleme ve dönme dönüşümlerinin
öğretiminde kullanılmasının bağlamsal öğrenme boyutundan incelenmesi. Ondokuz Mayıs
Üniversitesi Eğitim Fakültesi Dergisi, 35(1), 119-139.
[5] Baltacı, S. & Yıldız, A. (2015). Matematik öğretmen adaylarının GeoGebra yazılımı yardımıyla
analitik geometrideki bir konuyu öğrenme süreçleri, Kırşehir Eğitim Fakültesi Dergisi, 16(3),
295-312.
[6] Baltacı, S., Yıldız, A. & Kösa, T. (2015). Analitik Geometri Öğretiminde GeoGebra Yazılımının
Potansiyeli: Öğretmen Adaylarının Görüşleri. Turkish Journal of Computer and Mathematics
Education, 6(3), 483-505.
[7] Baykul, Y. (2009). İlköğretim matematik öğretimi 6-8. Ankara: Pegem A Yayıncılık.
[8] Cuban, L., Kirkpatrick, H. & Peck, C. (2001). High access and low use of technologies in high
school classrooms: Explaining the apparent paradox. American Educational Research Journal,
38(4), 813-834.
[9] Davenport, J.H. (1994). Computer algebra-past, present and future. Euromath Bulletin, 1(2), 25-
44.
[10] Dikovic, L. (2009). Implementing dynamic mathematics resources with GeoGebra at the college
level. International Journal of Emerging Technologies in Learning, 4(3), 191-203.
[11] Ertmer, P.A. & Ottenbreit-Leftwich, A.T. (2010). Teacher technology change: How knowledge,
confidence, beliefs, and culture intersect. Journal of Research on Technology in Education, 42(3),
255–284.
[12] Ertmer, P.A., Addison, P., Lane, M., Ross, E. & Woods, D. (1999). Examining teacher beliefs
about the role of technology in the elementary classroom. Journal of Research on Computing in
Education, 32(1), 54-72
[13] Hohenwarter, M. & Jones, K. (2007). Ways of linking geometry and algebra: The case of
GeoGebra. Proceedings of British Society for Research into Learning Mathematics, 27(3), 126-
131.
[14] Hohenwarter, M., Hohenwarter, J. & Lavicza, Z. (2008). Introducing dynamic mathematics
software to secondary school teachers: The case of GeoGebra. Journal of Computers in
Mathematics and Science Teaching, 28(2), 135-146.
[15] Hohenwarter, M. & Preiner, J. (2007). Dynamic mathematics with GeoGebra.
Journal of Online Mathematics and its Applications, 7. Retrieved January 30, 2017 from
http://www.maa.org/external_archive/joma/Volume7/Hohenwarter/index.html.
[16] Kaleli-Yilmaz, G. (2015). The views of mathematics teachers on the factors affecting the
integration of technology in mathematics courses. Australian Journal of Teacher Education,
40(8), 132-148.
[17] Karagiorgi, Y. & Charalambous, K. (2004). Curricula considerations in ICT integration: Models
and practices in Cyprus, Education and Information Technologies, 9(1), 21-35.
http://dx.doi.org/10.1023/B:EAIT.0000024259.91951.44.
[18] Kutluca, T. & Zengin, Y. (2011). Matematik öğretiminde GeoGebra kullanımı hakkında öğrenci
görüşlerinin değerlendirilmesi, Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 17, 160-
172.
[19] López, Y.M. (2011). Arguments for the definition of the ICT skills for prospective teachers:
University student perception about the role of teachers of Mathematics in secondary. Ciência &
Educação (Bauru), 17(3), 757-769.
Pre-service mathematics teachers’ views about geogebra and its use 89
Volume 10 Number 3, 2017
[20] Majerek, D. (2014). Application of Geogebra for teaching mathematics. Advances in Science and
Technology Research Journal, 8(24), 51-54.
[21] MoNE (2013). Ortaokul Matematik Dersi (5, 6, 7 ve 8. sınıflar) Öğretim Programı. Ankara:
M.E.B. Retrieved 10 April, 2014 from http://ttkb.meb. gov.tr/program2.aspx?islem=2&kno=215.
[22] Mwingirwa, I.M. & Miheso-O’Connor, M.K. (2016). Status of teachers’ technology uptake and
use of GeoGebra in teaching secondary school mathematics in Kenya. International Journal of
Research in Education and Science (IJRES), 2(2), 286-294.
[23] Mishra, P. & Koehler, M. (2006). Technological pedagogical content knowledge: A framework
for teacher knowledge. Teacher College Record, 108, 1017–1054.
[24] NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM
Publications.
[25] Niess, M. (2005). Preparing teachers to teach science and mathematics with technology
developing a technology pedagogical content knowledge, Teaching and Teacher Education, 21,
509–523.
[26] Patton, M. Q. (2002). Qualitative Research & Evaluation Methods. Thousand Oaks, CA: Sage
Publications.
[27] PISA (2015). PISA 2012 araştırması ulusal nihai raporu. Retrieved January 30, 2017 from
http://pisa.meb.gov.tr/?page_id=22.
[28] Radakovic, N., & Aizikovitsh-Udi, E. (2012).Teaching probability by using Geogebra dynamic
tool and implemanting critical thinking skills. Procedia - Social and Behaviour Sciences, 46,
4943–4947.
[29] Seloraji, P. & Kwan-Eu, L. (2017). Students’ performance in geometrical reflection using
GeoGebra. Malaysian Online Journal of Educational Technology, 5(1), 65-77.
[30] Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational
Researcher, 15(2), 4–14.
[31] Sträßer, R. (2001). Cabri-Géomètre: Does a dynamic geometry software (DGS) change geometry
and its teaching and learning? International Journal of Computers in Mathematics Learning,
3(6), 319-333.
[32] Sträßer, R. (2002). Research on dynamic geometry software (DGS) - An introduction.
Zentralblatt Didaktik der Mathematik, 3(34), 65.
[33] Tatar, E. (2013). The effect of dynamic software on prospective mathematics teachers’
perceptions regarding information and communication technology. Australian Journal of Teacher
Education, 38(12), 1-16.
[34] TIMSS (2016). TIMSS 2015 Ulusal Matematik ve Fen ön raporu 4. ve 8. sınıflar. Retrieved
January 30, 2017 from http://timss.meb.gov.tr/wp-
content/uploads/Timss_2015_ulusal_fen_mat_raporu.pdf.
[35] Van De Walle, J.A, Karp, K.S. & Bay-Williams, J.M. (2012). İlkokul ve ortaokul matematiği
gelişimsel yaklaşımla öğretim. (Soner Durmuş, Trans.). Ankara: Nobel Yayın Dağıtım. (Original
work published in 2010).
[36] Yıldırım, A. & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin
Yayıncılık.
[37] Zakaria E. & Lee, S.L. (2012). Teacher’s perceptions toward the use of GeoGebra in the teaching
and learning of Mathematics. Journal of Mathematics and Statistics, 8(2), 253-257.
[38] Zengin, Y., Kağızmanlı, T.B., Tatar, E. & İşleyen, T. (2013). Bilgisayar destekli matematik
öğretimi dersinde dinamik matematik yazılımının kullanımı. Mustafa Kemal Üniversitesi Sosyal
Bilimler Enstitüsü Dergisi, 23(10), 167-180.
Authors
Tuğba Horzum (Corresponding Author), Ereğli Faculty of Education, Necmettin Erbakan
University, Konya, Turkey, e-mail: thorzum@gmail.com
Melihan Ünlü, Aksaray Faculty of Education, Aksaray University, Aksaray, Turkey, e-mail:
melihanunlu@yahoo.com
90 Tuğba Horzum, Melihan Ünlü
Acta Didactica Napocensia, ISSN 2065-1430