Pre-service elementary mathematics teachers' opinions about using GeoGebra in mathematics education with reference to 'teaching practices

Pre-service elementary mathematicsteachers’opinions about using GeoGebrain mathematics education with reference

to ‘teaching practices’

BEKIRKU« RS� ATDORUK�,MUHARREMAKTU« MENANDCAHITAYTEKINElementary Mathematics Education Department, Faculty of Education, Ahi Evran University, K|rs� ehir, Turkey

�Email: [email protected]

[Submitted November 2012; accepted March 2013]

This study involved 34 pre-service teachers who did teaching practices in schools. It wasintended to assess the opinions of pre-service teachers on the use of GeoGebra, dynamicmathematics software, inmathematics education. Analysingdata collected through inter-views and a questionnaire leads to important conclusions regarding the problems encoun-tered by pre-service teachers who had been trained for a semester in GeoGebra and usedGeoGebra in some of their practices, the advantages of GeoGebra for students, the pre-service teachers’ preferences regarding the use of GeoGebra in teaching practices, usingit when they become teachers and the reasons behind these preferences. These findingsare the basis for several proposals that will contribute to the integration of GeoGebrainto their classes by pre-service teachers.

1. IntroductionThe book, Principles and Standards of School Mathematics, published by the National Council of

Teachers of Mathematics (NCTM, 2000), stressed the significance of technology in mathematics

education, arguing that electronic technologies such as computers are essential tools for teaching,

learning and doing mathematics. It also suggested that technological facilities should be provided in

mathematics classrooms to make it easier for students to learn mathematics. In tandem with techno-

logical advances, computer algebra systems (CAS) have become beneficial tools in mathematics

education (Aksoy et al., 2007; Bulut et al., 2007), and dynamic geometry software (DGS) that

assist students with visualizations related to the properties of geometric figures have become important

auxiliaries in effective mathematics education (Healy & Hoyles, 2001; Guven, 2008; Dikovic, 2009;

Guven et al., 2010). GeoGebra is a dynamic mathematics software that brings together the properties

of dynamic geometry software and computer algebra systems with the aim of providing ease of use. It

is free software and used in all levels of teaching, learning and exploring mathematics (Hohenwarter &

Preiner, 2007; Fahlberg-Stojanovska & Stojanovsk, 2009). Moreover, it is becoming more and more

widespread as a tool for teaching mathematics due to its ease of use and its availability in multiple

languages (Hohenwarter & Lavicza, 2007; Kutluca & Zengin, 2011). In GeoGebra software, the

algebraic expressions of items produced in the graphics window can be seen in the algebra

Teaching Mathematics and Its Applications (2013) 32, 140^157doi:10.1093/teamat/hrt009 Advance Access publication 26 April 2013

� The Author 2013. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications.All rights reserved. For permissions, please email: [email protected]

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window, and a modification of either window takes effect simultaneously in both windows. In the

GeoGebra 5.0 Beta version, it is now possible to create 3D objects using the software (Aktumen et al.,

2011a).

Although technology has rapidly penetrated all spheres of life, the effective utilization of it is still

not widespread in the teaching and learning of mathematics. At all levels of mathematics education

there is minimal integration of technology with education. Furthermore, the process of successfully

integrating technology into the teaching and learning of mathematics is proceeding slowly and is

becoming increasingly complex (Cuban et al., 2001; Monaghan, 2001; Lavicza, 2008; Hohenwarter

et al., 2010).

There are many factors that influence the effective use of technology in mathematics class (Umay,

2004). However, teachers play the most important role in this since it is up to them to determine

whether a technological apparatus, or indeed, any teaching modality, is employed effectively or inef-

fectively (NCTM, 2000). Therefore, professional development opportunities should be designed to

enable teachers not only to use new software, but also to employ technology effectively in their

teaching practice and to prepare for emerging challenges in integrating technology into teaching

(Hohenwarter et al., 2010).

Investigating the opinions of pre-service teachers who know about GeoGebra on the use of this

software in mathematics teaching at schools is a good way to determine the important points that should

shape the professional development of mathematics teachers. Many recent studies have surveyed opin-

ions on the practicality of GeoGebra by interviewing mathematics teachers who had just learned about

this software in various workshops and/or in-service training (Preiner, 2008; Baydas� , 2010;

Hohenwarter et al., 2010; Kabaca et al., 2010; Aktumen et al., 2011b). At the end of these typically

short training sessions, teachers have mostly had positive views of the use of GeoGebra in teaching and

learning mathematics. However, these studies have failed to investigate adequately both the teachers’

views after working with GeoGebra and whether they continue to use it. On the other hand, studies do

show that there is not enough information about the extent to which these initial training sessions

achieve their objectives (Garet et al., 2001; Fishman et al., 2003; Lawless & Pellegrino, 2007). For this

reason, this study investigated the opinions on the practicality of GeoGebra of a group who interacted

with GeoGebra for a longer period, both before and after using it in mathematics classes in the school

environment. This study intended, thus, to collect detailed information about the opinions of pre-service

teachers who had been trained previously in GeoGebra, specifically regarding its use in mathematics

teaching, whether they use GeoGebra in the classroom, the benefits and problems they observe while

using it, and their reasons for not using it, when applicable.

2. Methods

2.1 Selection of participants

The participant pre-service teachers were selected using purposeful sampling. This method enables re-

searchers to work thoroughly on cases that are thought to have ample information (Patton, 1987). The

research involved 34 pre-service teachers who were final year students of mathematics education and

practicing teaching in elementary schools 1 day in a week as a component of their course in ‘teaching

practices’. [In the Turkish education system, elementary schools consist of two stages (primary and sec-

ondary). Students aged between 6 and 14 attend these schools. The first four grades (1–4) form the primary

school, whereas the last four grades (5–8) are called the secondary school. Students who graduate from

Elementary Education Mathematics Teaching departments at universities work in the secondary stage of

elementary schools.] After taking courses on basic ICT skills in their first year at university, pre-service

teachers interacted with GeoGebra in three courses. They were guided in these courses by a professor, who

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was an expert on GeoGebra and who had organized various in-service trainings on the use of GeoGebra in

mathematics education. Table 1 presents detailed information on the content of these courses, which are

based on a pedagogical approach.

Thirteen voluntary pre-service teachers from this group were selected by maximum variation sam-

pling to conduct semi-structured interviews (Y|ld|r|m & S� ims� ek, 2008). Thus pre-service teachers

were selected for interviews according to their genders, academic achievements, degree of success in

the GeoGebra training and levels of their interest.

2.2 Procedure

This research is qualitative, using interviews and a questionnaire with open-ended questions as data

collection instruments. Semi-structured interviews were conducted with 13 pre-service teachers on the

practicality of GeoGebra in mathematics courses before and after their teaching practices in schools.

The pre-interviews were intended to determine the participants’ general views on using GeoGebra in

mathematics teaching before using it in the classroom. The post-interviews, on the other hand, asked

whether pre-service teachers had employed GeoGebra in their teaching and about problems they had

with it. Moreover, these candidates were asked to use GeoGebra for at least 1 h of their classes. On the

other hand, the remaining 21 pre-service teachers were not asked to do anything with GeoGebra in

their teaching practices. A questionnaire with three open-ended questions was administered to them at

the end of their teaching practices. The questionnaire asked the pre-service teachers to indicate

whether they had employed GeoGebra in their teaching practices, whether they planned to use it in

their future professional lives and the reasons for their choices. Interviews were conducted in

the researchers’ offices when the pre-service teachers were available and were audio-recorded with

the interviewees’ permission. Along with the predetermined questions in the questionnaire form, the

interviews also used probes and follow-up questions to elicit detailed responses. Each interview lasted

approximately 20 min. The collected data were transcribed by researchers. Afterwards the common

TABLE 1. The content of courses which were included the use of GeoGebra

Course name, [grade level

and class hour(s) per week]

Course content

Exploration of Mathematical

Concepts through Dynamic

Geometry Software (2&2)

This course firstly focuses on the general properties (interface, tools, commands, etc.)

of GeoGebra. Then, using the pedagogical basis provided by GeoGebra, the activities

developed by the supervisor are performed. (For example, students were assigned to

draw a perpendicular line without using the relevant button. Toolbar buttons can be

hidden in GeoGebra, and thus students are prevented from doing what they are asked to

do with only one click. This way, students are prompted to make an effort that requires

thinking deep and developing different strategies.) In addition, applications that require

the use of multiple representations (algebra, graph and table) and opportunities to

develop one’s own GeoGebra applications were also included.

Methods of Teaching

Mathematics (3&4)

As part of this course, each pre-service teacher developed projects involving GeoGebra

applications. These applications were prepared by considering the acquisitions of the

Mathematics curriculum for sixth to eighth grades. Moreover, pre-service teachers were

guided to design these applications in such a way that would lead students to ques-

tioning, deep thinking and problem solving. These applications were presented and

discussed in the classroom. Also, several everyday life problems selected by the course

supervisor were modelled and examined in GeoGebra using advanced mathematics

(cf. Aktumen 2013; Aktumen et al., 2011a; Aktumen & Kabaca, 2012).

Analytic Geometry (3&3) In this course, GeoGebra is used only for the purpose of presentation when needed

(e.g. examining the change in the vector when it is multiplied by a scalar, or examining

the impacts of scalars in parabolic, elliptic and hyperbolic equations, etc.).

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codes were identified and codes conflicts were resolved in a group discussion. Finally, the themes were

identified from common codes.

3. FindingsThe following themes emerged after analysing the data: GeoGebra’s benefits for mathematics educa-

tion; its problems, limitations and negative aspects in practice; content areas where GeoGebra could

be used effectively; GeoGebra courses for students; frequency of using GeoGebra in teaching prac-

tices; planning to use GeoGebra in their professional lives; the popularization of GeoGebra in

schools; comparing the use of GeoGebra with the use of other software or technologies; pre-service

teachers’ prior experiences and trainings in GeoGebra. The data obtained from pre- and post-inter-

views and the questionnaire were grouped together in the appropriate common themes. Under each

theme heading, pre-service teachers’ opinions before and after teaching practice were also compared.

3.1 GeoGebra’s benefits for mathematics education

While some benefits of GeoGebra, expressed by pre-service teachers, are unique to GeoGebra, some

others are generalizable to all ICT. These opinions are summarized in Table 2.

Here is an example of these opinions:

. . . I think concretising abstract issues is very important for children, especially for those in elem-

entary education. GeoGebra ensures this in a very nice way. For example, you break a hexagon into

pieces using GeoGebra and then show that triangles are formed, that is, you teach them that they can

go through triangles while dealing with a hexagon. It would be highly time-consuming if you tried to

do this the old way, like, showing on the board or bringing materials in the class. But in GeoGebra,

you can show this to students in a very short time and in a very good way. I think the most important

contribution of GeoGebra is availability of 3D, because children really struggle to see in 3D.

It was determined that there was parallelism between the opinions stated by pre-service teachers

before and after teaching practice and the opinions expressed in the questionnaire by those pre-service

teachers who were not required to use GeoGebra in teaching practice. However, it was observed that

some pre-service teachers had stronger opinions on the benefits of using GeoGebra in mathematics

teaching after the practice. Some example responses are presented below:

Of course it is a useful tool; I was working with GeoGebra earlier but now I have more positive

opinions on its benefits after practicing it concretely with students at school.

I think it is definitely useful; we applied it in teaching practice and showed students some important

relevant points. For example, I taught the area of triangles; the shape of the triangle was changing

but the lengths of base and altitude were not; so here GeoGebra clearly demonstrated students that

the area did not change.

3.2 Problems, limitations and negative aspects in practice

Some problems with GeoGebra or its use in mathematics education were reported by the pre-service

teachers in their interviews. While some of these problems are unique to GeoGebra, some others are

generalizable to all ICT.

Problems that could be generalized to ICT: It negatively affects eye health as it requires working on

a computer for a long time. The initial excitement of using GeoGebra goes away over time. It is boring


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to work on GeoGebra for a long time. A great deal of effort is needed to become competent in

GeoGebra. GeoGebra is complicated. Learning it takes time and is quickly forgotten.

Problems unique to GeoGebra: It is very difficult to transcribe mathematical expressions into

GeoGebra. It is highly sensitive while entering an equation. It is inadequate for 3D work (version 5.0

of GeoGebra, which has the 3D feature, is still in Beta). It is difficult to rotate figures (the older version).

There is the possibility of disruptions in the activity during class and problems with the new 3D version.

GeoGebra is not suitable for teaching some basic concepts. It cannot be used for all subjects. It is difficult

to prepare GeoGebra materials. Here are some relevant comments by pre-service teachers:

We cannot put everything into GeoGebra. Especially in the field of mathematics, it is highly

problematic. For example, writing an equation is very difficult, there are commas and all, I

mean, it is so unfamiliar. You cannot get the equation if you make a tiny comma mistake, and

then you get angry, because you try to do it for hours. These are very difficult aspects of GeoGebra.

. . . it is also a program that is very difficult to learn. You forget what you just did very easily. For

example, you do something, then the professor asks how you did it, but you cannot remember. It is

complicated.

Our professor (who taught us GeoGebra at the university) says that he sometimes wakes up at three

in the morning and gets occupied with GeoGebra. I do not think I could be like him. OK, I can use it

for simple stuff, but I do not think I can use it for more advanced things. It requires skill and it takes

time. I think I will teach what I can to my students using materials.

Pre-service teachers mentioned the following main problems that may be encountered if a teacher

wants to use GeoGebra in mathematics teaching: problems stemming from limited technical facilities,

TABLE 2. Pre-service teachers’ opinions regarding the GeoGebra’s benefits for mathematics education

Types of benefits Improving motivation Instructional benefits Affective benefits Benefits for teachers

Benefits that could be

generalized to ICT

Working with com-

puter, visuality,

concretizing of

concepts, easy use

of different colours

Learning through

experience, com-

prehending mathe-

matics better,

discovering one’s

own mistakes, per-

ceiving concepts

more accurately

since the software

is explanatory,

concretizing

abstract concepts,

permanent learning

Increased interest in

mathematics,

effective and

enjoyable mathe-

matics education,

love for mathe-

matics and reduced

or eliminated fear

of mathematics

Saving time, making

teaching enjoyable,

facilitating situa-

tions in which the

use of concrete

materials is diffi-

cult, replacing tra-

ditional approaches

Benefits unique to

GeoGebra

Dynamism, preparing

animations and

moving figures

(thanks to slider),

the students’ pro-

ductive agency,

interactivity,

Concretizing alge-

braic concepts,

improving spatial

skills, envisaging

3D objects, the

ability to explore

mathematical rules,

the ability to link

ideas with real life

Making easier to

draw, controlling

various situations

easily, teaching

difficult subjects

that require 3D

thinking


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the problem of not having a command of GeoGebra, the problem of students’ exam preparation

concerns; the problem of teachers’ rush to cover the entire curriculum, the problem of unavailable

ready documents, the problem of students’ inability to utilize the internet and computer consciously,

the problem of disrupted classroom discipline and problem of students perceiving GeoGebra activities

as a computer game.

When the opinions expressed before and after teaching practice were compared, it was seen that

while pre-service teachers at first talked mostly about problems that could be pertinent to entire ICT;

they focused, in the interviews conducted after the practice, more on those problems that stem from the

structural characteristics of GeoGebra and problems that they encountered during the practice. Also, it

was observed that they specified more problems in the interviews conducted prior to practice.

We also compared the opinions of pre-service teachers who were more successful in GeoGebra

trainings or who have positive experiences in using it and those who do not. We found that the pre-

service teachers who have more positive attitudes towards the use of GeoGebra mentioned problems

such as having difficulty in preparing activities and inability to find proper materials for each subject,

and they also touched upon some technical problems related to the software and limited technical

facilities in the school where they practice taught. The pre-service teachers in the other group, on the

other hand, are mostly of the opinion that it is difficult to learn and use GeoGebra.

3.3 Content areas where GeoGebra could be used effectively

A large majority of pre-service teachers believe that GeoGebra could be used more effectively to teach

geometry. Only two pre-service teachers stated that it could be used in all areas for visualization. Some

of them, on the other hand, argued that more expertise, effort and imagination are needed to be able to

use GeoGebra in areas other than geometry. A limited number of pre-service teachers stated that

GeoGebra should not be used in areas other than geometry. It was also determined that pre-service

teachers consider the GeoGebra activities available while selecting the subjects on which they would

do practice at schools, because, they argued, it is difficult to prepare activities for all subjects. Here are

some example comments that exemplify pre-service teachers’ opinions regarding the areas in which

GeoGebra should be used.

Since geometry requires abstract thinking, and we need to have concrete things in our hands in order

to be able to develop abstract thinking skills, this requires visuality. For this reason, GeoGebra could

be used.

GeoGebra could be used in all fields of mathematics. You can use visuals everywhere, for example

you can use it by combining algebra with geometry. But if I had to pick one area, I would say

geometry, because it is highly visual.

it can be suitable for every subject as long as the teacher has competence, or imagination. For

example, in order to show that both sides of an equation are equal to each other, you can use it. But I

think geometric figures are most appropriate for GeoGebra.

No, it cannot be used in every field. Those that involve figures are more suitable, functions, graphic-

drawing, 3D figures, area-volume calculations. I mean, how can I use GeoGebra to calculate

probability?

When pre-service teachers’ relevant comments in the pre- and post-interviews were compared, the

opinion that GeoGebra cannot be used in all subjects but this stems from their own incompetence

became more prevalent among pre-service teachers after teaching practice.


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3.4 GeoGebra courses for students

A significant portion of pre-service teachers stated that it would be beneficial if a separate course

aimed at teaching how to use GeoGebra were offered to students in elementary schools, and that such a

course would help students explore mathematics, overcome fear of mathematics, enjoy producing on

their own, actively learn, adapt their everyday lives into GeoGebra, and raise their interest in and liking

for mathematics. For example:

I think it would be very good, it would be more beneficial than computer courses, because for

children to learn practically and to explore on their own would improve their intelligence, then they

would not content themselves with the teacher and try to learn things on their own.

Some pre-service teachers were of the opinion that such a course is not suitable for students. It was

observed that the reasons through which these pre-service teachers justified their arguments are not

unique to GeoGebra, but are generalizable to ICT. Some of them, on the other hand, believe that such a

practice would be beneficial for special students with more skills and more curiosity about computers.

Others, however, stated that students would not be interested in such a course, that GeoGebra educa-

tion would not be useful since students consider computers to be tools for gaming, that GeoGebra

education would be too hard for students, that it would be hard to maintain control in such a course,

and that the education system is not suitable for such a course.

When the opinions on giving a GeoGebra course at schools to students expressed before and after

teaching practice were compared, it was observed that three pre-service teachers expressed after

practice that exam-oriented education system might be an obstacle and it would be difficult to maintain

control in such a classroom. Some example responses given after teaching practice are presented

below.

The system here in Turkey is not very much open to this; we are all exam-oriented, so are students.

This is why they will not be able to concentrate on such practices.

Unlike us at their age, students now are very spoiled and future generations will be even more

spoiled. For example, some students disregard the teacher completely even though the teacher is a

tough person. It thus becomes very hard to maintain control. When you take them to the lab, they

start browsing on the internet or playing games.

Another pre-service teacher expressed after the practice the positive change in her opinions as

follows:

I said ‘no’ in the previous interview, but now I say ‘yes’; because the student is active in this

process. I prepared and taught as a teacher, but it is not like a student’s own efforts in his/her own

project assignment. For example, I recall my own term project in my student days; it was a turning

point for me. Before that, I had not taught at all that I would study in the quantitative field. I think it

would be very useful if students work with GeoGebra in such assignments; they would be moti-

vated. I believe it would serve for them as a beginning in a quantitative course.

3.5 Frequency of using GeoGebra in teaching practices

In the interviews conducted at the end of teaching practices, it was observed that none of the 13 pre-

service teachers who had been asked to use GeoGebra at least in one class used GeoGebra other than in

this class. They gave the following reasons for this: limited technical facilities, the software’s unsuit-

ability for every subject, the limited number of class hours given to them for teaching, their unpre-

paredness for teaching practices, their lack of command of GeoGebra and perceived lack of a need for


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GeoGebra. In the questionnaires administered to 21 pre-service teachers who were not required to use

GeoGebra in teaching practices, two of them stated that they had used GeoGebra for once in their

teaching practices and that students had liked it. Those who did not use GeoGebra, on the other hand,

expressed reasons similar to the ones listed above.

3.6 Planning to use GeoGebra in their professional lives

Most of the pre-service teachers reported that they plan to use GeoGebra in mathematics courses in

their professional lives. Some of them, on the other hand, stated that it depends on the school’s

facilities, the availability of GeoGebra activities, and their own improvement in GeoGebra.

Some pre-service teachers said that they want to use GeoGebra in their future professional lives, but

feel incompetent using it. They reported that teachers need to improve in GeoGebra, not limiting

themselves to the formal GeoGebra training. Activity books at the elementary level need to be

prepared, materials prepared by experts need to be used in classes, and an expert need to be available

in every city to ensure the effective use of GeoGebra in classes. Pre-service teachers reported that their

inability to fully learn GeoGebra stems from reluctance during training, late acquaintance with com-

puters, and a lack of competence with computers, adding that the training they received during their

university education was not sufficient and thus required more individual effort. Here are some ex-

amples of such responses:

Right now, I am rather illiterate about GeoGebra, but I am sure I will use it, I mean, I have to. I took

a course, but you forget it if you do not use it. But I can relearn it with little effort.

It looks like I cannot use it now, but I think I can if I work on it for a while. First, I have to learn it

myself so that I can teach it. I would like to learn it to help students.

One of the participants stated that she wanted to teach GeoGebra to students in a separate course

rather than using it in mathematics courses. Another participant stated that she would use materials

prepared in GeoGebra in classes, but that she would not teach GeoGebra to students.

Those pre-service teachers who stated that they do not plan to use GeoGebra in mathematics courses

in their future professional lives gave the following reasons: giving priority to preparing students for

exams and keeping up with the curriculum, not having learned GeoGebra sufficiently, inability to use

it, the boringness of GeoGebra, the priorities of the existing education system, the need to make up the

basic deficiencies of students, deeming it more important to teach mathematics in a paper and pencil

setting, and the lack of a need for technology in mathematics. Here is an example of such responses:

. . . I saw that students are highly incompetent in mathematics. I did not expect them to be so. For

this reason, it is more important to teach more basic subjects, rather than spending time on

GeoGebra

In addition, some pre-service teachers said that they had met in-service teachers who had trained in

GeoGebra, but were unwilling to use GeoGebra in their classes. The pre-service teachers said that they

would immediately come to resemble these in-service teachers as soon as they, too, become involved

in the existing education system. Here are two of these responses:

Teachers are rather ill-disposed to using GeoGebra. When we mentioned this software they said that

we would become just like them after trying to be idealistic for a couple of years. I mean they really

do not like it. I do not think they would teach it.

I guess most teachers have been trained by our professor (the one who taught GeoGebra to us) in a

seminar, but most teachers do not consider using it, and they think it is unnecessary.


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When the opinions expressed before and after teaching practice were compared, it was seen that two

pre-service teachers, who stated that they do not plan to use GeoGebra in their future professional

lives, expressed conservative opinions in the interview conducted prior to practice, but their views

became more moderate in the second interview conducted after practice.

One of them, Demet, who had a better academic record and performed better in the GeoGebra

course, stated the following in the first interview: ‘I will not use GeoGebra when I become a teacher,

because it requires skills and it is time-consuming. I believe that I can teach what I am supposed to

teach by using materials. For me, I do not think it would be useful; I took the GeoGebra course for two

years and my view of it did not change significantly. Also, it does not appeal to me even though I am a

mathematician. I know people who think the same; I mean the majority think the same, so you need to

listen to the majority’. However, she expressed as follows her plans to use GeoGebra in her profes-

sional life in the interview conducted after the teaching practice, in which she taught the subject of

perspective drawing through 3D visuals prepared in GeoGebra:

In fact, I can use it, because there are subjects in mathematics that are very difficult to teach without

using visuals. So, I can use it for these subjects. For example, the subject I taught that day is a

difficult one that requires thinking spatially (perspective). Most people are unable to think like that,

because it is a matter of visual intelligence. When students saw that subject with GeoGebra; they

realized what changes depending on which angles, and thus they comprehended the subject more

easily and this is why I always received correct answers to my questions.

The other pre-service teacher, Inci, who had a lower academic record, performed worse in the

GeoGebra course and had a conservative attitude in mathematics teaching stated the following in

the first interview: ‘In mathematics, I believe that one must write on a paper; this is a must; I think

mathematics is the course of pen . . . I do not really like to have students sitting in front of computers

or using slide rules while learning mathematics. I think the kids should use a paper and pencil, or

maybe concrete materials, to do mathematics.’ On the other hand, the opinions she stated after the

teaching practice are the following: ‘How should I say, I think mathematics is done with a pen and a

paper; I almost spent half of the class hour in my teaching practice writing on the board. I used

GeoGebra at the end of the class hour; but I can use it more frequently in the future after practicing

more with it. I think it would have been better for students’ learning if I had used it right after the

subject I taught’.

To a question if she considers using GeoGebra in her future professional life, the same pre-service

teacher responded in the first interview as follows: ‘Well, I am not yet a teacher, but I would like to use

it if I have time. I mean, as you know, first a plan is made and then you are supposed to follow that

plan and complete the tasks within the given time. But, as I said, I believe there will be other instru-

ments which will provide more permanent learning. I think GeoGebra is a rather time-wasting tool’. In

the second interview, on the other hand, she gave the following response:

After I plan and design something, I would use it in presentations. But I do not think, as a math-

ematics teacher, I would be occupied with teaching what GeoGebra is beforehand and then expect

students to work with it. But still, I would prepare an application myself and then use it in my classes

to attract students’ attention and to motivate them.

It was observed that some pre-service teachers have cynical ideas about the national education

system and teachers currently teaching at schools. Pre-service teachers expressed such opinions both in

the first and second interviews, but the frequency of them was slightly higher in the latter. It was

observed in the interviews conducted after teaching practice that pre-service teachers talked about their


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impressions and observations that supported their cynical opinions and they expressed that the behav-

iours and cynical ideas of in-service teachers influenced them. Some example statements are presented

below:

I saw a teacher in classes teaching from his armchair. Already at the age of retirement, he did not use

any supportive instruments. There are not many teachers who are concerned with being helpful to

students. As far as I observed, most teachers’ primary concern is getting rid of their tasks. This is a

general problem in the country; nobody tries to make the best of their job.

We receive feedback from the teachers working at the school we practiced; they say, ‘We also tried

in the first 2-3 years to do what we had been told like you, but eventually we gave up because of lack

of time available’ and ‘You will be like us in five years’.

For example, a teacher told me, ‘Oh, do you spend time with these things when kids do not even

know how to read’. I do not think I can endure it for long. How to say, I am not sure if I can

withstand the pressure of these discouraging words alone.

It was observed in the interviews conducted before teaching practice that some pre-service teachers

were uncertain about planning to use GeoGebra in their future professional lives and that they ab-

stained from making precise statements without practicing with GeoGebra in a real classroom. It was

determined that a slightly positive tendency of using GeoGebra in future teaching life emerged among

these pre-service teachers after teaching practice. Responses given by a pre-service teacher before and

after practice teaching are given below as examples:

. . . I need to first practice this in the classroom; I can decide only after that. I cannot say that I will

use GeoGebra this much before first experiencing it. (first interview)

I would use it depending on the subject. For example, I would use it at the eighth grade more than at

sixth and seventh grades; because the subjects at the eighth grade have more fields of learning based

on geometric figures. This is why I can use it in six or seven out of ten class hours; but this is not

possible at the sixth and seventh grades. (second interview)

3.7 Popularizing GeoGebra in schools

It was observed that the opinions expressed by pre-service teachers on the benefits of increasing the

use of GeoGebra at schools and obstacles in front of it are mostly generalizable to ICT, rather than

being unique to GeoGebra.

The majority of the participants stated that popularizing GeoGebra in elementary schools

would be beneficial, that it would positively contribute to social development, that it is a requirement

for today’s world and that it would support the implementation of new approaches. However,

they listed the following obstacles to the popularization of GeoGebra in schools: the lack of technical

facilities, the students’ lack of computer competence, the negative attitudes towards the use

and learning of GeoGebra of most teachers currently employed in schools, the need for long-term

training for teachers, and the fact that the existing education system compels students to prioritize

exams.

When their relevant expressions in the two interviews were compared, it was observed that they

emphasized in the first interviews more on the potential benefits that such an effort could yield,

whereas they concentrated more on obstacles such as teachers’ negative attitudes and lack of basic

facilities at schools in the interviews conducted after teaching practice.


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3.8 Comparing the use of GeoGebra with the use of other software or technologies

It was observed that pre-service teachers did not have significant experiences with software or tech-

nologies other than GeoGebra, except for the Maple software that they encountered and dealt with as

part of the courses of Mathematics Teaching through Computer Algebra Systems in the final year of

their studies. In the interviews, some pre-service teachers suggested that GeoGebra is more advanta-

geous than Maple thanks to its dynamism, whereas others stated that GeoGebra is more useful

compared to Maple for students at the secondary stage of elementary education. Some example

responses are given below:

GeoGebra’s difference stems from its dynamism. For example, when we do the same in Maple, the

figures it shows are less animated; that is, it also has the visual aspect but it lacks the motion.

We now learn Maple; it is good for you if you are a mathematician. I mean, it is good for math-

ematicians attending university, but it is boring for elementary school students; because it does not

have figures, and it does not concretize the abstract. GeoGebra, on the other hand, has these features;

you can draw a triangle or a square or you can calculate the area in GeoGebra. In Maple, however,

you can calculate derivative and integral.

3.9 Pre-service teachers’ prior experiences and trainings in GeoGebra

Six of the pre-service teachers spoke positively of their experiences and trainings in GeoGebra.

However, some of them also reported that they had experienced difficulties during GeoGebra trainings.

Two responses of a pre-service teacher are presented below:

On the day when our professor showed us GeoGebra first time; I was thinking about GeoGebra

before going to sleep, and then I did this: I am from Konya, so I am familiar with whirling dervishes.

I thought about their whirling angles and tried to reflect it on GeoGebra. I planned it and tried to

produce something meaningful on my own all night long. Anyway, I could not produce something

pretty in the end, but still I made an effort, I investigated somethings. I think it is something good for

students.

Our proffesor taught the subject of functions using GeoGebra. I struggled for around one month to

find something in that subject, because it is very difficult to transfer formulas to GeoGebra. When

you make a tiny little mistake, all your efforts go down the drain. This is why it was very hard, it

required great efforts.

It was observed that five of the pre-service teachers were of the opinion that they are not competent

enough in GeoGebra although they had been trained in GeoGebra for long times. They expressed the

following reasons: not sparing time to GeoGebra outside classes, lack of interest in GeoGebra, the

‘help’ menu in the English language (in the beginning), incompetence in using computer, and com-

plexity of the software. However, it was observed in practices and interviews that these pre-service

teachers are actually capable of using GeoGebra in classes, and that some of them consider themselves

incompetent because they compare their skills with those of the professors who taught them GeoGebra.

Besides, these pre-service teachers stated that they did not make further efforts to improve their skills

and stopped being interested in GeoGebra after learning the basics of GeoGebra. The words of a pre-

service teacher, who utilized GeoGebra successfully in teaching practice and who designed the

GeoGebra activity herself, are quoted below as an example:

We took a GeoGebra course for a semester and our professor was good, but still the course failed to

endow us with motivation and this is why we did not develop an interest in learning more about


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GeoGebra. As I said, I am not that competent in GeoGebra, but my GeoGebra works were not very

hard to prepare. If students during the practice had asked me a different question or asked me to do

something different in GeoGebra, I am afraid I would not have done it.

The pre-service teachers took the last course related to GeoGebra and its use in mathematics

teaching a year ago. It is understood from their responses in interviews that most of them stopped

dealing with GeoGebra after passing the course. For this reason, mostly they had difficulties in de-

veloping the activities they would use in practices, whereas some of them used the activities that they

had prepared while taking the course. It is seen, from the expressions of some of the pre-service

teachers, that they were aware of online resources while taking the GeoGebra course. However, it is

understood that they were not able to access ample resources that are available today, and that they

stopped keeping track of the development of the resources that are available online. However, it was

observed that a few number of pre-service teachers stayed informed about developments related to

GeoGebra as they talked about their experiences with the 3D version (GeoGebra 5.0 Beta). Here are

some relevant comments by pre-service teachers:

I learned it last year. I had the expansion of the prism; for practice, I tried to rearrange it, but I could

not do anything at all. It is very sad that I forgot what I learned.

The document problem is a big problem for GeoGebra; we could not find the documents that we

looked for when we were at the second grade. I had a project in mind; I was going to build a website

where I could collect the documents of different teachers who worked with GeoGebra. There was

this website called GeoGebra Turkey, I planned to contact them and bring together all those docu-

ments under separate categories. I was going to add instructions for use as well; and put videos from

different sources abroad in order to enable teachers to learn and use through this website.

I think one of the most important benefits of GeoGebra is that it enables the viewer to see in 3D; you

can see any dimension by turning the figure in GeoGebra 3D. For example, when you put a diagonal

from one corner to another in a cube, the child also sees and does exactly the same thing.

4. Conclusion and suggestionsThis research intended to determine the opinions on the use of GeoGebra in mathematics education of

pre-service mathematics teachers, whether they use GeoGebra in their teaching, and their reasons for

not using it. Most of the participant pre-service teachers feel that GeoGebra is a useful tool for

mathematics education. They reported that, not only does GeoGebra have instructional benefits, but

also it provides affective benefits such as increasing interest in mathematics, ensuring effective and

enjoyable mathematics education, making students like mathematics and overcoming their fear of

mathematics. They also think that it facilitates better mathematics teaching and can help them over-

come and surpass traditional approaches. This finding is in accord with the findings of other re-

searchers (Aktumen et al., 2011b; Kutluca & Zengin, 2011).

On the other hand, some pre-service teachers pointed to the following limitations: ‘A great deal of

effort is needed to become competent in GeoGebra. GeoGebra is complicated. Learning it takes time

and is quickly forgotten. It is very difficult to transcribe mathematical expressions into GeoGebra. It is

highly sensitive. Minor details cause errors. It is hard to use the new 3D version. It is not suitable for

teaching some basic concepts. The initial excitement of using GeoGebra goes away over time. It is

boring to use GeoGebra for a long time.’ This contradicts the findings of earlier studies in which

teachers labelled GeoGebra as ‘user-friendly’ and as ‘easy to use as a teaching tool’ (Preiner, 2008;


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Baydas� , 2010; Kabaca et al., 2010). It might be thought that teachers in these studies might not have

had enough time to learn and practice GeoGebra, so that they might not have encountered the potential

problems with GeoGebra. On the other hand, there are studies in the literature indicating that

GeoGebra has certain problems regarding its use (Hohenwarter et al., 2010; Kutluca & Zengin, 2011).

Moreover, pre-service teachers think that they will encounter the following problems if they choose

to use GeoGebra: a lack of technical facilities, incompetence in GeoGebra, students’ exam preparation

concerns, teachers’ haste to cover the entire curriculum, unavailable documents, students’ inability to

utilize the internet and computer properly, disrupted classroom discipline, and students’ erroneous

perception of GeoGebra activities as a computer game. Most of these problems overlap with the

findings of other studies of this subject (Baydas� , 2010; Aktumen et al., 2011b). Pre-service teachers

deemed the problems related to technical infrastructure most important. However, Kabaca et al. (2010)

determined that the teachers they interviewed felt that no serious problem pertaining to infrastructure

would be encountered during the integration of GeoGebra into teaching environments. This disparity

might have stemmed from pre-service teachers’ lack of knowledge about the recent technological

advances in schools or from the lack of technological facilities in the schools where they did their

teaching practice.

A large majority of pre-service teachers believe that GeoGebra could be used more easily and

effectively to teach geometry, and that more expertise, effort and imagination are needed to use

GeoGebra in other areas. It was also determined that pre-service teachers do consider the GeoGebra

activities available when selecting topics to practice teach in schools, because, they argued, it is

difficult to prepare activities for all topics. In fact, GeoGebra is a dynamic mathematics software

and one of its main features is, as its name suggests, revealing the connections between geometry and

algebra (Hohenwarter & Preiner, 2007; Hohenwarter & Jones, 2007). It is notable that pre-service

teachers reported that GeoGebra is more suitable for the field of geometry, although they use it for

many different subjects, such as probability and fractions in their teaching practices.

More than half of pre-service teachers reported that they plan to use GeoGebra in their future

professional lives, whereas a considerable number of them stated that they would like to use it but

feel incompetent using it. Some of them stated that in order to overcome this problem elementary level

activity books need to be prepared, materials prepared by experts need to be used in classes, and

teachers need to improve their skills, not confining themselves to the training they receive in university

courses. Similar findings were also reported by Aktumen et al. (2011b). Pre-service teachers probably

feel unconfident using GeoGebra because they have been assigned onerous tasks during their univer-

sity GeoGebra training. Studies show that those teachers who feel comfortable while learning about

new software are more inclined to integrate the software into their classes than teachers who experi-

ence difficulties at the beginning (Mously et al., 2003). For this reason, it might be best to avoid

assigning excessively difficult tasks to pre-service teachers who are learning about such software in

university courses.

Although the pre-service teachers were trained in GeoGebra for a semester, had encountered

GeoGebra applications in various courses, and think that GeoGebra is a useful instrument for math-

ematics education, they did not use GeoGebra to an adequate extent in their teaching practices. This

shows that teaching teachers about useful educational tools does not guarantee that they will use them

in their classes (Mously et al., 2003). Teachers should be trained not only in using new software, but

also in various ways of successfully using technology for teaching (Hohenwarter et al., 2010). One of

the major needs of pre-service teachers is learning how to integrate the new educational tools that they

see during their university education into traditional classroom environments. As Clark-Wilson (2009)

wrote about in-service teachers; in order to improve pre-service teachers’ level of incorporating tech-

nology into mathematics courses, it is necessary to introduce the technical properties of a technology


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(e.g. GeoGebra) to pre-service teachers and then to improve their personal competence and self-con-

fidence in using that technology in their classes.

Those pre-service teachers who stated that they do not plan to use GeoGebra in their future teaching

lives were influenced not only by their own incompetence and attitudes towards the software, but also

by the cynical attitudes of the teachers that they met in the teaching practice schools. Therefore, it

could be argued that in-service teachers have a significant influence on the training of pre-service

teachers. For this reason, the professional development of in-service teachers should be seen as just as

important as teaching the use of new technologies and their integration into education to pre-service

teachers in universities.

Also, it is inferred from the comments of pre-service teachers that they need to communicate and

interact with in-service teachers who work at schools, use GeoGebra, and observe its contribution to

teaching mathematics by experiencing it. Pre-service teachers might be influenced positively or nega-

tively by in-service teachers. It might be possible to turn this situation into an advantage for pre-service

teachers to use GeoGebra more effectively in practice teaching as well as in their future professional

lives. Clark-Wilson (2009) stated that the possibility of sharing exemplar approaches, experiences and

resources with a larger body of teachers via TV or web was provided to the in-service teachers who

participated in the project aimed at disseminating technology use in mathematics courses. Similarly, a

medium could be set up that will enable in-service teachers who have positive experiences related to

GeoGebra to share classroom stories about their experiences with GeoGebra that contributed students’

learning of mathematics, and exemplar approaches that they used to incorporate technology into their

classes with pre-service teachers who learn GeoGebra in universities. Thus, pre-service teachers can be

helped to develop positive attitudes towards using GeoGebra before encountering in-service teachers at

teaching practice schools who have cynical opinions on using ICT in classes. Such an effort might also

help them have higher self-confidence in using GeoGebra for courses. Videos of in-service teachers

who have relevant positive experiences might be shown to pre-service teachers in GeoGebra courses;

the media and internet resources might be used for this purpose.

The following observations were made after comparing the responses given by pre-service teachers

in the interviews conducted before and after teaching practice in order to see the impact of practices

upon their tendencies to use GeoGebra in mathematics courses in their future teaching lives:

� It was observed that they had stronger opinions after practice teaching on the benefits of using

GeoGebra in mathematics education. Also, positive changes were observed in second interviews in

the opinions of pre-service teachers with conservative attitudes. In this change, different and posi-

tive reactions, which were received from students after using GeoGebra in classroom environments

where the conventional approach was dominant, might have played a role. Another reason might be

that pre-service teachers got the chance of practicing their theoretical technological knowledge and

that they observed the need for these instruments in order to ensure students’ meaningful learning.

� They must have seen the potential problems to be encountered while using GeoGebra in mathem-

atics education.

� They must have realized after teaching practice that they are incompetent in preparing materials for

different subjects in mathematics.

� On the subject of giving GeoGebra course outside the mathematics course to students at schools; a

few number of pre-service teachers were of the opinion after teaching practice that the education

system is not suitable for this.

� The pre-service teachers who had expressed cynical opinions in the first interview talked in the

second interview about their observations that supported their cynical opinions, and some pre-ser-

vice teachers stated that they had been influenced by such views of in-service teachers working at


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teaching practice schools. As also stated by Shantz (1995), pre-service teachers might sometimes get

highly confused between the demands of their university education or of their university professors

and the views and demands of teachers working at practice schools; because it will not be possible

for them to experiment new approaches if they try to teach like cooperating teachers do, despite the

fact that it is a method different from what they learned in university.

This general picture shows that although practice teaching endows pre-service teachers with some

benefits regarding the use of GeoGebra in courses, there are several problems caused by the practice

school and in-service teachers. These findings are in parallel with those of several studies that point to

the presence of various problems experienced in teaching practice, which has the role of preparing pre-

service teachers to the professional life (Kiraz, 2002; Gokce and Demirhan, 2005; Eraslan, 2008).

Also, it is understood that there is a need for measures to be taken to prevent pre-service teachers from

being affected by the negative attitudes of cooperating teachers. Therefore, as also suggested in several

studies, the process of selecting schools and supervisors for teaching practice might be managed more

carefully (Eraslan, 2008; Alaz ve Birinci-Konur, 2009).

Significant investments have been made in technology in Turkey with the aim of supporting

teaching and learning. One of the most important prerequisites for receiving the fruits of these efforts

is well-trained teachers who are capable of using technology in classes. Findings of this research

indicate that although pre-service teachers receive the necessary training and believe that GeoGebra is

highly beneficial for mathematics education, they fail to fully incorporate this into their practices. The

GeoGebra training that the pre-service teachers received did not only cover the technical properties of

the software, but also included its use in mathematics teaching. In addition, it was observed that the

majority of pre-service teachers have positive opinions on the trainings in GeoGebra that they had pre-

viously received, although some of them consider this training to be insufficient. A consideration of

all these findings together brings to mind the question of what causes this insufficiency in practice.

One possible reason is the fact that most pre-service teachers had already stopped working with

GeoGebra when they made it to the final grade. Pre-service teachers who are in the final year

of their university education are required to take an exam to become teachers. The fact that they

had to intensively prepare for this multiple choice exam, through which their theoretical know-

ledge about educational science are tested and that does not include any practice, might have

caused them to ignore teaching practices. Pre-service teachers are concerned more with passing this

exam and begin working as soon as possible rather than being preoccupied with getting genuinely

prepared for teaching mathematics. Moreover, the fact that the in-service teachers working at practice

schools mostly have conventional approaches and attitudes might have influenced the degree to which

pre-service teachers utilized GeoGebra while teaching. Given the fact that education is a system

composed of numerous wheels; a problem in one of the wheels inevitably affects others as well. As

long as such problems are not overcome, it is not possible to take full advantage of the investments

made in technology.

It would be useful to conduct a study in the future with the participant pre-service teachers, who will

start teaching in different regions of Turkey at the end of the year this research is carried out, with the

aim of investigating their attitudes towards and opinions on using GeoGebra after they have fully faced

the realities of the school environment and the problems of mathematics teaching.

AcknowledgementsThis paper was presented and discussed at the International GeoGebra Institute Conference in Warsaw,

Poland, 21–23 September 2012.


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FundingAhi Evran University (PYO-EGF.4006.12.006).

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Documents

Pre-service elementary mathematics teachers' opinions about using GeoGebra in mathematics education with reference to 'teaching practices