Theorem 22 For the solution of problem (7), the following coercive stability estimate
T
C
C
T
C
C
C
t
L
f
L
T
q
x
a
M
L
w
0,
2
,
0,
2
2
2
0,
0,
,
,
,
,
,
,
0,
holds.
The proof of Theorems 1 and 2 can be given in a similar manner by the proof given in
[8, Theorem 2.1 and Theorem 2.2].
References:
1 L. Yan, C.L. Fu, F.L. Yang, The method of fundamental solutions for the inverse heat source
problem, Eng. Anal. Bound. Elem. 32 (2008) 216–222.
2 O.M. Alifanov, Inverse Heat Transfer Problems, International Series in Heat and Mass
Transfer Series, Springer, 2011.
3 A. Ashyralyev, A.S. Erdogan, O. Demirdag, On the determination of the righthand side in a
parabolic equation, Appl. Numer. Math. 62 (2012) 1672– 1683.
4 V. Borukhov, P. Vabishchevich, Numerical solution of the inverse problem of reconstructing
a distributed righthand side of a parabolic equation, Comput. Phys. Commun. 126 (2000) 32 –
36.
5 J.R. Cannon, H.M. Yin, Numerical solutions of some parabolic inverse problems, Numer.
Meth. Part. D. E. 6 (1990) 177–191.
6 M. Dehghan, Determination of a control parameter in the twodimensional diffusion
equation, Appl. Numer. Math. 37 (2001) 489–502.
7 V. Isakov, Inverse Source Problems, volume 34 of Mathematical Surveys and Monographs,
American Mathematical Society, 1990.
8 A.S. Erdogan, A note on the righthand side identification problem arising in biofluid
mechanics, Abstract and Applied Analysis 2012 (2012) 1–25.
123
УДК 51
1
Guvercin S.,
2
Chakir A.,
3
Almas A.
1
Assistant Prof. PhD, Suleyman Demirel University, Almaty,Kazakhstan
selim.guvercin@sdu.edu.kz
2
PhD Candidate, International Black Sea University,Tbilisi,Georgia, ahmetcak @yahoo.com
3
PhD Candidate, Suleyman Demirel University, Almaty,Kazakhstan
abdullah.almas@sdu.edu.kz
VIEWS OF PRESERVICE TEACHERS ABOUT USING THE TECHOLOGY INTO
MULTILINGUAL MATHEMATICS CLASSES
Аннотация. В данной статье исследуются результаты количественного
исследования о взглядах будущих учителей математики об использовании технических
устройств в многоязычных математических уроках.
Это будет полезно для будущих учителей математики, для учителей средней
школы, а также для исследователей в области преподавания математики. В этой статье
рассматриваются следующие вопросы:
“Каковы преимущества и недостатки
использования технологических устройств в образовании?”, “Каковы взгляды учителей
математики об использовании технологических устройств?” и “Нужна ли нам
интеграция технологий на уроках математики?”. Для проведения исследований нами
были подготовлены две анкеты для будущих учителей математики от Университет
имени Сулеймана Демиреля кафедры математики и естественных наук. Для одного из
вопросников использована шкала Лайкерта, которая включает 20 тестовых вопросов.
Эта анкета исследует взгляд учителей математики об использовании технологических
устройств на уроках математики и на любых других уроках. Второй опросник состоит из
10 классических вопросов на разных языках, которые выявляют текущие позиции,
потребности и убеждения учителей математики о существующих технологических
устройствах и их использовании. Было выяснено, что интеграция технологий и
многоязычие во многих школах находятся на достаточно хорошем уровне, но педагоги
должны развивать свои навыки по использованию технологических устройств.
Администраторы должны мотивировать будущих учителей математики для такой
интеграции. Кроме того, путем адаптации технологических устройств, большинство
учителей считают, что многоязычное математическое образование и интеграция
технологий дают множество преимуществ для дальнейшего карьерного роста в
квалифицированных перспективах.
LITERATURE REVIEW
Educators who can effectively manage and use the increasing amount of information to
solve a lot of complex problems and make important decision making. Reigeluth (1999) said
that traditional system of education is incompatible with the evolving demands of new age. The
general characteristics of the new students are as “born with internet” or “born with
technology”, so we call them as digital natives or the Net Generation. A very young child can
easily use a computer and other technological devices. The students spend lots of their time
using computer, cell phone, iPad and other media devices.
We can conclude that, technology is an integral part of the lives of the Net Generation
(Prensky, 2007; Oblinger, 2008). The best style of education for the Net Generation is to learn
in a classroom with integrated technology. According to Bebell et al. (2004) there is no direct
and clear definition of technology integration but, we can say that technology integration is
viewed as the use of technology for instructional purposes.
Consequently, we need to insert technological devices into classroom environment. The aim of
technology integration is to improve student’s learning (Hew & Brush, 2006). But, which
devices are the best for teaching mathematics? Also, is it enough to put only these devices into
124
classroom? Who and how will use these devices? What are the most useful software for these
devices? How can we motivate the teachers to use them? These are the questions that we need
to answer before integrating the technological devices into classroom.
It is a fact that, if the teacher do now want to use the technology in his/her lesson, inserting any
type of technological device into classroom will not have any meaning. So, before inserting
these expensive devices into classroom we need to know two important things:
1) How useful each particular technology is (Moffatt, 2000);
2) The beliefs of teachers about the integration of technology into classroom.
When the teachers believe the effectiveness of the use of technological devices they will force
the administrators to buy that devices.
Technological devices are quite expensive devices. So, knowing the usage of them
effectively, is essential. There are many researches in this area. PLATO (Programmed Logic
for Automatic Teaching Operations) was made by Donald Bitzer at 1959 in Illinois University
and it was the first research on the effect of use of computers in education (Woolley, 1994).
After Bitzer, every year hundreds of researchers made different researches in this area. Some
of them are as follows:
1972, Vinsonhaler, Bass & Ronald compared computer assisted teaching and traditional
teaching by analyzing 10 different researches; 1981, Simon proved that computers are more
effective than traditional education methods;1991, Kulik & Kulik made a meta–analysis on the
results of 254 researches about the results of computer aided teaching and its’ effects on the
achievement and attitudes of the students from kindergarten to university level;1994, Baker,
Gearhart & Herman made the evaluation of the Apple Classrooms of Tomorrow;
1998, Sivin–Kachala analyzed 219 researches from 1990 to 1997 to assess the effect of
technology on learning and achievement across all learning domains for different ages of
learners;2001, Vale & Leder investigated the relation between the length of time using
computer in mathematics and nature of the learning environment;
2005, Miller, Glover & Averis made the research about the effective use of the
interactive whiteboard in the mathematics classroom;
2007, Kennewell, Tanner, Jones & Beauchamp analyzed the influence of ICT on the
interactivity of teaching. When we say technological devices we mean any of computers (PC,
Notebook, Netbook, tablet …), projectors (LCD, wide screen TV, overhead …), networks
(internet, local network …), iPad, interactive whiteboard, smartphone, video cameras and other
devices.
Linnenbrik & Pintrich (2003) offer that motivation is a fundamental concern among teachers
and motivating students is a continual problem throughout education. There are no clear cut
solutions for motivating the students but there are several strategies to help teachers on this
problem. One of these strategies is using the technology in classroom more efficiently. Granito
& Chernobilsky (2012) made a research and conclude that it is easier to motivate the students
by using the technology, if they are not taught to hate technology at an early age.
By using technological devices teachers save time and may use this time to interact
with the students and activate them. Liu, at al. (2007) conclude that there is evidence about the
use of technology increase achievement and selfefficacy of the students. Computer programs
and software are designed to control used time in teaching process, to supervise different types
of learner styles and to check different levels of the students and that will help students to
increase the achievement. Educators suggest that different students have different abilities to
learn a topic. By using the technology, the teacher may use more than one method to explain
the topic and it will help more students to understand the topic. Tunçok (2010) suggest that
welldeveloped, computerassisted education programs and tools support Gardner's Multiple
Intelligence Theory (MIT).In every classroom there are different problems that may affect the
teachers to pay attention to all students at the same time. So, the students need to study alone to
learn the topics. Warschauer (2004) said that, by using personal computers, tablet PC,
smartphone or another type of technological device, any student may learn or find the answers
125
of their questions personally. According to Koşar (2002) educational technology provide the
personal education and learning. Wortham (2006) said that 70% of the students at the age of 4
– 6 can easily use the computers. According to Kung (2002) modern technology is convenient
to support both of independent and collaborative learning environments.Kinder (1973) made an
experiment in the University of Texas and said that: In a fixed time, people memorize 10% of
the information that they just read, 20% of the information that they listen, 30% of the
information that they see, 50% of the information that they see and listen, 80% of the
information that they see, listen and talk about, 90% of the information that they touch, see,
listen and talk about. That means, when we insert more sense to process of education we can
learn and remember better. By using the educational technology a teacher may use more senses
of students actively, and by this way the students learn better. Use of technology help both of
the teachers and students to use time more efficiently (Akkoyunlu, 1998). The teachers may
prepare the needed documents and manage the time before the lesson. So, they can decide and
manage used time for checking homework or classwork, managing special activities during the
lesson, explanation part of the topic, problem solving time and any other activities that will
take place in the lesson.
. So, the students need to be comfortable to use it. All students and people of this age must
have a level of technological background. Using the technology in education help us to give
this necessary part of the knowledge of the technology for our students.
We can find many other advantages of using the technology in education. But, using all
these advantages depend on the teacher. So, their beliefs on the integration of technology has
crucial importance. Trench (2007) said that the most important thing in order to use the
technological devices effectively is to educate the teachers. For example, if we do not teach all
properties of the interactive whiteboard, the teachers will use them like a normal whiteboard,
without using its rich potential.
Besides of these advantages, technology has also some challenges. Some of these
challenges are: Lack of the technological devices, time to prepare materials, teachers’
performance and motivation, socio–psychological development of students, ability to use
technology, cost, lack of resources, materials and software, waste usage of technology,
technical problems, and laziness in studying, curriculums or political problems, rapid change in
technology and organizational factors. We can write articles for each of these factors one by
one but, knowing only these captions will be enough for this article.
METHODOLOGY
The research that we used two questionnaires was prepared for mathematics teachers. It
is limited with 40 teacher candidate from mathematics department. Results and contents of the
questionnaires also include general ideas of teachers about usage of technology for education.
So, the results may help other teachers and administrators.
As we see from the previous part, the technology has a lot of advantages for teachers but I
know from my own experience and the teachers from teacher groups and communities that,
majority of the teachers do not use this technology effectively. For example, some teachers use
the interactive whiteboard like a normal whiteboard. They do not use its’ properties and
activities. So, I understand that there are some barriers that effect teacher’s use of technology.
As everybody knows, teachers will integrate the technological devices into their lessons. So,
the most important right of audience belongs to teachers. Because of this, I prepared a Likert
scale questionnaire including 20 multiple choice items. It was about the beliefs of the teachers
on the integration of technological devices into classroom. By looking at results, I saw that a
great majority of the teachers believe the benefits of technology integration. So, I prepared
another questionnaire that include some open ended and some check box questions to
distinguish current conditions of mathematics classrooms and abilities of teachers. From the
responses I get valuable results. The most responsible person for the integration of technology
is
126
This is an expected result. As I mentioned before, the teachers are the most important
people in the integration of the technology into education. If they want to use any invention in
their lessons they can do it without looking at any obstacle. Because of this, we need to
motivate the teachers to use the technological devices in their lessons.
CONCLUSION
By looking at the recent researches and the first questionnaire we can conclude that, use
of technological devices in education has uncountable number of benefits. It increases the
achievement of students, attitudes of students towards mathematics lessons and motivation of
the students. Technology can offer different teaching methods for teachers and different
learning methods for students. By this way it can satisfy needs of different types of learners.
Technology integration convert our boring lessons to entertainment and attract attention of
more students. When students like a lesson they study more and learn more. By this way it
helps to increase achievement. Teachers can bring authentic materials into classroom
environment and by this way they can take attention of the students and increase their
motivation.
By using technology we can save the time in the lesson. Teachers do not need to waste their
valuable time by writing on the board. Instead of this they prepare written materials before the
lesson and use this free time in different activities like classroom management and dealing with
more students. Technology integration make the lessons richer and entertaining by multimedia.
So, the learned topics become more permanent in students’ storage.
Use of technological devices are not so difficult. Integration of technology into classroom has
advantages for both of the students and teachers. Teachers feel more comfortable in the lessons
when they use the technology. Integrated technology in the classroom effect the interaction
between the teacher and students and so, more students want to join the lessons. Also, we can
decrease the anxiety of students towards the lessons and especially we can eliminate the
negative effect of intangible mathematics lessons on students.The average of the first
questionnaire is 4.24 in a 5point scale, which is a very good result. It shows that the use of
technology is very effective in all levels and subjects of education including mathematics in
particular. Almost all teachers believe the benefits of the technology integration in education
but they have got some barriers to use them efficiently. If the administrators and heads of
departments eliminate these barriers, the teachers will teach their lessons more effectively.
We know that all of the benefits of technology are connected by the teachers’ abilities
and usage of technology. So, the most important thing is to teach the teachers to use the
technology. After this we can expect the benefits of technology.
Administrators have two important roles in technology integration. First, they must believe the
benefits of technology integration and buy the best qualified devices and software for their
51%
34%
6%
2% 1%
6%
Responsibility Chart
Teachers
Administrators
Ministry of Education
Students
Publishers
Others
127
teachers. Second, they need to support their teachers. This support may be in two ways; by
words or behavior towards the teachers who use more technology and by solving their
problems related with the technology and technical problems.
As a result, greatest responsibility in technology integration belongs to teachers. So, we
need to motivate the teachers to integrate technological devices into their lessons. When they
believe they can solve all types of barriers and give more valuable lessons to their students.
Also, educational faculties have great responsibility to teach usage of the technological devices
and preparation of educational software. These lessons may be some elective lessons but at
least some of the teachers need to know preparation of the software.
Further researches may generalize my results for other lessons. Also, it will be beneficial if we
search the methods for educating the teachers because, the most important things to use the
technology made by the teachers; they need to find the programs, they must prepare the
software and other needed materials. Seminars and courses for training the teachers have
crucial importance. But, contents of these seminars must be controlled before. If we waste the
time of teachers for some unnecessary seminars they will not be motivated to join other and
maybe more important seminars.Some devices, like smartphone, need to be investigated and
researchers must find the methods to integrate it into education because they are the most used
technological devices of our century.
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128
УДК 51
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