International Journal on New Trends in Education and Their Implications (IJONTE)

January 2016

Volume: 7 Issue: 1

ISSN 1309-6249

http://ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 ISSN 1309-6249

Contact Addresses

Prof. Dr. Zeki Kaya, Gazi Üniversitesi, Gazi Eğitim Fakültesi, Eğitim Bilimleri Bölümü Teknik Okullar Ankara/Türkiye E. Mail: [email protected]

Prof. Dr. Uğur Demiray, Anadolu Üniversitesi, İletişim Bilimleri Fakültesi, Yunusemre Kampüsü, 26470 Eskişehir/Türkiye E. Mail: [email protected] Phone: +905422322167

Abstracting & Indexing

International Journal on New Trends in Education and Their Implications (IJONTE) is currently indexed, abstracted and listed starting with the first issue in:

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 ISSN 1309-6249

Sponsors

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 ISSN 1309-6249

Editors

Prof. Dr. Zeki Kaya, Gazi University- Turkey Prof. Dr. Ugur Demiray, Anadolu University- Turkey

Associate Editors

Assoc. Prof. Dr. Beyhan Zabun, Gazi University- Turkey Assist. Prof. Dr. Ilknur Istifci, Anadolu University- Turkey Dr. Nazan Dogruer, Eastern Mediterranean University- TRNC Dr. Ramadan Eyyam, Eastern Mediterranean University- TRNC Dr. Ufuk Tanyeri, Ankara University- Turkey

Assistant Editor

Ipek Menevis, Eastern Mediterranean University- TRNC

Editorial Board

Prof. Dr. Ali H. Raddaoui, University of Sfax- Tunisia Prof. Dr. Abdul Hakim Juri, University of Kuala Lumpur- Malaysia Prof. Dr. Ali Murat Sunbul, Selcuk University- Turkey Prof. Dr. Ahmet Pehlivan, Cyprus International University- TRNC Prof. Dr. Ali Simsek, Anadolu University- Turkey Prof. Dr. Antoinette J. Muntjewerff, Amsterdam University- Netherlands Prof. Dr. Antonis Lionarakis, Hellenic Open University- Greece Prof. Dr. Augustyn Bańka, Nicolaus Copernicus University- Poland Prof. Dr. Boriss Misnevs, Transport and Telecommunication Institute- Latvia Prof. Dr. Charlotte Nirmalani (Lani) Gunawardena, University of New Mexico- USA Prof. Dr. Christine Howe, University of Cambridge- United Kingdom Prof. Dr. Cevat Celep, Kocaeli University- Turkey Prof. Dr. Cleborne D. Maddux, University of Nevada- USA Prof. Dr. Coskun Bayrak, Anadolu University- Turkey Prof. Dr. Danièle Moore, Simon Fraser University- Canada Prof. Dr. Emine Demiray, Anadolu University- Turkey Prof. Dr. Erol Yildiz, Alpen-Adria University- Austria Prof. Dr. Esmahan Agaoglu, Anadolu University- Turkey Prof. Dr. Francis Glasgow, Guyana University- South America Prof. Dr. Gonca Telli Yamamoto, Okan University- Turkey Prof. Dr. Gul Nurgalieva, Joint-stock company,"National Center of Information"- Kazakhstan Prof. Dr. Harold Bekkering, University of Nijmegen- Netherlands Prof. Dr. H. Ferhan Odabasi, Anadolu University- Turkey iii Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 ISSN 1309-6249

Prof. Dr. Heli Ruokamo, University of Lapland- Finland Prof. Dr. I. Hakki Mirici, Hacettepe University- Turkey Prof. Dr. Jim Flood, Open University- United Kingdom Prof. Dr. Jozef Gašparík, Slovak University of Technology in Bratislava- Slovakia Prof. Dr. Kiyoshi Nakabayashi, Kumamoto University- Japan Prof. Dr. K. M. Gupta, Motilal Nehru National Institute of Technology- India Prof. Dr. Liliana Ezechil, University of Piteşti- Romania Prof. Dr. Manuel Alberto M. Ferreira, Lisbon University Institute- Portugal Prof. Dr. Marie J. Myers, Queen's University- Canada Prof. Dr. Mehmet Durdu Karsli, Çanakkale Onsekiz Mart University- Turkey Prof. Dr. Mehmet Kesim, Anadolu University- Turkey Prof. Dr. Meral Aksu, Middle East Technical University- Turkey Prof. Dr. Min Jou, National Taiwan Normal University- Taiwan Prof. Dr. Modafar Ati, Abu Dhabi University- United Arab Emirates Prof. Dr. Mohamed Abolgasem Artemimi, Zawia Engineering College- Libya Prof. Dr. Mufit Komleksiz, Cyprus International University- TRNC Prof. Dr. Mustafa Cakir, Anadolu University- Turkey Prof. Dr. Nedim Gurses, Anadolu University- Turkey Prof. Dr. Paul Kawachi, Bejing Normal University- China Prof. Dr. Ramesh C. Sharma, Indira Gandhi National Open University- India Prof. Dr. Richard C. Hunter, University of Illinois at Urbana-Champaign- USA Prof. Dr. Roberta E. (Bobby) Harreveld, Queensland University- Australia Prof. Dr. Rozhan M. Idrus, School of Distance Education, University Sains- Malaysia Prof. Dr. Santosh Panda, Indira Gandhi National Open University- India Prof. Dr. Selahattin Gelbal, Hacettepe University- Turkey Prof. Dr. Sharif H. Guseynov, Transport and Telecommunication Institute- Latvia Prof. Dr. Tamar Lominadze, Georgian Technical University- Georgia Prof. Dr. Tanja Betz, Goethe University- Germany Prof. Dr. Tony Townsend, University of Glasgow- United Kingdom Prof. Dr. Valentina Dagiene, Institute of Mathematics and Informatics- Lithuania Prof. Dr. Xibin Han, Tsinghua University- China Prof. Dr. Yavuz Akpinar, Bogaziçi University- Turkey Prof. Dr. Yoav Yair,The Open University of Israel- Israel Prof. Dr. Yuksel Kavak, Hacettepe University- Turkey Assoc. Prof. Dr. Carlos Machado, Vrije University- Belgium Assoc. Prof. Dr. Danny Bernard Martin, University of Ilinois at Chicago- USA Assoc. Prof. Dr. Demetrios G. Sampson, University of Piraeus- Greece Assoc. Prof. Dr. Irfan Yurdabakan, Dokuz Eykul University- Turkey Assoc. Prof. Dr. Natalija Lepkova, Vilnius Gediminas Technical University- Lithuania Assoc. Prof. Dr. Nigel Bagnall, The University of Sydney- Australia Assoc. Prof. Dr. Ozgen Korkmaz, Mevlana University- Turkey Assoc. Prof. Dr. Piet Kommers, University of Twente- Netherlands Assoc. Prof. Dr. Rositsa Doneva, Paisii Hilendarski University of Plovdiv- Bulgaria Assoc. Prof. Dr. S. Raja, ASL Pauls College of Engineering and Technology- India Assoc. Prof. Dr. Shivakumar Deene, Karnataka State Open University- India Assoc. Prof. Dr. Steve Wheeler, University of Plymouth- United Kingdom Assist. Prof. Dr. Katherine Sinitsa, International Research and Training Center- Ukrania Assist. Prof. Dr. Roxana Criu, Cuza University- Romania Assist. Prof. Dr. Zdena Lustigova, Charles University- Czech Republic Dr. Carmencita L. Castolo, Polytechnic University- Philippines iv Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 ISSN 1309-6249

Dr. Hisham Mobaideen, Mu'tah University- Jordan Dr. Simon Stobart, University of Teesside- United Kingdom

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 From Editors ISSN 1309-6249

Dear IJONTE Readers,

International Journal on New Trends in Education and Their Implications- IJONTE appears on your screen now as Volume 7, Number 1. In this issue it publishes 10 articles. And this time, 14 authors from 2 different countries are placed. These are Turkey and USA.

Our journal has been published for over five years. It has been followed by many people and a lot of articles have been sent to be published. 362 articles have been sent to referees for forthcoming issues. They will be published according to the order and the results. Articles are sent to referees without names and addresses of the authors. The articles who get positive responses will be published and the authors will be informed. The articles who are not accepted to be published will be returned to their authors.

We wish you success and easiness in your studies.

Cordially,

1st January, 2016

Editors Prof. Dr. Zeki KAYA, Gazi University, Ankara- TURKEY Prof. Dr. Ugur DEMIRAY, Anadolu University, Eskisehir- TURKEY

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Contents ISSN 1309-6249

FROM EDITORS………………………………………….………………………………………………………………………………..……………....vi

CONTENTS……………………………………………………….………………………………………………………………………………………….vii

ARTICLES

01. OPINIONS OF TEACHERS ON ERASMUS+ KEY ACTION 1: A CASE STUDY……………………………………………………1 Prof. Dr. İlhan GÜNBAYI, Rabia VEZNE – TURKEY

02. PRE-SERVICE PRIMARY MATHEMATIC TEACHERS’ SKILLS OF USING THE LANGUAGE OF MATHEMATICS IN THE CONTEXT OF QUADRILATERALS…………………………………………………………………………………………………………………………..………13 Res. Assist. Pınar GÜNER, Assoc. Prof. Dr. Dilek Ç. GÜLTEN - TURKEY

03. COMPARISON OF INSTRUCTOR AND SELF-ASSESSMENTS ON PROSPECTIVE TEACHERS' CONCEPT MAPPING PERFORMANCES THROUGH GENERALIZABILITY THEORY…………………………………………………..…………28 Assist. Prof. Dr. Göksu GÖZEN, Assist. Prof. Dr. Kaan Zülfikar DENİZ- TURKEY

04. GAMIFICATION AND EFFECTS ON STUDENTS’ SCIENCE LESSON ACHIEVEMENT ……………………………………..41 Assist. Prof. Dr. Mehmet Can ŞAHİN, Res. Assist. Nihan ARSLAN NAMLI- TURKEY

05. THE EVALUATION OF LEARNING ENVIRONMENT DESIGNED FOR USING THRE DIMENSIONAL DYNAMIC GEOMETRY SOFTWARE: TEACHER VIEWS………………………………….48 Hilal KALAY, Assist. Prof. Dr. Temel KÖSA– TURKEY

06. USING ICE-BREAKERS IN IMPROVING EVERY FACTOR WHICH CONSIDERED IN TESTING LEARNERS SPEAKING ABILITY…………………………………………………………………………………………………….58 Dr. Parisa YEGANEHPOUR, Prof. Dr. Mehmet TAKKAÇ- TURKEY

07. A MODEL PROPOSAL FOR THE IMPROVEMENT OF INTERNSHIP ACTIVITY IN OFFERING GASTRONOMY EDUCATION PROGRAMS AT THE HIGHER EDUCATION INSTITUTIONS…………………………………………………………………………………….……………69 Assist Prof. Dr. Mehmet SARIOĞLAN- TURKEY

08. THE IMPACT OF CHARTER SCHOOLS ON STUDENT ACHIEVEMENT IN THE UNITED STATES……………………..74 PhDc. Sajid Ali Yousuf ZAI -USA

09. TECHNOLOGY EDUCATION IN PRESCHOOL: AN APPLIED SAMPLE LESSON……………………………………………..81 Gökben TURGUT, Res. Assist. Yeliz TUNGA, Assist. Prof. Dr. Tarık KIŞLA- TURKEY

10. THE RELATIONSHIP BETWEEN 7th AND 8th GRADE STUDENTS' CONCEPTUAL LEARNING AND MATHEMATICS SELF-EFFICACY LEVELS OF SUBJECT OF “ALGEBRAIC EXPRESSIONS AND EQUATIONS”…………………………………………………………………………………………………………………………………..…..93 Assoc. Prof. Dr. Sare ŞENGÜL, Assist. Prof. Dr. Yasemin KABA, Prof. Dr. Yusuf AYDIN- TURKEY

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

OPINIONS OF TEACHERS ON ERASMUS+ KEY ACTION 1: A CASE STUDY

Prof. Dr. İlhan GÜNBAYI Akdeniz University Faculty of Education Antalya- TURKEY

Rabia VEZNE Akdeniz University International Relations Office Rectorate 603 Antalya- TURKEY

ABSTRACT

The aim of this research was to classify the opinions of principals and teachers working in High Schools on the Erasmus+ Key Action 1 Project regarding their reasons for joining this Project, the preparations made before joining the Project, and the benefits derived from participating in the Project. The research is a qualitative study with a multiple holistic case study design. Data were collected from interviews using semi-structured interview forms. At the end of the research, conclusions were classified under three themes. The first theme was that the main reason for joining the project was professional development. The second theme was that the preparations made by high school principals and teachers before participating in the Project consisted of language education, research on the subject of training, as well as collecting information about transport and the host country. The final theme indicated that the benefit of the Project was the opportunity to learn the use of technology in lessons.

Keywords : Erasmus+ Project, Teachers, Principals.

INTRODUCTION

Teaching needs continuous development as a profession which educates individuals in providing a continuation of society in a rapidly changing world. In particular, teachers need continuous development, and support in the fields of information and technology in order to address the needs of students who adapt easily to rapid change in the information and communications era. Teaching is an intellectual activity, requiring decision- making which is complex and contextualized (Ball, 1995. Butler et al, 2004). For this reason, the professional development of teachers should be planned continuously and in a multidimensional way.

Professional development is defined as “the body of systematic activities to prepare teachers for their job, including initial training, induction courses, in-service training, and continuous professional development within school settings” (OECD, 2010: 19). Professional development is the essential requirement behind knowledge, skills, competence, and learning in the profession (Seferioğlu, 2004). Teachers need continuous support in order to have the necessary skills to meet the needs of different student groups in a rapidly changing world.

Tang ve Choi (2009) draw our attention to the symbiotic relationship between professional development and school development, illuminated by research on school improvement. The approach stresses the importance of creating organizational conditions that make the working environment into a learning environment for teachers. This learning environment should include resources, time and structural conditions that allow

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

teachers to have the space and energy they need to devote to their professional development. The culture and ethos of the school should also support the professional development of the teacher.

According to Kwakman (2003), communities of professionals as settings for learning are a significant source of learning in addition to the learning taking place in the workplace. Therefore, it is important that teachers coordinate working and learning activities within the school for the benefit of both their professional development and the development of the school.

Bull & Buechler (1997) and Desimone (2009) state that the qualities needed for effective professional development include being individualized and school-based, using coaching and other follow up procedures, engaging in collaboration, and embedding practices into the daily lives of teachers (Nishimura, 2014).

According to Liljedahl (2014), teachers come to any professional learning opportunity with a list of wants and needs. Therefore, while planning these professional learning opportunities, the needs of teachers should be researched, and the planning should be carried out in accordance with their requirements.

In his paper with the title “Transforming Professional Development to Professional Learning”, Steward (2014), states that learning for teachers in a professional community with other colleagues is more effective. In other words, it is more effective if professional learning activities take place within a working environment, are informed by data, and are centred on student work.

The OECD carried out their Teaching and Learning International Survey (TALIS) in order to help countries develop a high-quality teaching profession by better understanding who teachers are and how they work. There are 9 different professional development activities defined in this survey: • Informal dialogue to improve teaching, • Courses and workshops, • Reading professional literature, • Education conferences and seminars, • Professional development network, • Individual and collaborative research, • Mentoring and peer observation, • Observation visits to other schools, • Qualification programmes.

According to the TALIS survey, with the participation of more than 100,000 teachers and principals from 34 countries, the type of professional development most often mentioned was “Informal dialogue to improve teaching”, with 93% of teachers on average reporting this activity during the survey period. After “Informal dialogue to improve teaching”, the most frequently reported activities were “attending Courses and workshops” (81%) and “Reading professional literature” (78%). The least common types of professional development was “Observation visits to other schools” (28%) and “Qualification programmes” (25%).

TALIS survey found that fewer than one in three teachers believe teaching is a valued profession in society. It is important that those countries where teachers feel valued tend to perform better in PISA. The Survey also shows that too many teachers still work in isolation. Over half report rarely or never team-teaching with colleagues, and only one third observe their colleagues while they are teaching. 46% of teachers report that they never receive any encouragement to do this from their school leader. Another finding of the Survey is that teachers who engage in collaborative learning have higher job satisfaction and confidence in their abilities. Moreover, according to TALIS, teachers are open to change and keen to learn and develop throughout their careers. At the same time, they need to take more initiative to work with colleagues and school leaders, and take advantage of every opportunity for professional development. According to the findings about Turkey in TALIS, the professional perception of teachers is so interesting that teachers who participated in the Survey do not see themselves as unsatisfied and they do not feel the need for professional development. However,

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

Turkey’s PISA scores are extremely low, and it is impossible that this cannot be related to the professional development of teachers.

It is stated in the “Education for All” EFA report from 2005 that the level of qualifications of teachers is high in Canada, Finland, Cuba and the Republic of Korea, where high standards of educational quality have also been achieved. It is emphasized that the teaching profession is highly respected in Canada, and although there is need for more teachers, the selection criteria are high. Teachers in Canada attend 40 days of in-service training a year, participation is compulsory, and the participants receive financial rewards. When the main factor behind Cuba’s rising success is put under the microscope, it is seen that teachers form a learning community called the “Colectivo pedagogico”. In the “Colectivo pedagogico”, teachers come together frequently to develop a common curriculum, teaching methods and materials. In the Report, it is emphasized that investments in teachers and school-based professional training are necessary to increase the quality of education. It is also clearly stated in the Report that the reason for high quality in education, and high scores in PISA, is that the professional development of teachers is supported.

The Key Data on Teachers and School Leaders in Europe, based on data collected through the Eurydice network, Eurostat, and the TALIS, TIMSS and PISA international surveys, gives an exhaustive picture of data relating to the teaching professions in 32 European countries covering 62 indicators. It also provides standardised and readily comparable quantitative and qualitative indicators which offer a wide-ranging overview of key issues related to the teaching profession in Europe. Continuing Professional Development (CPD) has gained in importance over recent years, and is considered a professional duty in a majority of countries; participation in CPD is necessary for promotion in terms of career advancement and salary increases in Bulgaria, Spain, Lithuania, Portugal, Romania, Slovenia and Slovakia. In many European countries schools are obliged to have a CPD development plan for the whole school staff, but less than a third oblige individual teachers to have a personal plan.

Teachers’ professional development is also one of the priorities of the European Union (EU) as can be understood from Key Data on Teachers and School Leaders in Europe. The European Commission emphasizes improving the quality and efficiency of education and training, and enhancing creativity and innovation, including entrepreneurship, at all levels of education and training in the Education and Training 2020 Strategic Framework. The European Union supports schools and teachers with the Erasmus+ Programme, which will be implemented between the years 2014 and 2020. Erasmus+ Key Action 1 Learning Mobility of Individuals aims to improve the competences of school staff, and provide professional development opportunities abroad. There are two kinds of activities under this key action: • Teaching assignments: this activity allows teachers or other school education staff to teach at a partner school abroad;

• Staff training: this activity supports the professional development of teachers, school leaders or other school education staff in the form of: a) participation in structured courses or training events abroad; b) a job shadowing/observation period abroad in a partner school or other relevant organisation active in the field of school education. Even though the Erasmus+ Programme only started in 2014, 1,658 Erasmus+ KA1 project applications have been submitted in Turkey. 93 projects out of the 1,658 applications were approved and funded by the Turkish National Agency. This high number of applications shows that teachers have a high level of interest and desire to participate in a structured training course in Europe. (Türkiye Ulusal Ajansı). The aim of this research is to classify the opinions of the principals and teachers working in High Schools on the Erasmus+ Key Action 1 Project regarding their reasons for joining this Project, the preparations made before the Project, and the benefits of the Project. To achieve this aim, the answers to these questions were sought: 1. What are the reasons for participating in the Erasmus+ KA1 Project? 2. How is the preparation process before the Erasmus+ KA1 Project? 3. What are the benefits of the Erasmus+ KA1 Project ? 4. What do teachers think the Erasmus+ KA1 Project training is like?

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

METHODS

Sampling This study was conducted in Göynük Science High School from July 1 st , 2015 to September 30 th 2015. One principal, 3 vice-principals and 20 teachers working in Göynük Science High School participated in the Erasmus KA1 Project during the 2014/2015 academic year. A non-probability sample technique based on the purposive sampling method was used because ‘the sample derives from the researcher targeting a particular group, in the full knowledge that it does not represent the wider population, it simply represent itself. This is frequently the case in small scale research, for example, as with one or two schools, two or three groups of students, or a particular group of teachers, where no attempt to generalize is desired; this is frequently the case for qualitative researches such as action ethnographic or case (Cohen, Manion & Morrison, 2007).

Table 1: Participant status and accompanying data collection Code Position Study-field Interview A Teacher Physical Education Yes B Teacher Mathematics Yes C Teacher Turkish Yes D Teacher History Yes E Teacher Biology Yes F Teacher Mathematics Yes G Vice-principal English Yes H Principal Religion Yes

As seen in Table 1, the informants in this study were principals and teachers. Face-to-face interviews were done with 8 administrative and teaching staff members from Göynük Science High School. The participants were volunteers, and there were no restrictions on the ages and seniority of principals and teachers.

METHOD

The method of this research is qualitative study. The research is a case study with a holistic single case. Data were collected via face-to-face interviews by using semi-structured interview forms. According to Yıldırım and Şimşek (2000:19), qualitative study is a study which uses a process to present perceptions and events in a holistic and realistic way in their natural environment. Data collection methods such as observation, interviews and document analyses are used in qualitative study. The case study present results by observing them in their real context which determines the reasons and results. In qualitative research design, the case study method allows investigators to retain the holistic and meaningful characteristics of real-life events such as individual life cycles, small group behaviour, organizational and managerial processes, school performance, and interpersonal relations in real contexts (Cohen et al, 2007; Yin, 2012).

Data Collection In order to classify the opinions of the principals and teachers working in the High School on Erasmus+ Key Action 1 Project as the reasons of joining this Project, the preparations before the Project and the benefits of the Project, semi-structured individual interviews were used because this would provide an in-depth exploration of the topic. It would also allow the flexibility, for example, to change the order of questions, simplify the questions, and to probe the interviews (Cohen et al, 2007). Data were collected from July 1 st 2015 to September 30 th 2015. Face-to-face interviews were used and informants' experiences, thoughts and feelings were recorded in a taped diary.

Data Analysis Data analysis began with repeated readings of interview transcripts from conversations with principals and teachers. The purpose was to determine the essence of the phenomenon and structures of experiences of the principals and teachers who participated in the Erasmus+ Key Action 1 Project. During data analysis, the data 4 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

were organized categorically and chronologically, reviewed repeatedly and continually coded. Interview transcripts were regularly reviewed. In addition, the data analysis process was aided by the use of a qualitative data analysis computer program called NVIVO 10. These kinds of computer programmes do not actually perform the analysis but facilitate and assist it. That is to say, NVIVO 10 does not perform the analysis but only supports the researcher doing the analysis by organizing data and recodes, nodes etc. (Kelle, 1995; Cohen et al, 2007).

Ethical Considerations Participants were briefed about the aims of the research, kept informed at all stages and offered anonymity. A consent form was signed between researcher and each participant about the use of the data in terms of how its analysis would be reported and disseminated. Care was also taken not to impose the researcher’s beliefs on others since researcher’s beliefs were secondary, and it was the participants thinking which was required.

Interview Process and Mapping The purpose of this study was to classify the opinions of the principals and teachers who were working in a High School on the Erasmus+ Key Action 1 Project. Thus the mapping of interview questions was carried out on four levels. Firstly, the principals and teachers were asked why they participated in the Project, secondly what preparations they made before the Project started, thirdly what the benefits of the Project were, and finally what they thought of the Project and why.

Validity and Reliability In order to ensure the reliability and validity of the study, some steps were followed: (i) data were collected from various sources such as interviews (individual) and documents in terms of triangulation (ii) data were used as direct quotations from the interviews without making any comments on them, (iii) a purposive sampling method based on voluntarism was used in order to get the opinions and experiences of principals and teachers in Göynük Science High School (iv) data were coded by two independent researchers and Cohen's kappa coefficient was calculated to determine inter-rater reliability of themes coded -0.92 perfect agreement- for inner reliability (Landis & Koach, 1977) and (v) records of interviews, documents and participant observations were kept for outer reliability.

FINDINGS

In this study, we tried to present the opinions of the principals and teachers working in a Science High School on the Erasmus+ Key Action 1 Project. The opinions of the principals and teachers were classified according to reasons for joining this Project, preparations made before the Project, and the benefits of the Project. During the research process, participants were offered anonymity.

1. Reasons for participating in the Erasmus+ KA1 Project Principals and teachers were asked about their reasons for participating in the Erasmus+ KA1 Project. The data can be seen in Table 2.

As can be understood from the frequency analysis of the reasons for participating in the Erasmus+ KA1 Project in Table 2, 37.5% of principals and teachers stated that the main reason for participation was professional development. The opinions of the participants are as follows:

My reason for participating in a training course abroad is to develop myself in my profession, and to be more helpful to students at school (A1, 15) …the third reason is of course I thought that it would contribute to my professional development (G1, 15) The reason for participating in a training course abroad is entirely about professional development (H1,15) Next, 25% of principals and teachers stated that the reasons for participation were comparing educational systems, knowing about different cultures, learning about different implementations and using them, and personal development. The opinions of the participants are as follows: Seeing on site and comparing the education systems in my country and abroad (B1, 5)

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

Table 2 : Reasons for participating in the Erasmus+ KA1 Project A B C D E F G H f %

1 Comparing the developments and activities in the field √ 1 12.50% 2 Learning the developments in the field √ 1 12.50% 3 Taking part in scientific studies √ 1 12.50% 4 Researching scientific studies √ 1 12.50% 5 Comparing educational systems √ √ 2 25.00% 6 Increasing the awareness about educational facilities √ 1 12.50% 7 Recognising the similarities in educational systems √ 1 12.50% 8 Recognising the ability to live in a different country √ 1 12.50% 9 Knowing about different cultures √ √ 2 25.00% 10 Learning about different implementations and using them √ √ 2 25.00% 11 Meeting with colleagues from different countries √ 1 12.50% 12 Learning the socio-cultural structure of the hosting country √ 1 12.50% 13 Personal development √ √ 2 25.00% 14 Curiosity √ 1 12.50% 15 Professional Development √ √ √ 3 37.50% 16 Seeing a new country √ 1 12.50% 17 Knowing about new cultures √ 1 12.50%

Researching the educational structure of that country, systematically comparing the educational structures of Turkey and that country, and getting the opportunity to do this (H1, 5) Our school, being a science high school, has science events and other socio-cultural courses and I want to learn about the socio-cultural richness of the country where the training course is organised and share these with students (A1,9) Secondly, I want to know different cultures (G1,9) Another reason is to see different educational implementations in European countries, seeing them on site and transferring good applications to school (A1, 10) Learning how the course subject is perceived and processed in other countries (C1,10) Contributing to my personal development by having new friends (C1,13) First, personal development (G1,13) 12.5% of principals and teachers stated that the reasons for participation are comparing developments and activities in the field, learning the developments in the field, taking part in scientific studies, researching scientific studies, increasing their awareness about educational facilities, recognising the similarities in educational systems, recognising the ability to live in a different country, meeting with colleagues from different countries, learning the socio-cultural structure of the host country, curiosity, seeing a new country, and knowing about new cultures. The opinions of the participants are as follows: I am curious about the similarities and differences in the developments and activities between Turkey and abroad in my field (F1,1) I attended this course to take part in scientific studies (E1,3) … I researched scientific studies of that country (E1,4) My awareness about their and our educational facilities increased (F1,6) I see that although the cultures are different, the educational systems have basic similarities (D1,7) I want to see how can I live in a country where people speak another language and my problem solving capacity (D1,8) Again, first of all, it is impressive to meet colleagues with different countries and sharing (F1,11) Curiosity (F1,14) Seeing a new country (D1, 16) Knowing about new cultures (C1,17 ) When the opinions of the principals and teachers on the reasons for participation in the Erasmus+ Key Action 1 Project generally were analyzed, principals expected professional development, personal development,

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

comparing educational systems, and knowing about different cultures. Accordćngly, it was understood that teachers participated in the Project to learn about different implementations and use them, personal development, comparing developments and activities in their field, learning about developments in their field, taking part in scientific studies, researching scientific studies, increasing their awareness about educational facilities, recognising the similarities in educational systems, recognising the ability to live in a different country, meeting with colleagues from different countries, learning the socio-cultural structure of the hosting country, curiosity, seeing a new country, and knowing about new cultures.

2. The preparations before Erasmus+ KA1 Project Principals and teachers were asked about their preparations before the Erasmus+ KA1 Project. The data can be seen in Table 3.

Table 3: Preparations before the Erasmus+ KA1 Project A B C D E F G H f % 1 Language education √ √ √ 3 37.50% 2 Getting information about the places to be √ √ 2 25.00% visited 3 Research about the training subject √ √ √ 3 37.50% 4 Researching about culture √ √ 2 25.00% 5 Getting information about transport √ √ √ 3 37.50% 6 Getting information about the country √ √ √ 3 37.50% 7 Comparing countries √ 1 12.50% 8 Getting information about the educational √ 1 12.50% system of the host country 9 Getting information about the host √ 1 12.50% organization

As can be understood from the frequency analysis of their preparations before the Erasmus+ KA1 Project in Table 3, 37.5% of principals and teachers stated that the preparations they did before the Project were language education, research about the training subject, and getting information about transport and the country. The opinions of the participants are as follows:

I went on a course to make English practice before the training course. To have easy communication (A2,1) I tried to learn enough English terms for myself (B2,1) I studied English a little and learnt basic sentences and structures (D2,1) I made research about the course subject (C2,3) Secondly, I made research about the environment, which is the course subject in the environment and on the internet (G2,3) We collected information about the metro map and transport from the airport to the city centre in that country. We identified the easiest and cheapest form of transport. Besides, we planned to find cultural places and visit them (A2,5) I examined the metro infrastructure of the city in the country where I was going (B2,5) I researched the transport facilities and good places in the city (F2,5) I got information about the country we went to (C2,6) One, I made research about the country I went to from the internet (G2,6) I can say that the preparation we did before the training course abroad was getting information about the country (H2,6) Next, 25% of principals and teachers stated that the preparations they did before the Project were getting information about the places that would be visited and research about culture. The opinions of the participants are as follows: We did preparations before the training course, got information about hotels, transport, the training venue, the region and the places that can be visited there (A2,2) I did research about the place I went to (D2,2) 7 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

I researched the culture of the country we went to (E2,4) First of all, I researched the climate and the eating and drinking culture of the country I went to (F2,4) 12.5% of principals and teachers stated that the preparations they did before the Project were comparing countries, getting information about the educational system of the host country, and getting information about the host organization. The opinions of the participants are as follows: Getting information about the educational system of that country (D2,8) I also got information about the organization which organises the training course (A2,9) When we interpret the opinions of the principals and teachers on the preparations they did before the Project generally, principals and teachers both stated that they did research about the training subject and getting information about the country.

3. Benefits of Erasmus+ KA1 Project Principals and teachers were asked about the benefits of the Erasmus+ KA1 Project. The data can be seen in Table 4.

Table 4: Benefits of the Erasmus+ KA1 Project

A B C D E F G H f %

1 Converting my studies into a documentary √ 1 12.50% 2 Improving environmental awareness √ 1 12.50% 3 Using technology in the lessons √ √ √ √ 4 50.00%

4 Sharing good practices in education √ 1 12.50% 5 Transferring training subjects to school subjects √ 1 12.50% 6 Effect on professional development √ 1 12.50% 7 Preparation for events done at school √ 1 12.50% 8 Broadening horizons √ √ 2 25.00% 9 Learning about video shooting √ √ √ 3 37.50% 10 Improving foreign language √ 1 12.50%

As can be understood from the frequency analysis of the benefits of the Erasmus+ KA1 Project in Table 4, 50% of principals and teachers stated that the main benefit of the Project was using technology in the lessons. 37.5% of principals and teachers stated that the secondary benefit of the Project is learning about video shooting. The opinions of the participants are as follows: I learnt technology use in lessons (A3,3) Besides, I used technology and reinforced the effect of technology on courses practically (F3,3) I can talk about two kinds of effect here, first more effective media tools use in the courses and how to use them (G3,3) Our main aim is in the science and technology use, … increasing technology use skills in science teaching, our technology use skills improved and we had a chance to implement this in our school (H3,3) How to shoot video with students, fine details in video shooting (A3,9) I learnt some specifics that should be known in video shooting (B3,9) I learnt what to do and how to be careful for successful video shooting (D3,9) Next, 25% of principals and teachers stated that the benefit of the Project is broadening horizons. The opinions of the participants are as follows: Broadening my horizons with project work done abroad (E3,8) … also I think that my horizons will broaden by travelling abroad (H3,8) 12.5% of principals and teachers stated that the benefits of the Project were converting their studies into a documentary, improving environmental awareness, sharing good practices in education, transferring the 8 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

training subject to school subjects, effect on professional development, preparation for events done at school, and improving foreign language. The opinions of the participants are as follows: The most important benefit to me is to transfer my field study and laboratory work into a documentary (E3,1) Secondly, educational studies to increase environmental awareness of not only students but also people in the environment (G3,2) … we shared good practices in education (H3,4) We learnt how to transfer the training subject to our lessons (C3,5) This training course organised abroad had a big effect on our professional development (H3,6) … also I learnt what to do in social events organised at school, how to distribute the roles, preparatory work for it, work during the event, and things to be done after the event (A3,7) Well… I improved my foreign language and I was motivated more to learn a foreign language (A3,10) When the opinions of the principals and teachers on the benefits of the Project were analysed generally, the principals’ opinions were compatible with the reasons for participation. They stated that the benefits of the Project are using technology in their lessons, learning about video shooting, sharing good practices in education, professional development, and broadening horizons. Having similar opinions, teachers stated that the benefits of the Project were converting studies into a documentary, improving environmental awareness, transferring the training subject to school subjects, and preparation for events done at school, and improving foreign language.

4. Metaphors for Erasmus+ KA1 Project Training Metaphors formulated by the 8 participants can be categorized under five themes as in Table 5: nature, place, person, things, and activity. Three of the participants formulated nature metaphors in defining the Project training. A described the training as a tree: “the training course I attended was like a fruit tree. The more you look after a fruit tree, the more you get fruit. For me also, the more careful and patient I am, the more I learn and improve my skills, and if we think of the skills I get as a fruit, I am planning to share them with students. Therefore, I described it as a tree. Namely, I aim to share what I get from the training course as a fruit shared with others” . Similarly, B used a rainbow metaphor for describing the training: “It was like a rainbow because the people from all over the world were colourful for me”. As for C, he defined training as a mineral: “It was like an unprocessed mineral because I added good knowledge to mine and made it more functional and contemporary”.

Table 5: Metaphors for the Erasmus+ KA1 Project Training A B C D E F G H f % 1 Nature √ √ √ 3 37.50% 2 Place √ √ 2 25.00% 3 Person √ 1 12.50% 4 Things √ 1 12.50% 5 Activity √ 1 12.50%

Two of the participants formulated place metaphors in defining training. H described training as a school: “It was like a different school because I felt that I entered a different world and it made positive contributions to my personal development and world perspective, I can summarize it shortly like this”. F described training as a workshop: “It was like a workshop because we continually practiced what we learnt in theory, and applied it to daily life. This training course was functional not static for me”. Three other participants used different metaphors for training. Participant D used a person metaphor and she thought training was like a student : “It was like a student who starts primary school. Life changes suddenly, a new and anxious environment, many things to learn”. On the other hand, participant E formulated a thing metaphor and she defined training as a ship: “It was like a ship in deep-sea because its horizon was broad and you do not know which port it will go”. Finally, G defined training as an activity and defined it as a game: “In my opinion, it was like an enjoyable game because the trainer was so joyful, and the training was funny”. As can be understood from the frequency analysis of metaphors defined by teachers in Table 5, the training course was perceived as a fruitful, effective, interesting and generally positive phenomenon.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

DISCUSSION AND CONCLUSION

This study was done to understand and classify the opinions of the principals and teachers working in a Science High School on the Erasmus+ Key Action 1 Project regarding their reasons of joining this Project, the preparations made before the Project, and the benefits of the Project. Accordingly, data were collected through semi-structured individual interviews.

The reasons given by the principal and teachers for participation in the Erasmus+ Key Action 1 Project were professional development, comparing educational systems, knowing about different cultures, learning about different implementations and using them, and personal development. When the reasons for participating in the Project are interpreted generally, it could be said that these reasons are compatible with “support learners in the acquisition of learning outcomes (knowledge, skills and competences) with a view to improving their personal development, support the professional development of those who work in education and training, enhance the participants' foreign languages competence, and raising participants' awareness and understanding of other cultures and countries”; the aim of Erasmus+ Programme Key Action 1 Learning Mobility of Individuals, which is carried out by the European Commission between the years 2014 and 2020 (EC, 2016). The opinions of the principal and teachers on the reasons for participation in the Erasmus+ Key Action 1 Project are also compatible with the findings of Kippax’s (1999) study called “The Leonardo da Vinci project qualifying training in low vision”. According to this study, it is important that colleagues and project participants from different disciplines should be eager for successful cooperation (Kippax, 1999: 42).

The preparations before the Project were language education, research about the training subject, and getting information about transport and the country. When the preparations before the Project are interpreted generally, it can be said that these are compatible with “enhance the participants' foreign languages competence, raise participants' awareness and understanding of other cultures and countries”; the learning aims of Erasmus+ Programme Key Action 1 Learning Mobility of Individuals, which is carried out by European Commission between the years 2014 and 2020 (EC, 2016). At the same time, language education as a preparation before the Project is compatible with the findings of Minasowicz, Nowak, Sołtyska’s (2004) study called “Methodology of English language courses for construction engineers and managers in Poland and Portugal”. According to this study, it is stated that the Leonardo da vinci project will make English language use easier in addition to knowledge transfer (Minasowicz, Nowak and Sołtyska 2004: 104).

When the benefits of the Project are interpreted generally, it can be said that these are compatible with “Support learners in the acquisition of learning outcomes (knowledge, skills and competences) with a view to improving their personal development, support the professional development of those who work in education and training, enhance the participants' foreign languages competence, raise participants' awareness and understanding of other cultures and countries.”; the principle of the European Commission (EC, 2016). The opinions of principals and teachers on the benefits of the Erasmus+ Key Action 1 Project are also compatible with the findings of Kippax’s (1999) study called “The Leonardo da Vinci project qualifying training in low vision”. According to this study, the benefits of the Leonardo da Vinci project are learning about good practices in vocational education and getting new perspectives (Kippax, 1999: 42).

The Erasmus+ KA1 Project in Turkey has important benefits such as; professional development, comparing educational systems in the EU and Turkey, and personal development. For that reason, Erasmus+ KA1 projects are essential for high schools.

According to the findings of this study, the following ideas are suggested by the researcher: Teachers should be informed more about different training courses which are specific to their field of study given under Erasmus+ Key Action 1, and they should attend those training courses in order to increase their Professional development. Teachers should be informed about the Erasmus+ KA2 Strategic Partnership Projects writing and application process in order to get the benefit of partnership projects.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

IJONTE’s Note: This article was presented at World Conference on Educational and Instructional Studies- WCEIS, 05- 07 November, 2015 by IJONTE Scientific Committee.

BIODATA AND CONTACT ADDRESS OF AUTHORS

Prof. Dr. Ilhan GUNBAYI completed his BA studies on English Language Teaching, his MA in Educational Administration and Supervision, his PhD on Educational Administration, Supervision, Planning and Economy at Hacettepe University in Turkey, and his Post Doctorate Study on Qualitative Research Methods at Sheffield Hallam University in the UK. He has been working as an Associate Professor in the Educational Sciences Department of Akdeniz University Faculty of Education since 2003. He is scholarly interested in qualitative research methods, organizational communication, organizational culture and climate, motivation at work, job stressors and school leadership, vocational education and training linked to employment issues and national development, particularly in Turkey but also in Central/Western Asia and Europe.

Assoc. Prof. Dr. Ilhan GUNBAYI Akdeniz University Faculty of Education Educational Sciences Department Dumlupinar Bulvari Kampus 07058 Antalya- TURKEY E. Mail: [email protected]

Rabia VEZNE completed her BA studies in English Language Teaching at the Middle East Technical University, and her MA on Educational Administration and Supervision in Kırıkkale University. She is doing a PhD on Adult Education in Ankara University in Turkey. She has been working as an EU Projects Advisor since 2009, and she has been working in the Akdeniz University International Relations Office as an EU Projects Advisor since 2013. She is scholarly interested in vocational education and EU projects.

Rabia VEZNE Akdeniz University International Relations Office Dumlupinar Bulvari Kampus 07058 Antalya- TURKEY E. Mail: [email protected]

REFERENCES

Butler, D.L., Lauscher, H.N., Jarvis-Selinger, S., Beckingham, B. (2004). Colloboration and self-regulation in teachers’ professional development. Teaching and Teacher Education . 20, 435-455.

Cohen, L., Mannion, L. and Morrıson, K. (2007). Research Methods in Education. UK: Routledge, Taylor & Francis Group.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 01 ISSN 1309-6249

EFA Küresel İzleme Raporu 2005. UNESCO,2004. 49-52.

European Commission (2016). Erasmus+ Programme Guide . Version 1 (2016): 20/10/2015

Key Data on Teachers and School Leaders in Europe. Eurydice Publication, 2013.

Kippax, J. (1999). The Leonardo da Vinci project qualifying training in low vision. Visual Impairment Research , 1 (1), 41-43.

Kwakman, K. (2003) Factors affecting teachers’ participation in Professional learning activities, Teaching and Teacher Education , 19, 149-170.

Landis, J. R. & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics , 33(1), 159-174.

Liljedahl, P. (2014). Approaching Professional learning: what teachers want. The Mathematics Enthusiast. Vol.11, No.,1 109-122.

Minasowicz, A, Nowak, P. and Sołtyska, D. (2004). Methodology of English language courses for construction engineers and managers in poland and portugal. Studıes about Languages, 5, 103-107.

Nishimura, Trisha. Effective Professional Development of Teachers: A Guide to Actualizing Inclusive Schooling. International Journal of Whole Schooling . Vol. 10, Number 1, 2014.

Seferioğlu, S. S. Öğretmenlerin Yeterlilikleri ve Mesleki Gelişim. Bilim ve Aklın Aydınlığında Eğitim . 58, 40-45. 2004.

Steward, C. Transforming Professional Development to Professional Learning. Journal of Adult Education. Vol. 43. Number 1. 2014.

OECD, 2014. TALIS-Teaching and Learning International Survey.

Sylvia Yee Fan Tang & Pik Lin Choi (2009) Teachers' professional lives and continuing professional development in changing times. Educational Review. Vol.61. Number 1, 1-18.

Türkiye Ulusal Ajansı. Eramus+ Okul [Internet-23.06.2015] http://www.ua.gov.tr/programlar/erasmus- program%C4%B1/okul-e%C4%9Fitimi-program%C4%B1

Yıldırım, A. ve Şimşek H. (2000). Sosyal Bilimlerde Nitel Araştırma Yöntemleri . Ankara: Seçkin Yayınları.

Yin, R. K. (2012). Applications of case study research (Third Ed.). London: Sage Publications Ltd.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

PRE-SERVICE PRIMARY MATHEMATIC TEACHERS’ SKILLS OF USING THE LANGUAGE OF MATHEMATICS IN THE CONTEXT OF QUADRILATERALS

Rsrch. Assist. Pınar GÜNER İstanbul University Hasan Ali Yücel Faculty of Education İstanbul- TURKEY

Assoc. Prof. Dr. Dilek Ç. GÜLTEN İstanbul University Hasan Ali Yücel Faculty of Education İstanbul- TURKEY

ABSTRACT

Mathematics is defined as a discipline which has a specific language that emcompasses a variety of symbols, figures, and terms and which depends on the relationship among these properties. Effective learning and teaching of mathematics considerably depends on the accurate use of language. In line with these, this study aims to explore pre-service primary mathematics teachers’ skills of defining and expressing a variety of concepts and properties in the context of quadrilaterals using the language of mathematics. Another objective is to determine pre-service mathematics teachers’ opinions on using language in mathematics teaching and explore the relationship between their opinions and their skills of using the language of mathematics. For this aim, data collection tools include the “Language in Mathematics Teaching Scale” and a test which involves six open-ended questions that cover the sub-dimensions of defining a concept, expressing conceptual properties with a verbal and a symbolic language, and using symbols to represent the properties of shapes. A variety of categories were created in line with the fourth grade pre-service primary teachers’ responses to the open- ended questions. Percentage and frequency values were therefore determined and the data obtained from the scale were interpreted with the help of the SPSS programme. The findings were discussed in line with the literature and some suggestions were presented.

Keywords: Language of mathematics, quadrilaterals, pre-service teacher.

INTRODUCTION

Even though it is hard to define mathematics, which is a broad concept, it can be basically defined as a language which is composed of systems and patterns (Goldenberg, Cuoco & Mark, 1998) that use certain symbols, signs, numbers and shapes to prove the relationship among these representations (Reysi Suydam, Lindquist, & Smith 1995). The research studies in the literature involve different approaches to mathematics. Some suggest that math is a universal language. Others suggest that it has its own language, and the rest suggest that it is difficult to define mathematics (Moschkovich, 2012). Using the language of mathematics means a lot more than possessing its vocabulary. It is necessary but not sufficient to know the mathematical terms and concepts because the language of mathematics encompasses defining patterns, making generalizations and supporting what is meant with representations (Moschkovich, 2012). Meaney (2005) groups the language of mathematics under three headings: everyday language, mathematical concepts and symbolic language. Learning takes place when students can make a connection between these three fields and make transitions. This structure of the language of mathematics enables students to represent their understanding of mathematics and convey the results they come up with (Ní Ríordáin, 2009).

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Although mathematics is a widely-used instrument in the daily life, school is the place where one encounters the use of language in mathematics in the broadest sense (Başaran,1998). Students have to learn the language of mathematics in order to work on the problems, organize their thoughts relying on a particular structure and express them in a clear and comprehensive way, understand their own and others’ mathematical thinking and problem solving processes, and gain flexibility in their skills to interpret and express their thoughts (National Council of Teachers of Mathematics, 2000). Many researchers argue that it is essential for students to use the language of mathematics because those who can use it effectively, in other words, who can read, write and comprehend the mathematics contents, can understand mathematics better and achieve in this discipline (Buchanan, 2007). The best way for students to learn mathematics is to use it. Understanding the language of mathematics enables students to develop their skills of internalizing newly introduced concepts, thinking over and discussing them (Chard, 2003). In addition to this, the language of mathematics is also important for students to attach meanings to the newly introduced mathematical concepts and interpret the differences among them.

Success in mathematics teaching is directly linked to the accurate use of the language of mathematics (Ferrari- Luigi, 2004; Pimm, 1987). Therefore, it is necessary to pay attention to several properties (level suitability, accurateness, ability to represent concepts, usage etc.) of the language in a classroom environment (Bali- Çalıkoğlu, 2002). The way of understanding mathematics is closely linked to expressing mathematical concepts accurately and using mathematical terms properly (Buchanan, 2007). A teacher should pay attention to their language of mathematics so as not to cause misinterpretations in students and also take into account the language of students. Therefore, the students have the opportunity to fix their errors (if any) while using the language of mathematics and develop their skills. At this point, while Glasersfeld (1995) argues that the interaction between the teacher and the student is important, Gökkurt, Soylu, Gökkurt (2012) argue that teachers need to transfer the way they understand mathematical concepts, express their definitions, explain their analyses, and ensure that the students have an opportunity to comment on the mathematical topics they have learned. Because when students describe what they think and do, it will enable both the student himself and the teacher to assess the students in terms of mathematical understanding (Doğan & Güner, 2012). As mathematics progresses cumulatively, the language of mathematics used in this process prospers. For this reason, innacurate and faulty usages during the formation of the basis of the language of mathematics starting from the pimary level education would cause the students to carry this incorrect language into future. In this context, the language of mathematics a teacher uses at the primary to secondary level interfaces is quite important (Aydın &Yeşilyurt, 2007). A teacher has great influence on enabling students to use the accurate language of mathematics (Raiker, 2002). Teachers’ knowledge is mostly formed and shaped during their education period in faculties of education (Bozkurt & Koç, 2012). Therefore, it is important to study pre-service teachers’ skills of using the language of mathematics accurately and to detect their errors.

Çakmak, Bekdemir and Baş (2014) emphasize the importance of using verbal and symbolic languages, which are a part of the language of mathematics, in the classroom and showing the connections between them clearly. This would make it easy for students to understand the transition between these languages. The studies conducted prove that students have difficulty expressing the concepts with a verbal and symbolic language (Capraro & Joffrion, 2006), and fail to use the mathematical area language (Doğan & Güner, 2012; Yeşildere, 2007). In addition to this, many teachers use the language of mathematics carelessly, represent a mathematical concept with a different concept that is not corresponding such as expressing the term of amount with the term of number and confuse mathematical terms (Haylock & Thangata, 2007). The fact that students and teachers have good skills of using the language of mathematics would make it easy for teachers to see better student profiles (Larson, 2007) and increase both the teachers’ and students’ success.

The studies on the language use in mathematics prove that students generally face challenges in transferring mathematical situations and thoughts into the language of mathematics (Dur, 2010; Korhonen, Linnanmäki & Aunio, 2011; Rudd, Lambert, Satterwhite & Zaier 2008; Woods, 2009). Gür (2006) suggests that pre-service teachers make incorrect definitions. Orton and Frobisher (1996) suggest mathematical meaning attributed to a concept depends on a person and there is a risk of expressing a mathematical concept incorrectly based on the attributed meaning. Otterburn and Nicholson (1976) argue that even though students are familiar with

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

mathematical terms, they have difficulty in expressing and internalizing them. In addition to this, several research studies were conducted in this field to explore the significance of the language of mathematics (Barwell, Leung, Morgan, & Street, 2005; Forman & van Oers, 1998; Hoyles & Forman, 1995; Monaghan, 1999; Sfard, 2000; Sfard & Kieran, 2001). However, it is observed that there is little research available in Turkey when the number of studies in the other countries is considered (Aydın & Yeşilyurt, 2007; Çakmak vd, 2014; Çalıkoğlu-Bali, 2003; Doğan & Güner, 2012; Göktürk, Soylu & Örnek, 2013).

Using the language of mathematics in geometry is extremely important (Toptaş, 2015) since geometry, which is a part of mathematics, is a basic skill and is necessary for communication both in the daily life and classroom environment (Sherard, 1981). At this point, a teacher’s job is to pay attention to the accurateness of the language of mathematics and appropriateness to the student’s level. Explaining the generalization “Square is also a rectangle” to the students before a certain level leads to a confusion in students. Giving this information to students after they construct the necessary background would make the concept more meaningful to them (Baykul, 2000; van Hiele, 1986). Geometry has three dimensions: shapes representing the concepts, definitions, and the properties. In other words, a visual image that represents a geometric concept has a definition that helps make sense of the various properties and concepts and differentiate between them (Türnüklü, Alaylı & Akkaş, 2013). The studies conducted focus on the way pre-service teachers define some geometric concepts and the language of mathematics. The results suggest that pre-service teachers fail to use the language of mathematics and define geometric concepts (Çetin & Dane, 2004; Dane, 2008; Kuzniak & Rauscher, 2007; Pickreign, 2007; Sandt & Nieuwoudt, 2003). Researchers suggest conducting similar studies on different geometric concepts and collecting detailed information for the aim of identifying the pre-service teachers’ strengths and weaknesses and take precautions against them. The way of increasing students’ success in geometry is parallel to the quality of mathematics and geometry education at primary level education (Pusey, 2003). The data to be collected from the steps of drawing and defining a geometric shape, explaining its properties, and exemplifying them would be guiding for understanding a teacher’s proficiency (Çakmak, Konyalıoğlu & Işık, 2014). In addition to this, most of the research studies have been conducted with pre-school students, first level primary school students and pre-service teachers and not enough studies have been conducted with pre-service second level primary school teachers (Türnüklü et al, 2013). Accordingly, this study aims to identify the way primary pre-service teachers define the types of quadrilaterals, analyze the shapes they draw, examine the language of mathematics they use to express geometric concepts and properties, and to present the relationship between the pre-service teachers’ views on the language of mathematics and their skills of using the language of mathematics. Thereby, the research questions that guide this study are as follows: 1. What are the pre-service primary mathematics teachers’ skills of using the language of mathematics in the context of quadrilaterals? 2. What are the pre-service primary mathematics teachers’ views on using language in mathematics teaching?

METHOD

Research Model The research was designed in survey (descriptive-survey) model since it aims to investigate the current situation regarding pre-service primary mathematics teachers’ skills of using the language of mathematics in the context of quadrilaterals.

Study Group The research was conducted with 50 pre-service teachers in the 4th grade studying primary mathematics education at a state university located in a city in the north-west of Turkey during the academic year 2015- 2016. This study group was formed on a volunteer basis due to the fact that senior students have taken most of the mathematics education courses and have the necessary background.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Data Collection The data were collected using a test which consists of 6 open-ended questions related to defining quadrilateral types, expressing conceptual properties with a verbal and symbolic language, and representing these attributes by drawing shapes in an effort to explore the pre-service teachers’ skills of using the language of mathematics. The participants were asked to make a definition regarding the concepts of square, rectangle, parallelogram, rhombus, trapezium, and kite (deltoid), write their features verballly, express them symbolically and represent these properties by drawing their shapes. The test questions were prepared with the help of the studies on geometric concepts in the literature and kept in a similar nature.

The “Language in Mathematics Teaching Scale” developed by Bali-Çalıkoğlu (2002) was used to identify pre- service teachers’ views of using the language of mathematics. This scale is designed in a five-point Likert type and the answer possibilities range between “I do not agree at all” and “I strongly agree”. The reliability coefficient of the scale is 0.82. It is composed of four factors which are “written expression and written assigments”, “symbolic expression”, “problem formation”, and “verbal expression”.

Data Analysis An SPSS statistical package program was used for the analysis of the data obtained from the “Language in Mathematics Teaching Scale”, which was used to identify pre-service teachers’ views of using the language of mathematics. The findings were interpreted and the significance level was taken as p=.05. The responses given were labelled as 5- I strongly agree, 4- I agree, 3- I am not sure, 2- I do not agree, 1- I do not agree at all. The negative statements were inverted and included in the analysis. Arithmetic mean, standard deviation value, frequency and percentage values were calculated. The Cronbach’s alpha coefficient was calculated as 0.89. The arithmetic means were interpreted as follows: 18-32.4 corresponds to “I do not agree at all”, 32.4-46.8 corresponds to “I do not agree”, 46.8-61.2 corresponds to “I am not sure”, 61.2-75.6 corresponds to “I agree” and 75.6-90 corresponds to “I strongly agree”.

The responses given to 6 open-ended questions prepared in relation to investigating pre-service teachers’ skills of using the language of mathematics in the context of quadrilaterals were analyzed through content analysis method. Content analysis is a method which makes it possible to analyze, understand, organize, define and interpret the verbal and written data systematically and objectively (Sommer & Sommer, 1991). Accordingly, each teacher’s responses were studied detailedly, various categories were formed, concepts included in the categories were defined and interpreted (Patton, 2002). Some research studies in the literature (Fujita, 2012; Türnüklü, Gündoğdu-Alaylı & Akkaş, 2013; Erşen & Karakuş, 2013) were made use of to form categories in order to make the data analysis more easily and the evaluation criteria were identified and used. The data were labeled separately by two researchers and the percentage of conformity was found to be %89. Researchers reached a consensus after a meeting and matched the responses and categories. Percentage and frequency values corresponding to each category and response were presented in a table. In this way the data were analyzed and the categories were made reliable.

Categories in relation to describing the quadrilateral properties using verbal and symbolic language together were formed in order to interpret pre-service teachers’ skills of using the language of mathematics quantitatively. Six categories were merged into four categories. Therefore, the responses given to open-ended questions by the pre-service teachers were rated as follows: each statement in the category of “Correct Verbal Expression-Correct Symbolic Representation” was rated 3 points, the categories of “Correct Verbal Expression- Missing Symbolic Representation” and “Missing Verbal Expression-Correct Symbolic Representation” were merged and each statement in these categories was rated 2 points, “Correct Verbal Expression-Incorrect Symbolic Representation” and “Incorrect Verbal Expression-Correct Symbolic Representation” were merged into one and each statement was rated 1 point, the statements in the category of “Incorrect Verbal Expression- Incorrect Symbolic Representation” was labeled 0. It was agreed that those who got the score of 42-54 in the responses ranked as 0-3 used the language of mathematics both verbally and symbolically. Those who got the score of 30-42 used either of the verbal or symbolic languages. Those who got the score of 18-30 used either of

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

the verbal or symbolic language well and incorrectly used the other one. Those who got the score of 6-18 used the language of mathematics both verbally and symbolically incorrectly.

Table 1: Criteria Related to Interpreting the Language of Mathematics Used in the Context of Quadrilaterals Square Rectangle Parallelogram Rhombus Trapezium Deltoid Criteria Criteria of All sides Opposite Opposite sides Opposite sides The upper Formed by Describing have equal sides are are parallel are parallel and lower two Quadrilaterals length and of equal and of equal and all sides sides are isosceles all interior length and length have equal parallel triangles angles are all interior length with right angles are congruent angles right bases (90°). angles (90°). Criteria of At least At least Drawing a Drawing a Drawing a Drawing a Drawing three three four-sided four-sided four-sided four-sided Quadrilaterals corner corner closed shape closed shape closed shape closed shape and Displaying angles are angles are with opposite with opposite with upper formed by Properties by right right sides parallel sides parallel and lower two Symbols angles angles and of equal and all sides bases isosceles (90°). (90°). length and of equal parallel and triangles Drawing a Drawing a using length and using with four-sided four-sided notations using notations congruent closed closed notations bases and shape with shape with using all sides of equal notations equal opposite length and sides and using using notations notations Criteria of Specifying Specifying Specifying Specifying Specifying Specifying Explaining the properties properties properties properties properties properties Properties of such as such as such as such as such as “the such as “the Quadrilaterals “sides are “opposite “opposite “opposite upper and edges Verbally of equal sides are sides are sides are lower sides converging length”, of equal parallel and of parallel”, “all are parallel”, at two & “all angles length”, equal length”, sides are of “the angles opposite are right “all angles “opposite equal length”, on the ends corners are Criteria of angles” are right angles are “diagonals of each side equal by Expressing the (90°), angles” equal”, intersect which is not twos”, “one Properties of “opposite (90°), “diagonals vertically”, parallel of the Quadrilaterals sides are “opposite bisect each “the angles in are diagonals is Symbolically parallel”, sides are other”, and the corner supplement the bisector Through the “diagonals parallel”, “the angles on where ary angles”, of opposite Figures Drawn are of “diagonals either end of diagonals and angles”, equal are of each side are unite are “intermediat “opposite length” equal supplement bisectors” e base is angles are and length”, angles” with with parallel with equal”, “diagonals and appropriate appropriate other bases “diagonals intersect “diagonals mathematical mathematical and half the intersect vertically”, bisect each terms verbally terms verbally length of vertically and other”, and writing and writing two bases” and one

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

“diagonals with them in a them in a with diagonal are proper symbolic symbolic appropriate bisects the bisectors mathemati language language mathematic other one of interior cal terms al terms into two angles” verbally verbally and equal parts” with and writing them with proper writing in a symbolic appropriate mathemati them in a language mathematic cal terms symbolic al terms verbally language verbally and and writing them writing in a symbolic them in a language symbolic language

FINDINGS

Findings and Comments Regarding the Quadrilateral Test That Consists of Open-Ended Questions

Table 2. Percentage and Frequency Values Regarding Quadrilateral Definitions Definition Square Rectangle Parallelogram Rhombus Trapezium Deltoid Total

n % n % n % n % n % n % n % Correct 22 44 17 34 20 40 21 42 32 64 36 72 148 49 Faulty 15 30 14 28 19 38 13 26 1 2 5 10 67 23 Naming Too Many 8 16 14 28 1 2 - - 8 16 - - 31 10 Properties Incorrect 5 10 5 10 10 20 16 32 9 18 7 14 52 17 Blank ------2 4 2 1 Total 50 50 50 50 50 50 300

Looking at the definitions made by the pre-service primary teachers about quadrilaterals in Table 2, it is observed that 49% of the pre-service primary teachers made correct definitions, 23% of them made faulty definitions, and 17% made incorrect definitions. In addition to this, while 10 % tried to explain the concepts by mentioning the properties rather than making definitions, 1% could not define “kite” (deltoid). The findings obtained show that only half of the pre-service primary teachers expressed the types of quadrilaterals using the accurate language of mathematics. The other half, on the other hand, could not do that. It can be noted that pre-service primary teachers have inadequacies or fallacies with their knowledge about quadrilaterals. While the pre-service teachers could make the most number of correct definitions for kites (deltoid) and the least number of correct definitions for rectangles, they made the most number of incorrect definitions for rhombuses and the least number of incorrect definitions for squares and rectangles.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Table 3: Percentage and Frequency Values Regarding Quadrilateral Drawings Square Rectangle Parallelogram Rhombus Trapezium Deltoid Total Drawings n % n % n % n % n % n % n % Correct 38 76 37 74 10 20 11 22 32 64 39 78 167 56 Faulty 11 22 10 20 36 72 35 70 13 26 3 6 108 36 Incorrect 1 2 3 6 4 8 4 8 5 10 8 16 25 8 Total 50 50 50 50 50 50 300

Table 3 shows the classified values of the drawings made by the pre-service teachers related to the types of quadrilaterals. 56% of the quadrilateral types were correct, 36% were faulty and 8% were incorrect. Most of the pre-service teachers were observed to have faults in their drawings, and fail to display quadrilaterals using appropriate mathematical notions. This can be attributed to the fact that the pre-service teachers have difficulty reflecting the language of mathematics over the shapes and establishing the link between shape and notation. The rate of drawing correct shapes was high for the concepts of kite (deltoid), square, and rectangle, whereas it was low for the concepts of parallelogram and rhombus. The rate of drawing an incorrect shape was lowest for a square and highest for a kite (deltoid). The rate of drawing a faulty shape was the highest for a parallelogram and rhombus.

Table 4. Percentage and Frequency Values Related to Expressing the Properties of Quadrilaterals Verbally Verbal Square Rectangle Parallelogram Rhombus Trapezium Deltoid Total Expression n % n % n % n % n % n % n % Correct 142 94 105 93 94 85 91 90 45 74 36 70 513 87 Faulty 2 1 2 2 ------4 1 Incorrect 8 5 5 5 16 15 10 10 16 26 15 30 70 12 Total 152 112 110 101 61 51 587

Looking at the verbal language pre-service teachers used to explain the properties of quadrilateral types, it can be noted that the pre-service teachers use an accurate language in 87% of the quadrilateral properties, incorrect language in 12% and faulty language in 1%. The pre-service teachers were observed to express the properties of quadrilaterals with substantially correct mathematical concepts. According to the findings, the pre-service teachers best expressed the properties of a square using the correct verbal language. The worst expressed, on the other hand, were the properties of a kite. This situation might be attributed to the fact that pre-service teachers are more familiar with the properties of a square rather than a kite.

Table 5: Percentage and Frequency Values Related to Representing the Properties of Quadrilaterals Symbolically Symbolic Square Rectangle Parallelogram Rhombus Trapezium Deltoid Total Representation n % n % n % n % n % n % n % Correct 101 77 86 80 77 68 74 80 45 66 57 84 440 76 Faulty 10 8 6 5 9 8 1 1 - - 1 1 27 4 Incorrect 20 15 16 15 28 24 18 19 23 34 10 15 115 20 Total 131 108 114 93 68 68 582

Table 5 shows the findings in relation to the symbolic language the pre-service teachers used to explain the properties of quadrilateral types. According to the results, the pre-service teachers used a correct symbolic language in 76% of the quadrilateral properties, an incorrect symbolic language in 20% and a faulty symbolic language in 4%. Pre-service teachers were observed to show the quadrilateral properties using substantially correct mathematical symbols. According to the findings, the pre-service teachers best expressed the properties of a square using the correct symbolic language, and the worst expression for the properties of a

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

trapezium. This might be due to the fact that pre-service teachers are more familiar with the properties of a square than the properties of a trapezium.

Table 6: Percentage and Frequency Values Related to Using the Verbal and Symbolic Language Together in the Context of Quadrilaterals Language of Square Rectangle Parallelogram Rhombus Trapezium Deltoid Total Mathematics n % n % n % n % n % n % n % *Correct Verbal Expression- 80 49 67 51 56 45 58 50 20 27 29 40 310 46 Correct Symbolic Representation *Correct Verbal Expression- 17 11 14 11 24 19 15 13 17 23 2 3 89 13 Incorrect Symbolic Representation *Correct Verbal Expression- 36 22 23 17 12 10 17 15 7 9 5 7 100 15 Missing Symbolic Representation *Incorrect Verbal 4 3 4 3 8 6 4 3 7 9 5 7 32 5 Expression- Correct Symbolic Representation *Missing Verbal Expression- 20 12 17 13 20 16 17 15 15 21 23 32 112 15 Correct Symbolic Representation *Incorrect Verbal 5 3 7 5 5 2 5 4 8 11 8 11 38 6 Expression- Incorrect Symbolic Representation Total 162 132 125 116 74 72 68 1

Table 6 shows the interpretation findings related to using verbal and symbolic language together in the context of quadrilaterals. According to the table, the pre-service teachers expressed 46% of the properties with correct verbal language and represented them using a correct symbolic language. They expressed 13% of the properties with a correct verbal language and with an incorrect symbolic language. They represented 15% of the properties symbolically correctly but failed to express them verbally. They expressed 6% of the properties both verbally incorrectly and symbolically incorrectly. According to the findings, less than half of the pre-service teachers could use verbal and symbolic language correctly to express the properties of quadrilaterals. The majority failed to do so. Pre-service teachers could express the properties verbally correctly, but they could not represent them symbolically or they misrepresented them. Although they represented the properties symbolically, they could not explain them verbally or they misexplained them. The sum of these categories equals to 48% and the majority of the pre-service teachers were only successful in using one of the two languages. This case can be attributed to the fact that the pre-service teachers have difficulty switching between verbal and symbolic languages. Their skills of using language of mathematics can be interpreted as poor. 20 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Findings and Interpretations of the Quadrilateral Test and the Language Scale in Mathematics Teaching Table 7. Descriptive Statistics Regarding the Pre-service Teachers’ Scores of the Quadrilateral Test and the “Language in Mathematics Teaching Scale” N Average Ss The Lowest Score The Highest Score “Language in Mathematics Teaching 73.70 8.30 52 90 Scale” Test related to Quadrilaterals 50 29.06 11.53 7 53 Square 50 7.1 3.49 1 16 Reactangle 50 6.2 2.60 0 11 Parallelogram 50 5.06 2.76 0 11 Rhombus 50 5.02 2.62 0 14 Trapezium 50 2.54 1.70 0 7 Deltoid 50 3.08 2.39 0 8

As shown in Table 7, the arithmetic mean score obtained from the “Language in Mathematics Teaching Scale” was found to be 73.70 and the standard deviation value was found to be 8.30. The average of the data obtained, which is 61.2-75.6, fall within the range of “I agree”. It was concluded that pre-service teachers have positive views regarding the use of language of mathematics in mathematics teaching. Analyzing the scores of the test which was carried out to identify the skills of using the language of mathematics in the context of quadrilaterals, it was observed that the arithmetic mean score was 29.06, and the standard deviation value was 11.53. the average of the data was found to fall within the range of 30 and 18. It was concluded that the pre- service teachers used either of the verbal and the symbolic languages correctly and the other one incorrectly. These data support the finding that the pre-service teachers have difficulty using the verbal and symbolic language together. In addition to this, pre-service teachers were observed that they were most successful in explaining the properties of a square using the language of mathematics and least successful in explaining the properties of a trapezium using the language of mathematics. The pre-service teachers failed to effectively use the language of mathematics but had positive views of using the language in mathematics teaching.

CONCLUSION AND DISCUSSION

According to the research findings, half the pre-service mathematics teachers were successful in defining the types of quadrilaterals. The majority of the pre-service teachers did not mention some basic concepts while defining the types of quadrilaterals, so they made faulty definitions or misused the language of mathematics. The research studies regarding quadrilaterals in the literature also show that students have difficulty defining geometric shapes correctly (De Villiers, 1994; Erez & Yerushalmy, 2006; Fujita & Jones, 2007; Okazaki & Fujita, 2007). The pre-service teachers’ responses show that they include such concepts like “tetragonal area” and “geometric object” in their definitions, which means they have inadequate information about quadrilateral types, they express mathematical concepts using inappropriate terms and they confuse the concepts. The reason why the pre-service teachers could not make accurate definitions might be attributed to their insufficient conceptual information about geometric shapes (Linchevsky, Vinner & Karsenty, 1992). Bozkurt and Koç (2012) also suggest that the pre-service teachers fail to define geometric concepts and confuse geometric shapes and geometric objects. Besides, the research studies conducted at different levels of education in Turkey prove that students are poor in terms of conceptual knowledge and geometry learning (Toluk, olkun & Durmuş, 2002; Ergün, 2010; Aktaş & Aktaş, 2011; Aktaş & Aktaş 2012; Türnüklü et al., 2013). The study concludes that a considerable number of the pre-service teachers fail to draw the shapes of quadrilateral types and show by mathematical symbols the basic properties on the drawings. The pre-service teachers have difficulty displaying the notations on the drawings and building a connection between shapes and the language of mathematics. However, geometry requires the appropriate use of language of mathematics in all dimensions of shape, definition and properties. The faulty drawings by the pre-service teachers might be due to the fact that the pre-service teachers do not feel the need to represent some properties such as “all sides are parallel and of equal length”, and “angles are equal” rather than the fact that they do not know such features of the geometric shapes (Erşen & Karakuş, 2013). It can also be concluded that the rate of faulty drawings is high 21 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

because pre-service teachers have a habit of using quadrilateral images which they are familiar with rather than displaying the basic properties on geometric shapes (Üstün & Ubuz, 2004; Fujita & Jones, 2007; Okazaki & Fujita, 2007; Aktaş & Aktaş, 2012; Erşen & Karakuş, 2013).

Pirie (1998) explains the concepts of verbal and symbolic language, which are indispensable aspects of the language of mathematics and commonly used in mathematics classes (Çakmak, 2013; Emre, Sağ, Gülkılık & Argün, 2010; Yeşildere, 2007) as follows: Verbal language means the way of expressing mathematics in a verbal or written form using specific concepts and grammar structure. Symbolic language, on the other hand, means the way of representing mathematics with signs, symbols, and terms. The responses related to using verbal and symbolic languages to explain the properties of quadrilaterals indicate that a considerable number of the pre- service teachers explained the properties of quadrilaterals using verbal and symbolic language properly with the help of appropriate mathematical terms and notations. Although there was not a big difference between the rates of properly expressing the properties with a verbal language and representing the properties with a symbolic language, the difference was in favor of the verbal language. Capraro and Joffrion (2006) state that students experience challenges expressing mathematical information symbolically. The responses related to using verbal and symbolic languages together to express the properties of quadrilaterals proved that the pre- service teachers could not properly use verbal and symbolic languages together. What needs attention here is that the pre-service teachers were successful in using verbal and symbolic languages separately to express the different properties, whereas they failed to use both languages together. The pre-service teachers explained the properties of geometric shapes verbally; however, they failed to represent them symbolically and vice versa. This situation shows that they were either successful in using verbal or symbolic languages and they had difficulty understanding the connection between these two languages. Considering the skills of defining geometric shapes with appropriate mathematical concepts, drawing shapes and displaying mathematical notions on the shapes, using correct verbal and symbolic languages together to explain the features of a geometric shape, it can be concluded that the pre-service teachers have poor skills of using the language of mathematics The research studies on the language of mathematics also indicate that students have problems expressing properly the mathematical information with the language of mathematics (Bozkurt & Koç, 2012; Dur, 2010; Gökkurt vd, 2013; Korhonen vd, 2011; Palabıyık & İspir, 2011; Rudd vd, 2008; Woods, 2009, Yeşildere, 2007, Yeşildere & Akkoç, 2010;). The inadequacies in the pre-service teachers’ knowledge regarding the basic mathematical concepts are considered to act as a barrier to using the language of mathematics correctly (Yeşildere, 2007).

According to the findings, it can be noted that pre-service teachers have positive views of the necessity of using the language of mathematics in mathematics teaching. In addition to this, the pre-service teachers were observed to use either of the verbal or smbolic language properly while they used the other one incorrectly. They have difficulty using both languages together. Besides, it was found that although the pre-service teachers have poor skills of using the language of mathematics in the context of quadrilaterals, they have positive views of using the language in mathematics teaching.

The following are a number of suggestions for further research: Students should be given the opportunity to define the concepts in a verbal and written form, draw the shapes depending on the definitions, do activities using the verbal and symbolic languages together at all levels (from primary to university) in an effort to use the language of mathematics better and to overcome the challenges. Since teachers have a significant role in helping students improve their language of mathematics, they should pay attention to the ways of using verbal and symbolic languages that constitute the language of mathematics and enable the students to notice the transition and connection between these languages (Çakmak et al, 2014). Therefore, further studies should be conducted to explore the pre-service teachers’ skills of using the language of mathematics. Besides, similar studies should be undertaken with a different sample and various possible variables.

IJONTE’s Note: This article was presented at World Conference on Educational and Instructional Studies- WCEIS, 05- 07 November, 2015 by IJONTE Scientific Committee.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

BIODATA AND CONTACT ADDRESSES OF AUTHORS

Assoc. Prof. Dr. Dilek CAĞIRGAN GULTEN, currently employed as an Associate Professor Doctor at Istanbul University, Hasan Ali Yucel Faculty of Education, Department of Mathematics Education. She is specifically interested in contemporary approaches in instruction, approaches and techniques of teaching, creative drama, curriculum evaluation, lifelong learning, individual differences in learning, the teaching of mathematics and learning of mathematics.

Assoc. Prof. Dr. Dilek CAĞIRGAN GULTEN Istanbul University, Hasan Ali Yucel Faculty of Education Department of Elementary Education, Istanbul- TURKEY E. Mail: [email protected]

Pınar GÜNER is a research assistant at Istanbul University, Hasan Ali Yucel Faculty of Education, Department of Elementary Mathematics Education. She is specifically interested in teaching methods for mathematics education, teacher training, professional development, proof, creative drama.

Rsrch. Assist. Pınar GÜNER Istanbul University, Hasan Ali Yucel Faculty of Education Department of Elementary Education, Istanbul- TURKEY E. Mail: [email protected]

REFERENCES

Aktaş C. , M. & Aktaş, D.Y. (2011). 8. Sınıf öğrencilerinin dörtgenleri köşegen özelliklerinden yararlanarak tanıma sürecinin incelenmesi, 10. Matematik Sempozyumunda sözlü olarak sunulmuştur. İstanbul, Işık Üniversitesi.

Aktaş, D.Y. & Aktaş C., M. (2012). 8. Sınıf Öğrencilerinin Özel Dörtgenleri Tanıma ve Aralarındaki Hiyerarşik Sınıflamayı Anlama Durumları. İlköğretim Online , 11(3), 714-728.

Aydın, S. & Yeşilyurt, M. (2007). Matematik öğretiminde kullanılan dile ilişkin öğrenci görüşleri. Elektronik Sosyal Bilimler Dergisi, 6(22), 90-100.

Bali-Çalıkoğlu, G. (2002). Matematik öğretiminde dil ölçeği. Hacettepe Üniversitesi Eğitim Fakültesi dergisi , 23, 57-61.

Bali-Çalıkoğlu, G. (2003). Matematik öğretmen adaylarının matematik öğretiminde dile ilişkin görüşleri. Hacettepe Üniversitesi Eğitim Fakültesi dergisi , 25, 19-25.

Barwell R., Leung C., Morgan C. & Street B. (2005). (eds). Special issue: language and maths . Language and Education, 19.

Başaran, Ş. E. (1998). Eğitim psikolojisi . Ankara: Gül Yayınevi.

Baykul, Y. (2000). İlköğretimde Matematik Öğretimi ,4. Baskı, Pegem Yayıncılık Ankara.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Bozkurt, A. & Koç, Y. (2012). İlköğretim Matematik Öğretmenliği Birinci Sınıf Öğrencilerinin Prizma Kavramına Dair Bilgilerinin İncelenmesi, Kuram ve Uygulamada Eğitim Bilimleri; Educational Sciences: Theory & Practice, 12(4), 2941-2952.

Buchanan, T. (2007). The importance of teaching students how to read to comprehend mathematical language. Action Research Projects. Paper 5. http://digitalcommons. unl.edu/mathmidactionresearch/5.

Capraro, M. M. & Joffrion, H. (2006). Algebraic equations: can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology , 27 (2), 147-164.

Chard, David. Vocabulary Strategies for the Mathematics Classroom. Boston, MA: Houghton Mifflin, 2003.

Çakmak, Z. (2013). Sekizinci sınıf öğrencilerinin istatistik konusundaki matematiksel dil becerilerine ilişkin değişkenlerin yapısal eşitlik modeli ile incelenmesi, Yayınlanmamış Yüksek Lisans Tezi, Erzincan Üniversitesi Fen Bilimleri Enstitüsü, Erzincan.

Çakmak, Bekdemir & Baş (2014). İlköğretim matematik öğretmenliği öğrencilerinin örüntüler konusundaki matematiksel dil becerileri. Erzincan Üniversitesi Eğitim Fakültesi Dergisi , 16 (1), 204-223.

Çakmak, Konyalıoğlu & Işık (2014). İlköğretim Matematik Öğretmen Adaylarının Üç Boyutlu Cisimlere İlişkin Konu Alan Bilgilerinin İncelenmesi. Middle Eastern & African Journal of Educational Research , 8, 28-44.

Çetin, Ö. F. & Dane, A. (2004). Sınıf Öğretmenliği III. Sınıf Öğrencilerinin Geometrik Bilgilere Erişi Düzeyleri Üzerine, Kastamonu Eğitim Dergisi , 12(2), 427–436.

Dane, A. (2008). İlköğretim Matematik Öğretmenliği Programı Öğrencilerinin Nokta, Doğru ve Düzlem Kavramlarını Algıları. Erzincan Eğitim Fakültesi Dergisi , 10(2), 41-58.

De Villiers, M. (1994). The role and function of a hierarchical classisication of quadrilaterals. Learning of Mathematics , 14(1), 11-18.

Doğan M. & Güner, P. (2012). İlköğretim matematik öğretmen adaylarının matematik dilini anlama ve kullanma becerilerinin incelenmesi. X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi , Niğde Üniversitesi, Niğde.

Dur, Z. (2010). Öğrencilerin matematiksel dili hikâye yazma yoluyla iletişimde kullanabilme becerilerinin farklı değişkenlere göre incelenmesi, Yayınlanmamış Doktora Tezi, Hacettepe Üniversitesi, Sosyal Bilimler Enstitüsü, Ankara.

Emre, E., Sağ, Y.G., Gülkılık, H. & Argün, Z. (2010, Eylül). Matematik öğretmen adaylarının matematiksel dil kullanımları. Çalışma 9. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresinde sunulmuş bildiri. Dokuz Eylül Üniversitesi, Buca Eğitim Fakültesi, İzmir.

Erez, M. & Yerushalmy, M. (2006). If you can turn a rectangle into a square, you can turn a square into a rectangle: Young students’ experience the dragging tool. International Journal of Computers for Mathematical Learning , 11(3), 271-299.

Ergün, S. (2010). İlköğretim 7. sınıf öğrencilerinin çokgenleri algılama, tanımlama ve sınıflama biçimleri. Yayınlanmamış yüksek lisans tezi. Dokuz Eylül Üniversitesi, İzmir.

Erşen & Karakuş (2013). Sınıf öğretmeni adaylarının dörtgenlere yönelik kavram imajlarının değerlendirilmesi. Turkish Journal of Computer and Mathematics Education , 4(2), 124-146.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Ferrari-Luigi, P. (2004). Matematical language and advanced mathematics learning. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (pp. 383-390).

Forman E. & van Oers B. (eds). (1998). Mathematics learning in sociocultural contexts. Learning and Instruction, 8: 469–72.

Fujita, T. & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing, Research in Mathematics Education , 9 (1-2), 3-20.

Fujita, T. (2012). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomen. The Journal of Mathematical Behavior , 31, 60-72.

Glasersfeld, E. von (1995). Radical Constructivism: A Way of Knowing and Learning , London: Routledge/Falmer.

Gür, H. (Ed.). (2006). Matematik öğretimi (1. baskı). İstanbul: Lisans Yayıncılık.

Goldenberg, E. P., Cuoco, A. A. & Mark, J. (1998). A role for geometry in general education. In R. Lehrer & D. Chazan (Eds.), Designing Learning Environments for Developing Understanding of Geometry and Space, (pp. 3- 44), Hillsdale, NJ: Lawrence Erlbaum Associates, Publishers.

Gökkurt, soylu &Gökkurt (2012). Öğrencilerin Matematik Öğretiminde Kullanılan Dile Yönelik Görüşlerinin Karşılaştırılması. X. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi , Niğde Üniversitesi, Niğde.

Gökkurt, Soylu & Örnek (2013). Mathematical language skills of mathematics teachers. International Journal Of Academic Research , 5(6), 238-245.

Haylock D. & Thangata, F. (2007). Key concepts in teaching primary mathematics. London: SAGE Publications Ltd., doi: http://dx.doi.org/10.4135/9781446214503

Hoyles C. & Forman E. (eds). (1995). Special issue: Processes and products of collaborative problem solving: some interdisciplinary perspectives. Cognition and Instruction , 13.

Korhonen, J., Linnanmäki, K. and Aunio, P. (2011). Language and mathematical performance: a comparison of lower secondary school students with different level of mathematical skills, Scandinavian Journal of Educational Research , 1-12.

Kuzniak, A. & Rauscher, J.C. (2007). On the geometrical thinking of pre-service school teachers. Proceedings Cerme4, Sant Feliu de Guixols Spain.

Larson C. (2007). The importance of vocabulary instruction in everyday mathematics. Scottsbluff, Nebraska. In partial fulfillment of the MAT degree Department of Mathematics University of Nebraska-Lincoln. Retrieved from scimath.unl.edu/MIM/files/research/LarsonC.pdf

Linchevsky, L., Vinner, S. & Karsenty, R. (1992). To be or not to be minimal? Student teachers views about definitions in geometry. In W. Geeslin & K. Graham (Eds .), Proceedings of the sixteenth international conference for the psychology of mathematics education , Vol. 2 (pp. 48–55). Durham USA.

Meaney, T. (2005) ‘Mathematics as text’, in Chonaki, A. and Christiansen, I. M., eds., Challenging Perspectives on Mathematics Classroom Communication,Westport, CT: Information Age Publishing, pp.109-141.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Monaghan F. (1999). Judging a word by the company its keeps: the use of concordancing software to explore aspects of the mathematics of register. Language and Education 13: 59–70.

Moschkovich, J. (2012). Mathematics, the Common Core and language: Recommendations for mathematics instruction for ELs aligned with the Common Core. Paper presented at the Understanding Language Conference at Stanford University, Stanford, CA.

National Council of Teachers of Mathematics (NCTM; 2000) Principles and Standards for School Mathematic http://www.nctm.org/standards/content.aspx?id=16909s (27.10.2015).

Ní Ríordáin, M. (2009). The role of language in teaching and learning mathematics. Resource & Research Guides, 1(1), 1-4.

Okazaki, M. & Fujita, T. (2007) . Prototype phenomena and common cognitive paths in the understanding of the inclusion relations between quadrilaterals in Japan and Scotland. In J. Woo, H. Lew, K. Park & D. Seo (Eds.). Proceedings of the 31st Conference of the Internatıonal Group for the Psychology of Mathematics Education (Vol:4, pp. 41-48).

Orton, A. & Frobisher, L. (1996). Insights into teaching mathematics . London:Cassell.

Otterburn, M. K. & Nicholson, A. R. (1976). The language of mathematics. Mathematics in School , 5(5), 18- 20.

Palabıyık, U. & İspir, O. A. (2011). Örüntü Temelli Cebir Öğretiminin Öğrencilerin Cebirsel Düşünme Becerileri ve Matematiğe Karşı Tutumlarına Etkisi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi , 30 (2), 111-123.

Patton, M. Q. (2002). Variety in qualitative inquiry: Theoretical orientations. In C. D. Laughton, V. Novak, D. E. Axelsen, K. Journey, & K. Peterson (Eds.), Qualitative research & evaluation methods (pp. 132-133). London: Thousand Oaks.

Pickreign, J. (2007). Rectangle and Rhombi: How well do pre-service teachers know them? IUMPST, 1, 1-7. Retrieved January 22, 2013, from http://files.eric.ed.gov/fulltext/EJ835492.pdf

Pimm, D. (1987). Speaking mathematically: communication in mathematics classrooms. Routledge & K. Paul. London.

Pirie, S. E. B. (1998). Crossing the gulf between thought and symbol: Language as stepping-stones. In H. Steinbring, M. G. B. Bussi and A. Sierpinska (Eds.), Language and Communication In The Mathematics Classroom (pp.7-29). Reston, NCTM Publication.

Pusey, E.L. (2003). The Van Hiele model of reasoning in geometry: a literature review . Mathematics Education Raleigh. North Carolina State University.

Raiker, A. (2002). Spoken Language and mathematics. Cambridge Journal of Education , 32 (1), 45-60.

Reys, R., Suydam, M., & Lindquist, M. N. (1995). Helping children learning mathematics . Boston, MA: Allyn & Bacon.

Rudd, L. C., Lambert, M. C., Satterwhite, M. & Zaier, A. (2008). Mathematical language in early childhood settings: What really counts?, Early Childhood Education, 36, 75-80.

Sandt, S. & Nieuwoudt, H., D. (2003). Grade 7 teachers’ and prospective teachers’ content knowledge of geometry. South African Journal of Education .23(3), 199-205.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 02 ISSN 1309-6249

Sfard A. (2000). Symbolizing mathematical reality into being: How mathematical discourse and mathematical objects create each other. In P. Cobb, K.E. Yackel and K. McClain (eds). Symbolizing and communicating: perspectives on mathematical discourse, tools, and instructional design. Mahwah, NJ: Erlbaum, pp 37-98.

Sfard A. & Kieran C. (2001). Cognition as communication: Rethinking learning-by-talking through multifaceted analysis of students’ mathematical interactions . Mind, Culture, and Activity ,8: 42–76.

Sherard, W. H. (1981). Why is Geometry a Basic Skill?. Mathematics Teacher.

Toluk, Z., Olkun, S. & Durmuş, S. (2002). Problem merkezli ve görsel modellerle destekli geometri öğretiminin sınıf öğretmenliği öğrencilerinin geometrik düşünme düzeylerinin gelişimine etkisi. Beşinci Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi , 16-18 Eylül, Ankara.

Toptaş, V. (2015). Matematiksel dile genel bir bakış. International Journal of New Trends in Arts, Sports&ScienceEducation , 4(1), 18-22.

Türnüklü, E., Gündoğdu-Alaylı, F. & Akkaş, E. N. (2013). Investigation of prospective primary mathematics teachers’ perceptions and images for quadrilaterals. Educational Sciences: Theory & Practice , 13(2), 1225-1232. Üstün, I. & Ubuz, B. (2004). Geometrik kavramların Geometer’s Sketchpad yazılımı ile geliştirilmesi. Eğitimde İyi Örnekler Konferansı, 17 Ocak, İstanbul.

Van Hiele, P.M. (1986). Structure and Insight. A Theory of Mathematics Education. Orlando, Florida. Academic Press USA.

Woods, G. (2009). An investigation into the relationship between the understanding and use of mathematical language and achievement in mathematics at the foundation stage, Procedia Social and Behavioral Sciences , 1, 2191–2196.

Yeşildere, S. (2007). İlköğretim matematik öğretmen adaylarının matematiksel alan dilini kullanma yeterlikleri, Boğaziçi Üniversitesi Eğitim Dergisi , 24(2), 61-70.

Yeşildere, S. & Akkoç, H. (2010). Matematik öğretmen adaylarının sayı örüntülerine ilişkin pedagojik alan bilgilerinin konuya özel stratejiler bağlamında incelenmesi. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 29(1), 125-149.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

COMPARISON OF INSTRUCTOR AND SELF-ASSESSMENTS ON PROSPECTIVE TEACHERS' CONCEPT MAPPING PERFORMANCES THROUGH GENERALIZABILITY THEORY

Assist. Prof. Dr. Göksu GÖZEN Mimar Sinan Fine Arts University İstanbul- TURKEY

Assist. Prof. Dr. Kaan Zülfikar DENİZ Ankara University Ankara- TURKEY

Abstract

The purpose of the research is to examine, according to generalizability theory, a) the consistency between instructor assessments and self-assessments on concept mapping performance of 100 secondary school prospective teachers who attended Pedagogical Formation Certificate Program at Mimar Sinan Fine Arts University in 2014-2015 academic year, b) their severity-leniency behaviors in these assessments, and c) the difficulty levels of the performance criteria used in these assessments. Generalizability study was carried out by creating a p x c x r (p: person, c: criterion, r: rater) pattern obtained through scoring of the designed concept maps by the prospective teachers and instructor on the same assessment form. The following were found out based on the findings; - instructors and prospective teachers exhibited equal severity-leniency in scoring both throughout the assessment criteria and by comparison, - performance criteria were distributed across the different difficulty levels, - there was no consistency between prospective teachers’ self-assessments and the instructor assessments, and – self-assessments of prospective teachers were more positive compared to the instructor assessments.

Keywords: Instructional material design; concept map; performance assessment; self-assessment; generalizability theory.

INTRODUCTION

In line with the competencies targeted in the 21 st century teaching processes; it has become obligatory to implement principles such as learning through experience, reading, listening, gaining oral and written skills, providing solutions to problems through scientific approaches, making proof-based inferences and generalizations through research and analysis. The most important factor for the students to exhibit the aforementioned skills, undoubtedly, is the teachers who will enable the student to gain those skills. Therefore the literature focusing on teacher education is expanding on daily basis. As Avalos (2011) mentioned, the core of the recent scientific research on the professional development of teachers is not only concerned to teachers’ transforming their knowledge into practice for the benefit of students’ growth but also teachers’ learning processes, particularly their gaining knowledge and experience in the instructional methods and techniques as well as domain-specific and differential strategies and tools of assessment and evaluation to judge the quality of education.

Over the last three decades, the most common used assessment tools have been objective tests (i.e. with multiple choice items) in almost all education systems over the world as a means of measuring and monitoring the quality of education. Stecher (2010) and Chen & Brown (2013) stated that the nature of these tools do not reflect the nature of performance in the real world, therefore they are not well suited to judging students’ ability to express points of view, marshal evidence, and display other advanced skills since they have not focused primarily on the higher-order thinking and performance skills. In a similar way, Darling-Hammond & Adamson (2010) reported the evidence, which suggests that the nature and format of the assessments affects 28 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

the depth of knowledge and types of skills developed by students, and that performance assessments are better suited to assessing high level, complex thinking skills. Thus, within the studies comparing objective and essay exams with several kinds of alternative strategies for educational assessment and evaluation (i.e. İngeç, 2009; Moreira, 2006; Rafferty & Fleschner, 2010) , particularly based on performing association, inference and interpretation skills, concept mapping is proposed as a viable pedagogical tool for meaningful learning and understanding in almost every grades of education. It is defined as a way to represent knowledge schematically through establishing the most prominent and most useful cross-links (relationships) between several concepts, which involves what Bloom (1956) identified as high levels of cognitive performance, namely evaluation and synthesis of knowledge (Edmondson, 2000). This indirect method of observation is also supposed to be effective in reaching the goal of turning out people who can think and generate (İngeç, 2009; Novak & Cañas, 2007; Strautmane, 2012).

Literature contends that a teacher’s knowledge of concept map-based instruction and/or assessment influence how their students perceive the instructional content and execute students’ creation of acceptable concept maps to present their own way of learning. Thus, teachers need to understand the educational function of concept mapping in relation to the nature and quality of the graphical structures of such practices and in terms of how these structures impact and/or effectuate learning. Accordingly, Subramaniam & Esprívalo Harrell (2015) stated that teachers who are skilled concept mappers are able to (1) understand and apply the operational terms to construct a hierarchical/non-hierarchical concept map; (2) identify the legitimacy of the constructed concept map by verifying its graphical structure and its educational utility; and (3) determine the inherent ‘good’ and ‘poor’ qualities of the resulting graphical structure to reiterate the ‘good’ qualities and to coach and provide feedback to alleviate ‘poor’ qualities. Behind numeorus studies focusing on teachers’ knowledge and competencies to design concept maps or other several instructional materials (e.g. Novak & Cañas, 2008; Strautmane, 2012; Yelken & Alıcı, 2008; Yin, Vanides, Ruiz-Primo, Ayala, & Shavelson, 2005), in the present study this subject is handled from a different viewpoint, only which is established as a principle focus in limited number of studies (Cronbach, Linn, Brennan, & Haertel, 1997; Dochy, Segers, & Sluijsmans; 1999; Jimenez-Snelson, 2010; McClure, Sonak, & Suen, 1999; Plummer; 2008; Yin & Shavelson, 2008), and the consistency between the self-assessments of prospective teachers’ and assessments performed by their instructor on their concept mapping performances is investigated in conjunction with raters’ severity or leniency behaviours in the assessments and the difficulty of the criteria used in the assessments. Hence, apart from having the necessary knowledge and skills to contemplate qualified teaching and assessment materials that serve different purposes and meet different needs, teachers should have high order cognitive and affective skills of self-assessment, which, as a matter of fact, is a prerequisite for possession of qualified teaching competency. Individuals, of course, attain the vision and responsibility to see their deficiencies in their work or in the process of gaining the necessary technical and practical knowledge and skills related with that work and to compensate these deficiencies only through evaluating themselves objectively. From this point of view, the present study also takes prospective teachers’ self-assessment of their utilization level of the technical information learned in the process of designing the concept maps as an important dimension.

It is desired that all the assessment tools used and developed in all scientific research have a high reliability. As for performance based assessment, in which students must construct an answer, produce a product, or perform an activity rather than choosing among pre-determined options, reliable scoring becomes more important. Different variability sources mingled with the assessments and the interaction between these different sources are quite important from reliability standpoint (Brennan 2001; Cronbach, Gleser, Nanda, & Rajaratnam, 1972). In this context, historically, reliability issues in psychology and education have been addressed principally using Classical Test Theory (CTT), which postulates that an observed score can be decomposed into a true score (T) and a single, undifferentiated random error term (E).On the other hand, Generalizability Theory (G-Theory) that handles different sources of error and their interaction together and simultaneously and that liberalizes CTT as stated by Brennan (2001) is one of the useful methods not only in identifying the validity and reliability of different assessment tools (multiple choice tests, performance assessment tools, etc.), but also in making comparisons to see the consistency between the evaluations when there are more than one rater involved in the assessment (Atılgan, 2005; Güler, 2009, 2011; Nunally, 1982;

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

Nunally & Bernstein, 1994; Volpe, McConaughy & Hintze, 2009; Yelboğa, 2012; Yılmaz-Nalbantoğlu &Gelbal, 2011). The present study examined, based on the G-Theory, a) the consistency between instructor assessments and prospective teachers’ self-assessments on the concept maps the prospective teachers prepared, b) severity-leniency behaviors in the assessments, and c) difficulty levels of the criteria used in the assessments.

METHOD

Research Design In CTT, reliability coefficients having different meanings are obtained through different reliability methods for the same assessment. Considering these different measures related with the reliability estimation, Cronbach, Nageswari, & Gleser (1963) suggested the Generalizability Theory (G-Theory) both as an extension of and as a flexible alternative to CTT. This conceptual and statistical framework, for evaluating the dependability (reliability) of behavioral measurements (e.g., a test score) evaluates all sources of variance, e.g. rater, time, items, setting etc., in other words, all possible sources of error (in G-Theory, sources of variation are referred to as facets of measurement ) that may occur in an assessment process together and simultaneously and therefore tests the generalizability of the sample drawn from the universe of admissible observation to the universe (Brennan, 2001; Sanders, 2014; Webb, Shavelson & Haertel, 2006). The detailed information on every source of variance and their interaction makes G-Theory the recommended (Atılgan, 2005; Nunally & Bernstein, 1994) approach which enables making inter- and cross- comparisons in assessments that involve more than one rater.

Individuals (persons) were defined as object of measurement, and not considered sources of variance as in many assessments due to the fact that they are the targets of the assessment activity and process, and also that their variance is natural and systematic. On the other hand, each assessment criteria for the concept maps as a teaching tool and raters (instructor and prospective teachers making self-assessment) were considered a source of variance (facet) that can have an impact on individuals’ universe scores (these scores correspond to true scores in CTT). Each prospective teacher and instructor prepared and assessed their material according to the same 10 criteria. However, considering that these 10 criteria were picked randomly among the universe of admissible observation that can be used to measure the concerned feature and that the raters were randomly sampled among the universe of raters who are able to assess the performance of the prospective teachers on these criteria, it may be suggested that the research has a crossed two-facet random-effects design of G- Theory. Accordingly, the research pattern is symbolized as p x c x r , prospective teachers as p (persons), each assessment criteria c (criterion) and raters r (raters).

Variance components in G–Theory are derived from many sources like systematic variance of individuals that are the objects of measurement, multiple variance sources and the corresponding interaction between them (Crocker & Algina, 1986; Goodwin, 2001). These probable sources of variance are estimated together and simultaneously based on the variance analysis (ANOVA). In this study, in order to determine what portion of the total variance in the results arises from which source or the interaction of facets, ANOVA equations were used in line with p x c x r pattern and seven variance components listed below were obtained; • three main effects – persons ( p), criteria ( c) and raters (r), • three common impacts - person-criterion ( p x c ), person-rater ( p x r ) and criterion-rater ( c x r ), and • remainder effect ( p x c x r , e).

Instead of focusing on a specific measurement result or the score observed, G-Theory focuses on generalization of measurement results to the sample universe which is wider than a specific sample; more specifically, it concentrates on the effect of different dimensions of the universe on the test scores. In G-Theory, this effect is shown with generalizability coefficients similar to reliability coefficients in actual score model. Thus, instead of “reliability” which is one of the main concepts of CTT, “generalizability” which is a broader and flexible term in G-Theory is used (Güler, 2009, 2011; Anıl & Büyükkıdık, 2012). G-Theory enables estimating the reliability levels based on different sources of variance, i.e. test-retest reliability, internal consistency, reliability among raters etc. through one study and also facilitates reliability estimation of not only relative decisions as in CTT, but also of absolute decisions which focus on the level of an individual’s performance independent of others’ performance (cf. domain-referenced interpretations) (Shavelson & Webb, 1991; Yin & Shavelson, 2008).

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

Thereby different reliability coefficients, G and Phi (ɸ) (dependability), are produced based on two different decision making types which are relative and absolute. In the present study, both coefficients were used to obtain the indicators of reliability among raters (instructor assessments and prospective teachers’ self- asssessments).

Participants The participants were composed of 100 prospective secondary school teachers, who were attending the Pedagogical Formation Certificate Programme at Mimar Sinan Fine Arts University in the academic year 2014- 2015, of whom 23 are male ve 77 are female, and one educator who was their instructor in the spring semester of this academic year and lecturing the course entitled “Instructional Technologies and Material Design”, within which the prospective teachers designed the concept maps. The distribution of the prospective teachers by their specialties which constitute the basis for their assignment to the teaching profession are presented in Table 1.

Table 1: Distribution of prospective teachers by their specialties Specialty n Turkish Filology 36 History 23 Visual Arts 14 Philosophy Group (Sociology, Pyschology and Philosophy) 11

Mathematics 10 Health Sciences 4 Physical Training and Sports 2 Total 100

Research Instrument and Data Collection In this research, 100 prospective secondary school teachers were asked to draw a hierarchical concept map related to their teacher roles in the course entitled “Instructional Technologies and Material Design” after they were taught about the meaning, content, and construction of different kinds of concept maps and given several examples. Hierarchical concept maps that were designed by prospective teachers were scored by themselves and the instructor simultaneously and independently on a score sheet containing ten performance criteria in total with 0-1-2 scores. While scoring guidelines were being determined, criteria that required exhibition of minimal grammatical competence but good conceptual understanding (based on an effective visualing the sub- concepts that makes up a main concept) were taken into consideration. A moderation discussion that supports prospective teachers using and understanding the use of grade criteria was carried out prior to scoring. For each prospective teacher, two scoring series comprised of instructor assessments and prospective teachers’ self-assessments were obtained following use of the score sheet. Criteria, scores and definitions used in the assessments are listed in Table 2.

Table 2: Criteria, scores and definitions used in the assessments of hierarchical concept mapping Scores and Definitions Criteria 2 1 0 1.Legibility and Main concept is easily Main concept, even if Main concept within the clarity distinguished from other discernible, is not concept graphical concepts on the map. sufficiently distinguished structures is from other concepts on the indistinguishable. map.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

2. Hierarchical There is a hierarchical Even if there is a Hierarchical arrangement arrangement arrangement between the hierarchical arrangement and coherent design root concept and between the root concept cannot be observed subordinate concepts and and subordinate concepts, a between the root concept a coherent design can be coherent design cannot be and subordinate concepts. observed between the observed. concepts at the same level. 3.Relevance and The root concept and Some of the relations Relevant and Systemacity/Order subordinate concepts indicated between the root systematic/orderly have relevant and concept and subordinate relations cannot be systematic/orderly concepts are not relevant established between the relations. and systematic/orderly. root concept and subordinate concepts. 4.Visual links Visual links are Although there are visual Concepts maps only established between links between concepts, contain linking lines but concepts, directions of direction of them are not lack direction, linking visual links are correctly set, and unclear and phrases, labelled lines and set, and connections are incognizable statements are propositions. defined with coherent seen on some links. verbs and conjunctions. 5.Exampling Examples are provided for Examples are provided for No example was provided each concept. some concepts. for the concepts. 6.Use of material The content is enriched Some part of the content is The content is not with the support of supported by different supported by different different visual materials visual materials (pictures, visual materials (pictures, (pictures, drawings, drawings, photographs, drawings, photographs, photographs, cartoons, cartoons, designing with cartoons, designing with designing with various various materials, etc.). various materials, etc.), materials, etc.). only written elements are available. 7.Suitability Conceptual graphical Although very few, concepts Conceptual graphical structures are completely that are unsuitable for the structures are not suitable suitable for the development and learning for the development and development and learning level of student group are learning level of target level of the target student observed in the conceptual student group. group. graphical structures. 8.Consistency Conceptual graphical Some sub concepts in the Conceptual graphical structures, are consistent conceptual graphical structures, are not with cognitive structures are not covered consistent with cognitive attainments available in the cognitive attainments attainments available under the scope of the available under the scope of under the related the related the class/subject. the related class/subject. class/subject. 9.Design features A map that is appropriate Some design features are Design features were for all design features ignored, and this decreases ignored in such a way that (color, size, highlight, etc.) readability in some parts of it makes conceptual to allow easier reading of the conceptual graphical graphical structures conceptual graphical structures. unreadable. structures is prepared. 10.Form and How and for what How and for what purpose How and for what purpose purpose of use purpose (teaching, (teaching, repetition, (teaching, repetition, repetition, enhancement, enhancement, practice, enhancement, practice, practice, assessment and assessment and evaluation, assessment and 32 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

evaluation, etc.) the etc.) the concept map will evaluation, etc.) the concept map will be used be used is superficially concept map will be used is defined in detail. defined, and there are some is not defined. vague areas.

There is more than one technique used in determining the reliability of the abovementioned tools and the like utilized in performance based assessments. Some of these techniques provide the consistency level between the raters over the total scores attained by individuals for a specific performance, while the others address approach each performance criterion separately. In the context of this study, both techniques were utilized to study the reliability of the tool provided in Table 2. As a basis of the reliability study, concept map development performance of 50 prospective teachers out of 100 who formed the study group was evaluated simultaneously and separately by the instructor responsible for the class in which concept maps were developed and a second instructor observing the class. Under the scope of the techniques that reveal the consistency level between the raters over the total performance scores, the correlation technique was used, and the level of the relationship between the two instructors’ assessments on concept map development performances of 50 prospective teachers was found to be r xy = 0.96 (p<.001). This value was considered to indicate the consistency/coherence between the assesssments of the two instructors on prospective teachers’ performances. In order to obtain separate reliability indicators for each criterion, Cohen’s Kappa formula (Krippendorff, 2004) was used, which is a coefficient that provides more precise information than simple percentage consistency calculation as it also takes consistency percentage obtained by chance into consideration and is one of the non-parametric statistic types used for categorical variables. Symmetrical assessment values obtained regarding the criteria on the score sheet are listed in Table 3.

Table 3: S ymmetric measures for assessment criteria Measure of Agreement Criteria p Kappa Legibility and clarity 0.315 ** .002 Hierarchical arrangement 0.728 *** .000 Relevance and Systemacity/Order 0.401 *** .000 Visual links 1.000 *** .000 Exampling 1.000 *** .000 Use of material 0.791 *** .000 Suitability 0.865 *** .000 Consistency 1.000 *** .000 Design features 0.739 *** .000 Form and purpose of use 0.742 *** .000 ** p<.01 *** p<.001

Kappa consistency measure values presented in Table 3 show to what extent the consistency among the fixed number of raters is not random, and thus, suggest a high consistency among the raters if it is proximate to 1.00 (Reynold, Livinston & Wilson, 2006). According to this, each criterion used to evaluate the performance of prospective teachers allows both instructors to score objectively and nonfortuitously; in other words, it is suitable for producing a reliable scoring. On the other hand, the content validity of the assessment tool was tried to be ensured through the opinions of two measurement and evaluation experts.

Data Analysis In the present study, analyses based on the consistency between the two instructors in determining the reliability of the tool used for evaluating the prospective teachers’ performance in designing hierarchical concept maps were conducted using SPSS 20.00 software. In analyses under the scope of G-Theory to investigate the consistency between instructor assessments and prospective teachers’ self-assessments, the statistical software EduG 6.1 was used.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

FINDINGS

Instructor assessments and prospective teachers’ self-assessments were examined correlatively, and the findings of the generalizability study conducted to obtain information about scoring consistency, assessment behavior and difficulty of performance criteria are provided in Table 4.

Table 4: Estimated variance components and percentages for prospective teachers’ instructional concept map designs by ANOVA Source * Sum of Squares df Mean Square Estimated Variance Total Variance (%) Component p 93.69 99 0.95 0.003 0.7 c 85.37 9 9.49 0.032 7.5 r 32.26 1 32.26 0.029 6.8 p x c 379.33 891 0.43 0.134 31.2 p x r 61.24 99 0.62 0.046 10.7 c x r 25.32 9 2.81 0.027 6.2 p x c x r, e 141.18 891 0.16 0.158 37.0 * p: person, c: criteria, r: rater, e: error

Even though the analyses in generalizability studies are based on random-effects factorial ANOVA, as also suggested by Shavelson & Webb (1991) and Brennan (2001), this concept has nothing to do with the hypothesis test. Therefore, there are no F and p values in Table 4.

When Table 4 is analyzed, it is observed that the variance component of 0.003 estimated for person (p) main effect has the smallest share of variance and that it explains only 0.7% of the total variance. This variance component that is for the universal scores suggests that the individuals do not differ systematically from each other in terms of the characteristics assessed, in other words, the prospective teachers do not differ in performance of designing concept maps and that they exhibit similar performance levels. This variance component estimated for individuals is the universal score variance which corresponds to the actual score variance in CTT and therefore, the value is desired to be greater.

The value of the estimated variance component value for criteria (c) used in evaluating the prospective teachers’ hierarchical concept mapping performance is 0.032 which explains 7.5% of the total variance. Accordingly, it may be suggested that difficulty levels of some criteria differ from others, in other words, there are criteria that have difficult and easily achieved/fulfilled contents. Based on this finding, the criteria that are the most difficult and the easiest to achieve in terms of the assessments made by the instructor and the prospective teachers were examined separately, and the breakdown of the assessments conducted with scores 0, 1 and 2 for each criterion is shown in Table 5.

Table 5: Breakdown of criteria scores based on instructor assessments and prospective teachers’ self- assessments Score Distribution for Score Distribution for Instructor Prospective Teachers' Criteria Assessments Total Self-Assessments Total (n) (n) 0 1 2 0 1 2 Legibility and clarity 2 2 96 100 1 1 98 100 Hierarchical arrangement 13 20 67 100 - 6 94 100 Relevance and 6 8 86 100 - - 100 100 Systemacity/Order Visual links 7 3 90 100 8 4 88 100 Exampling 25 27 48 100 16 12 72 100 34 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

Use of material 38 25 37 100 12 17 71 100 Suitability 9 18 73 100 5 4 91 100 Consistency 10 14 76 100 9 8 83 100 Design features 28 17 55 100 3 2 95 100 Form and purpose of use 4 7 89 100 4 1 95 100

When Table 5 is analyzed, “Use of Material” and “Design Features” were observed to be the most difficult criteria to achieve based on the instructor assessments where respectively 38 and 28 prospective teachers scored 0 (zero). Accordingly, the easiest criteria to achieve are “Legibility and Clarity” and “Visual Links” where respectively 96 and 90 prospective teachers obtained full scores (2 points). On the other hand, based on their self-assessments, the most difficult criteria the prospective teachers mentioned that they hard time achieving were “Exampling”, and consistently with the instructor assessments “Use of Material” where respectively 16 and 12 prospective teachers evaluated themselves with 0 (zero) points. The criteria that they achieved the most easily were “Relevance and Systemacity/Order”, and again consistently with the instructor assessments “Eligibility and Clarity” where respectively all prospective teachers (100 individuals) and 98 prospective teachers evaluated themselves with full scores (2 points). However, it is important to note here that “Exampling” and “Use of Material” criteria, which were considered as two of the most difficult criteria by both the instructor and the prospective teachers, were scored 2 full points by the instructor for less than 50% of the prospective teachers as can easily be observed from a review of the row, while these criteria were scored 2 full points by 70% of the prospective teachers in self-assessment. Difficulty levels appear to differ from each other throughout the criteria and at the same time this difference is also seen during the independent assessments made by instructors and prospective teachers reciprocally.

Raters ( r) main effect shows whether or not the severity-leniency levels of raters scoring all the individuals differ. Table 4 shows that the estimated value for this variance component is 0.029 and that the total variance explained by this component is 6.8%. This value being proximate to zero indicates that the instructor and the prospective teachers themselves treat the prospective teachers with equal severity-leniency.

Persons-criteria common effect ( p x c ) shows whether or not a specific individual’s relative position (performance criteria) changes from one subject to another. The estimated value for this variance component is 0.134 and total variance explained by this component is 31.2%. Hence, the component based on the common interaction ranks second as per the total percentage it explains, in other words it has a significant place in the ranking due to its magnitude. Correspondingly, it is suggested that relative positions (performance criteria) of prospective teachers may differ from one criterion to another.

Persons-raters common effect ( p x r ) shows whether or not the raters and prospective teachers scored more severely-leniently by comparison. Table 4 shows that the estimated value for this variance component is 0.046 and total variance percentage explained this component is 10.7%. Accordingly, it may be suggested that raters’ scores may differ from one individual to another and, in other words, that individuals rated high by a rater is rated low by the other. Hence, in addition to what is presented in Table 4, when instructor assessments and prospective teachers’ self-assessments are thoroughly examined, it is found that prospective teachers’ assessments ( 18.29) are more positive compared to those of the instructor ( 15.75), and that the difference [t (198) =6,421, p<.001] between the assessments is significant. Hence, in parallel to this finding, Yılmaz-Nalbantoğlu’s study (2012), based on the findings of the t test used to compare students’ self- assessment scores to those of the rater, suggested that students had a significant tendency for a relatively more positive self-assessment.

Criteria-rater common effect (c x r) shows whether or not raters’ scores are stable from one criterion to another. In fact the value calculated for this variance component is 0.027 and that the total variance explained by this component is 6.2%. The component value being proximate to zero may suggest that the scoring made by both the instructor and the prospective teachers are stable to a great extent even though there is a minor difference from one criterion to another.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

Remainder effect variance ( p x c x r , e) are comprised of persons-criteria-rater common effect and random errors. Table 4 shows that the highest variance value of 0.158 belongs to this component with which 37.0% of the total variance is explained. The important place of the explained variance in the rank order serves as an indicator of the magnitude of the remainder effect. The magnitude of this effect not only means that the difference between the individuals’ scores is caused by the criteria and the raters, but also shows the possibility of variability due to the factors other than the ones in the research design. Hence, in addition to interpreting the main and common effects based on the relative magnitudes of variances obtained by G-study, the present study conducted a reliability estimation in respect of instructor assessments and prospective teachers’ self- assessments on hierarchical concept map performances based on G and Phi (ɸ) coefficients, and G coefficient was found to be 0.06, and Phi (ɸ) coefficient, which produces a stricter value, was found to be 0.05. In other words, it may be suggested that the magnitude of remainder effect variance is caused by the inconsistency between instructor assessments and prospective teachers’ self-assessments on concept maps. Hence, while the observations based on Table 5 explain this finding to some extent, the correlation analysis used to obtain an extra measurement of the aforementioned consistency showed a low level of relationship (r xy = 0.24, p<.05) between the instructor assessments and prospective teachers’ self-assessments. It is possible to come across studies with similar findings in the literature; for example Longhurst & Norton (1997) also found a correlation coefficient value (0.43), which was not high, in their research on the correlation between instructor and student scorings.

DISCUSSION AND CONCLUSION

Under the scope of the present study, a generalizability study was carried out by creating p x c x r (p: person, c: criterion, r: rater) pattern through scoring of the prospective teachers’ concept maps by the instructor and the prospective teachers themselves. Analysis based on estimated variance values revealed the following: • In terms of their performance on concept map design, prospective teachers are homogeneously dispersed. • Difficulty levels of the criteria used in the assessment vary. However, while the difficulty levels of the criteria vary throughout the criteria, this variance is also reciprocally observed in the instructor’s and the prospective teachers’ independent assessments. • An equal severity-leniency is observed in both the assessments made by the instructor for all prospective teachers and the self-assessments made by the prospective teachers. • Prospective teachers’ performance measurements differ from one criterion to another; in other words some prospective teachers were found to exhibit high performance in some criteria and low performance in some other criteria. • Scores given to concept map design performances of the prospective teachers vary based on the rater, and self-assessments are more positive compared to the instructor assessments. • Raters were found to be consistent (stable) in scoring in respect of the criteria in the scoring sheets. • The difference between the prospective teachers’ performances was found to have resulted from the criteria and the rater.

Another indicator that this difference was caused particularly by the raters is the low G and Phi (ɸ) coefficients (respectively 0.06 and 0.05) and the low correlation coefficient (0.24) between the scores of the raters. Considering the reliability evidence obtained based on the Kappa coefficient for each criterion of the scoring key that was initially found to be fit for reliable scoring based on the results obtained with regard to the fact that two different raters performed consistent scoring, one of the possible and the most important reasons why we cannot observe consistency between the raters is believed to the prospective teachers’ incapability to make a self-assessment which requires an objective self-evaluation behavior. On the other hand, as Ewing and Everett (2015) stated, from a realistic point of view, it is stipulated that the instructors have overall responsibility for the final agreed grade from a quality assurance perspective. On the opposite, people grading themselves usually tend to move out of the grade band. However, it is also known that self-assessment skills can be acquired and applied competently in adulthood if they are experienced as of childhood, and that especially where the education system is not supportive of the development of such skills starting from childhood, individuals assess themselves either as very low or very high performer when they become an adult. Considering that acquiring these skills began to be emphasized following the revisions after 2005 and were not 36 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

specifically emphasized among the main targets of our national Turkish education and training programs before this date, it is a usual to see the inconsistency between prospective teachers’ self-assessments and the instructor assessments on prospective teachers’ concept map design performances. The drawback here is that the prospective teacher who is incapable of self-assessment will be incompetent in defining and compensating own deficiencies related with the technical and applied information on his/her related field. Besides, another reason for the difference between the instructor assessments and the prospective teachers’ assessments throughout the criteria may be that the prospective teachers may not have comprehended the content of assessment criteria on concept map design performances well enough or that the prospective teachers may have not paid due care to the importance of aforementioned self-assessment practice. For example “Use of Material” criteria that increases the readability and attractiveness of the concept maps and the number of sense organs in learning was found to have one of criteria with the highest difficulty level (the most difficult) as mutually determined by the instructor and the prospective teachers. But on the other hand, this common opinion differs at a very important point; while more than 70% of the prospective teachers defined the “Use of Material” as the criterion that is achieved with the highest performance level, the instructor stated that only 37% of the group was able to achieve this criterion at high performance. Based on the above, it is suggested that the initiatives supporting the development of self-assessment skills that will help teachers and prospective teachers define and compensate their deficiencies may also assist them with acquiring sufficient technical knowledge and skills that are the foundation for developing quality teaching and assessment materials that support acquisition of high order mental skills such as concept maps.

BIODATA AND CONTACT ADDRESSES OF AUTHORS

Assist.Prof.Dr. Göksu GÖZEN is a full-time academic staff of Educational Measurement and Evaluation in the Department of Educational Sciences at Mimar Sinan Fine Arts University. She received BA (2000), and MA (2002) degrees in Educational Measurement and Evaluation at Hacettepe University, and PhD (2007) degree in the same area at Ankara University. Her research interests include developing measurement and assessment tools, test scoring methods, teaching and assessing higher order thinking skills (i.e. creative thinking and problem solving skills), project-based learning, and performance assessment. She has also published in the area of ethics in educational and psychological testing process..

Assist.Prof.Dr. Göksu GÖZEN Mimar Sinan Fine Arts University Department of Educational Sciences Cumhuriyet Mah. Silahşör Cad. No:71 34380 Bomonti, Şişli, İstanbu-l TURKEY E-Mail: [email protected]

Assist.Prof.Dr. Kaan Zülfikar DENİZ is a full-time Assistant Professor at Ankara University, Ankara, Turkey. He received BS (2001), and MS (2003) degrees in Measurement and Evaluation at Hacettepe University , Ankara, Turkey. He has completed his PhD dissertation (2008) at the Measurement and Evaluation, Ankara University, Turkey. His research interests include Scale development and measurement of affective properties. In the last 13 years he has worked as a full-time academic staff at Ankara University. He is a founding director of Ankara University Examination Management Center (ASYM).

Assist.Prof.Dr. Kaan Zülfikar DENİZ Ankara University

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

Institute of Educational Sciences 06590 Cebeci, Ankara- TURKEY E. Mail: [email protected]

REFERENCES

Anıl, D. ve Büyükkıdık, S. (2012). Genellenebilirlik kuramında dört facetli karışık desen kullanımı için örnek bir uygulama. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 3(2), 291-296.

Atılgan, H. (2005). Genellenebilirlik kuramı ve puanlayıcılar arası güvenirlik için örnek bir uygulama (Generalizability theory and a sample application for inter-rater reliability). Eğitim Bilimleri ve Uygulama (Educational Sciences and Practice) , 4(7), 95-108.

Avalos, B. (2011). Teacher professional development in Teaching and Teacher Education over ten years. Teaching and Teacher Education , 27 (1), 10-20.

Bloom, B. S. (1956). Taxonomy of Educational Objectives, Handbook I: The Cognitive Domain. New York: David McKay Co Inc.

Brennan, R. L. (2001). Generalizability theory . ACT Publications. Iowa City, Iowa.

Chen, J., & Brown, G. T. L. (2013). High-stakes examination preparation that controls teaching: Chinese prospective teachers’ conceptions of excellent teaching and assessment. Journal of Education for Teaching: International Research and Pedagogy , 39 (5), 541–556. doi:10.1080/02607476.2013.836338

Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory . Harcourt Brace Javanovich College Publishers, USA.

Cronbach, L. J., Gleser, G. C., Nanda, H., & Rajaratnam, N. (1972). The dependability of behavioral measurements: Theory of generalizability for scores and profiles . New York: John Wiley.

Cronbach, L. J., Linn, R. L., Brennan, R. L., & Haertel, E. H. (1997). Generalizability analysis for performance assessments of student achievement or school effectiveness. Educational and Psychological Measurement, 57 (3), 373–399.

Cronbach, L. J., Nageswari, R., & Gleser, G. C. (1963). Theory of generalizability: A liberation of reliability theory. The British Journal of Statistical Psychology, 16 , 137-163.

Darling-Hammond, L. & Adamson, F. (2010). Beyond basic skills: The role of performance assessment in achieving 21st century standards of learning. Stanford, CA: Stanford University, Stanford Center for Opportunity Policy in Education.

Dochy, F. J. R. C., Segers, M., & Sluijsmans, D. (1999). The use of self-, peer and co-assessment in higher education: A review. Studies in Higher education , 24 (3), 331-350.

Edmondson, K. M. (2000). Assessing science understanding through concept maps. In Mintzes, J. J., Wandersee, J. H., & Novak, J. D. (Eds.). Assessing science understanding: A human constructivist view (pp. 15-40). San Diego, CA: Academic Press.

Ewing, A. & Everett, S. (2015). Combining self-, peer- and tutor-assessment. Outside the Box Assessment & Feedback Practices, 1(1), 9.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

Goodwin, L. D. (2001). Interrater agreement and reliability. Measurement in Psychical Education and Exercises Science, 5(1), 13-14.

Güler, N. (2009). Genellenebilirlik kuramı ve SPSS ile GENOVA programlarıyla hesaplanan G ve K çalışmalarına ilişkin sonuçların karşılaştırılması (Generalizability theory and comparison of the results of G and D studies computed by SPSS and GENOVA packet programs.). Eğitim ve Bilim (Education and Science) , 34 (154), 93-103.

Güler, N. (2011). Rasgele veriler üzerinde genellenebilirlik kuramı ve klasik test kuramına göre güvenirliğin karşılaştırılması (The comparison of reliability according to generalizability theory and classical test theory on random data). Eğitim ve Bilim (Education and Science) , 36 (162), 225-234.

İngeç, Ş. K. (2009). Analysing concept maps as an assessment tool in teaching physics and comparison with the achievement tests. International Journal of Science Education , 31 (14), 1897-1915.

Jimenez-Snelson, L. (2010). Estimating the reliability of concept map ratings using a scoring rubric based on three attributes of propositions. Doctor of Philosofy Dissertation, April 2010. Brigham Young University, Department of Instructional Psychology and Technology. BYU ScholarsArchieve. Available at: http://scholarsarchieve.byu.edu/etd

Krippendorff, K. (2004). Reliability in content analysis: Some common misconceptions and recommendations. Human Communication Research , 30 (3), 411-433.

Longhurst, N., & Norton, L. S. (1997). Self-assessment in coursework essays. Studies in Educational Evaluation , 23 (4), 319-330.

McClure, J. R., Sonak, B., Suen, H. K. (1999). Concept map assessment of classroom learning: Reliability, validity, and logistical practicality. Journal of Research in Science Teaching , 36 (4), 475-492.

Moreira, M. (2006). Concept mapping: An alternative strategy for evaluation. Assessment & Evaluation in Higher Education , 10 (2), 159-168.

Novak, J. D. & Cañas, A. J. (2007). Theoretical origins of concept maps, how to construct them, and uses in education. Reflecting Education , 3(1), 29-42.

Novak, J. D. & Cañas A. J. (2008). The theory underlying concept maps and how to construct and use them. Technical Report IHMC CmapTools 2006-01 Rev 01-2008, Florida Institute for Human and Machine Cognition. Available at: http://cmap.ihmc.us/Publications/ResearchPapers/TheoryUnderlyingConceptMaps.pdf

Nunally, J. C. (1982). Reliability of measurement . Encylopedia of Educational Research , (5 th edition). Editor H.E. Mitzel. New York.

Nunally, J. C. & Bernstein, I. H. (1994). Psychometric theory (3 rd edition). New York: Mc-Graw-Hill.

Plummer, K. J. (2008). Analysis of the psychometric properties of two different concept-map assessment tasks. Doctor of Philosofy Dissertation, April 2008. Brigham Young University, Department of Instructional Psychology and Technology. BYU ScholarsArchieve. Available at: http://scholarsarchieve.byu.edu/etd

Rafferty, C. D. & Fleschner, L. K. (2010). Concept mapping: A viable alternative to objective and essay exams . Reading Research and Instruction, 32 (3), 25-34.

Sanders, P.F.(2014). Generalizability theory: Estimation. Wiley StatsRef: Statistics Reference Online: http://onlinelibrary.wiley.com/doi/10.1002/9781118445112.stat06695

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 03 ISSN 1309-6249

Shavelson, R. J. & Webb, N. M. (1991). Generalizability theory : A primer . Sage Publications, USA.

Stecher, B. (2010). Performance assessment in an era of standards-based educational accountability . Stanford, CA: Stanford University, Stanford Center for Opportunity Policy in Education.

Strautmane, M. (2012). Concept map-based knowledge assessment tasks and their scoring criteria: An overview. In Concept maps: Theory, methodolgy, technology. Proceedings of the Fifth International Conference on Concept Mapping, Valletta, Malta, 2012.

Subramaniam, K., & Esprívalo Harrell, P. (2015). An analysis of prospective teachers’ knowledge for constructing concept maps. Educational Research , 57 (3), 217-236. DOI:10.1080/00131881.2015.1050845.

Webb, N. M., Shavelson, R. J., & Haertel, E. H. (2006). Reliability coefficients and generalizability theory. In C. R. Rao & S. Sinharay (Eds.), Handbook of Statistics, Vol. 26 (pp. 81-124).

Volpe, R. J., McConaughy, S. H., & Hintze, J. M. (2009). Generalizability of classroom behavior problem and on- task scores from the direct observation form. School Psychology Review , 38 (3), 382-401.

Yelboğa, A. (2012). Dependability of job performance ratings according to generalizability theory. Education and Science , 37 (163), 157-164.

Yelken, T. Y., & Alıcı, D. (2008). Öğretmen adaylarının hazırladıkları performansa dayalı değerlendirme materyallerine ilişkin görüşlerinin ve değerlendirmelerinin incelenmesi. Jounal of Qafqaz University , 24 , 222- 235.

Yılmaz-Nalbantoğlu, F ve Gelbal S. (2011). İletişim becerileri istasyonu örneğinde genellenebilirlik kuramıyla farklı desenlerin karşılaştırılması. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 509-518.

Yılmaz-Nalbantoğlu, F. (2012). İletişim becerileri istasyonundan elde edilen öz değerlendirme ve puanlayıcı değerlendirmelerinin karşılaştırılması. Eğitim ve Öğretim Araştırmaları Dergisi , 2, 357-363.

Yin, Y., & Shavelson, R. J. (2008) Application of generalizability theory to concept map assessment research. Applied Measurement in Education, 21 (3), 273-291.

Yin, Y., Vanides, J., Ruiz-Primo, M. A., Ayala, C. C., & Shavelson, J. R. (2005). A comparison of two concept- mapping techniques: Implications for scoring, interpretation, and use. Journal of Research in Science Teaching , 42 (2), 166–184.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 04 ISSN 1309-6249

GAMIFICATION AND EFFECTS ON STUDENTS’ SCIENCE LESSON ACHIEVEMENT

Assist. Prof. Dr. Mehmet Can ŞAHIN Çukurova University Adana- TURKEY

Res. Assist. Nihan ARSLAN NAMLI Çukurova University Adana- TURKEY

ABSTRACT

This study aims to reveal students’ achievement based on gamification use. The study is a study of quantitative type and single-group pretest-posttest experimental design has been used. The study has been conducted in the spring semester of 2014/2015 academic year, candidates who are studying in 6. Grade of students. In the experimental group of this study while dramatized science teaching software is applied to control group, a lesson is carried out based on the curriculum and the program prepared by MEB, research is carried on for 8 weeks in total. In the research, as data collection devices “Multiple Choice Science Test” carried out in both groups and “Educational software” were applied to the experimental group and “Plain text” were applied to control group. After 8 weeks, Multiple Choice Science Test” carried out in both groups again. As a result of this research, gamification in a science lesson, it is found that there is a meaningful improvement in students’ problem solving skills.

Keywords: Gamification, Game-based learning, Computer-based learning.

INTRODUCTION

“Gamification” is a concept which aims to increase user experience and engagement with a system, while education is an area with high prospective for application of this concept. A lot of ideas about gamification has been growing over the past few years and a lot of interest on how to use gamification in education. “There is a lot of potential in the field of gamification in education because as humans we always have a desire to learn irrespective of age. This comes to us with a big question “how can we make education more interesting?”” (Surendeleg, 2014).

So, researchers always are looking for new techniques for better teaching and gamification is one of them. Lots of researchers agree with this idea. For example, according to Emekçi and Fidan, “game design programs use students to actively participate in the teaching process will enable the improvement of learning retention” (Emekçi, Fidan, 2012). On the other hand, Çatak thought that “The examination will be carried out on a learning culture in the educational field of computer games and it shows that students remaining passive and disinterested in traditional teaching could be carried out more efficiently and more effective learning” (Çatak, 2011).

Also, “gamification approach increases participation and motivation of the learner, the learning process will be more effective, efficient, attractive and fun” (Bozkurt, 2014). Gamification has an active role in learning process. There is a breath of research that identifies the range of benefits relating to gamification and it can be observed that in addition to benefiting learning, gamification enhances learning, student engagement and as a technological approach which is necessary and relevant to today’s learner Cheong, Kapp, Martin, 2011). It is revealed that empirical evidence exists that games can be effective tools for enhancing learning and understanding complex subject matter. gamification can play a big role when we incorporate into the learning process by enhancing student engagement, learning and through this student’s motivation levels are increased.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 04 ISSN 1309-6249

The use of technology can help to increase lesson engagement. Learning becomes a more active experience, stimulating students at a deeper level. Many education products employ the principles of gamification, which is the “use of game mechanics in nonentertainment environments to change user behavior and drive engagement”( Lowendahl, 2011). The use of games to teach students is not new and the importance of play in facilitating learning has long been recognized. Today’s technology provides for an even more immersive experience. Games increase enjoyment for students by providing rewards and feedback, which can improve students’ attitudes toward learning traditionally challenging subjects like mathematics or science. Studies trying to show whether educational gaming increases learning have been mixed, but they have shown increased student engagement and motivation (Rubin, 2011).

In this research, experimental and control group was used. There are other studies in the literature which were applied experimental studies. According to their results, Aral (2012) claimed that the results of the Learning Approach Scale of experimental and control groups determined the application made by puzzle educational material was the influence of students' scores. Games about children's rights issues were applied to the experimental group and constructivist teaching was applied to the control group. It has been proven that the experimental group was more successful than the control group (Torun, 2014). In addition, when students attitudes towards mathematics intended to measure, experimental group who were used gamification was more successful than control group (Özer, 2010). Gamification has a positive effect on students' achievement levels were seen (Türksever, 2011).

Aim & Scope The purpose of the current study is first to define the relation of 6. A grade students’ academic achievement for taking gamification in their science lessons. The following research questions were explored in this study:  Does student’s academic achievement correlate with using gamification in their science lessons?  Is there any significant difference between the students’ pre-test and post-test lesson grade?

METHOD

Participants Data were collected across a state school in Adana, in 2014-2015 spring semester. Participants were 6. Grade of students. At the end of semester 20 students participated in the study. Also, the study was conducted in a computer lab.

Research Model The study, which was conducted to determine relationships between vocational college students’ academic achievement and submitted online follow up tests, carried the characteristics of correlational research model.

Data Collection Tool To address the research questions, pre-test and post-test was applied. Firstly, a pre-test which was about the topic of vitamins was consisting of ten multiple-choice questions was applied 20 students. Then, a plain text which was about the topic of vitamins was given to a control group who were selected randomly and they were asked to learn by reading. Likewise, the experimental group was selected randomly. A gamified training software was given to them. It was asked to review the program in order to play games respectively. Finally, a pro-test was applied by asking the same questions in the pre-test to the experimental group and the control group. Fifteen minutes were given to answer the questions.

FINDINGS & DISCUSSIONS

Test results are determined by comparing the difference between the two groups’ pre-test and post-test scores. Whether there is a significant difference between the two averages are determined by paired samples T test and independent groups T test. In this section, the findings obtained as a result of the analysis of the data and the data obtained from the study are described in the form of tables arranged.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 04 ISSN 1309-6249

The paired samples T test for determining whether there is a significant difference between pre-test and post- test scores of the control group were applied and t-test results are presented in Table 1.

Table 1: Paired samples t-test results: For the comparison of the pre-test and post-test scores of the control group

Test Type N X Ss t p Pre-test 10 42 16,19 -1,103 0,299 Post-test 10 47 17,02 *P<, 05

The scores obtained in achievement test results analyzed by applying the paired samples t test. The mean of the control group pre-test was X = 42 and the standard deviation was seen as Ss = 16,19. On the other hand, the mean of pro-test was seen as X = 47 and the standard deviation appears to be Ss = 17,02. As a result of the analysis, it is observed that there is not a significant difference (t=-1,103; p>0.05) between pre-test and post- test scores of the control group.

The paired samples T test for determining whether there is a significant difference between pretest- posttest scores of the experimental group were applied and t-test results are presented in Table 2.

Table 2: Paired samples t-test results: For the comparison of the pre-test and post-test scores of the experimental group Test Type N X Ss t p Pre-test 10 34 14,46 -2,577 0,030 Post-test 10 56 15,05 *P<, 05

The scores obtained in achievement test results analyzed by applying the paired samples t test. The mean of the experimental group pre-test was X = 34 and the standard deviation was seen as Ss = 14,46. On the other hand, the mean of pro-test was seen as X = 56 and the standard deviation appears to be Ss = 15,05. As a result of the analysis, it is observed that there is a significant difference (t=-2,577; p<0.05) between pre-test and post-test scores of the experimental group. Because degree of freedom is negative, it means that the post-test scores’ means are much more than pre-test scores.

For the comparison of the experimental and control groups pre-test score, independent samples t-test results are shown in Table 3.

Table 3: Independent samples t-test results: For the comparison of the experimental and control groups pre- test scores Groups N X Ss t p Experimental 10 34 16,46 1,095 0,288 Control 10 42 16,19 P>, 05

The scores obtained in achievement test results analyzed by applying independent samples t test. The mean of the experimental group pre-test was X = 34 and the standard deviation was seen as Ss = 16,46. On the other hand, the mean of the control group pre-test was X = 42 and the standard deviation was seen as Ss = 16,19. As a result of the analysis, it is observed that there is not a significant difference (t=1, 095; p>0.05) between pre- test scores of both experimental and control groups.

For the comparison of the experimental and control groups post-test score, independent samples t-test results are shown in Table 4.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 04 ISSN 1309-6249

Table 4: Independent samples t-test results: For the comparison of the experimental and control groups post- test scores Groups N X Ss t p Experimental 10 56 15,05 -1,252 0,227 Control 10 47 17,02 P>, 05

The scores obtained in achievement test results analyzed by applying independent samples t test. The mean of the experimental group post-test was X = 56 and the standard deviation was seen as Ss = 15,05 On the other hand, the mean of the control group post-test was X = 47 and the standard deviation was seen as Ss = 17,02. As a result of the analysis, it is observed that there is not a significant difference (t=-1,252; p>0.05) between post- test scores of both experimental and control groups.

CONCLUSION & SUGGESTIONS

Gamification can motivate students to engage in the classroom, give teachers better tools to guide and reward students, and get students to bring their full selves to the pursuit of learning. It can show them the ways that education can be a joyful experience, and the blurring of boundaries between informal and formal learning can inspire students to learn in life wide, lifelong, and life deep ways. The challenges, however, are also significant and need to be considered. Gamification might absorb teacher resources, or teach students that they should learn only when provided with external rewards. On the other hand, playfulness requires freedom - the freedom to experiment, to fail, to explore multiple identities, to control one’s own investment and experience (Klopfer, Osterweil & Salen, 2009). In tandem with the creation of gamification projects, it must be developed meaningful assessments of whether they are achieving their aims. As gamification spreads throughout the real world, there is little question it will also impact schools. By leading to research-based, theory-driven gamification projects, it can be worked to ensure that the impact of gamification is a positive one. Gamification will be a part of students' lives for years to come. If teachers can harness the energy, motivation and sheer potential of their game-play and direct it toward learning, then teachers can give students the tools to become high scorers and winners in real life.

So, in this study, gamification project was applied and the results are compared. Firstly, in the light of the research questions, paired samples t-test results was shown in Table 1 for the comparison of the pre-test and post-test scores of the control group. However, there is not a significant difference (t=-1,103; p>0.05) between pre-test and post-test scores of the control group. It means that control groups’ scores does not change based on these two tests. In addition, paired samples t-test results was shown in Table 2 for the comparison of the pre-test and post-test scores of the experimental group and there is a significant difference (t=- t=-2,577; p<0.05) between pre-test and post-test scores of the experimental group. It means that experimental groups’ scores change based on these two tests. So, gamification application can change students’ academic achievement. After that, independent samples t-test results was shown in Table 3 for the comparison of the experimental and control groups pre-test scores and again, there is not a significant difference (t=1, 095; p>0.05) between pre-test scores of both experimental and control groups. Therefore, it can be said that there is not a huge difference between experimental and control groups’ knowledge level. At the end, independent samples t-test results was seen in Table 4 for the comparison of the experimental and control groups post-test scores. There is not a significant difference (t=-1,252; p>0.05) between post-test scores of both experimental and control groups. As it can be seen, there is a significant change only in Table 2. The reason of that can be gamified applications are typically goal-oriented with a clearly defined set of ‘win’ conditions and a number of obstacles to overcome in order to complete the activity (Figure 1).

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 04 ISSN 1309-6249

Figure 1: An interface of education software

From this definition, it is clear to see the similarity between games and learning, with players/learners being directed to undertake tasks in order to achieve a desired outcome, moving to the next level/mission in the case of a game, or complete understanding a complex topic in the case of education (Ames, 1990; Pintrich, 2003). This shared focus on achieving specific goals is a major reason for the applicability of gamification to education. If the literature was examined, according to Cansever (2015), gamification can be effective in satisfying their needs and it can be more interesting, making remarkable and enjoyable for students and with gamification, education will be fun and more remarkable (Bıçakcı, 2014). In short, most of the researchers agree with the idea of gamification. Although, there is both positive and negative side of it, positive effects outweigh the negative effects. In this research, the experimental group was more successful in their post tests. So, it can be said that gamification has positive effects. For the further researches, gamification can be applied in other lessons like social science or mathematics. Participants can be primary school students or university students.

IJONTE’s Note: This article was presented at 3rd International Technologies & Teacher Education Symposium, 9- 11 September, 2015, Trabzon-Turkey and was selected for publication for Volume 7 Number 1 of IJONTE 2016 by IJONTE Scientific Committee.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 04 ISSN 1309-6249

BIODATA AND CONTACT ADDRESS OF THE AUTHORS

(Res. Ass. Nihan ARSLAN NAMLI). I was graduated from Bilkent University both undergraduate degree and master without thesis degree. I had started my master degree in Middle East Technical University. Now, I am studying at the Çukurova University and I am continuing my master degree in here. My field of study is computer education and instructional technology.

Res. Assist. Nihan ARSLAN NAMLI Çukurova University Computer Education & Instructional Technology Department Adana- TURKEY E. Mail: [email protected]

Assist. Prof. Mehmet Can ŞAHİN I was graduated from METU with undergraduate degree. I had finished my master degree in Çukurova University and . I had finished my Phd degree in Anadolu University. Now, I am studying at the Çukurova University as an assistant professor.

Assist. Prof. Mehmet Can ŞAHİN Çukurova University Computer Education & Instructional Technology Department Adana- TURKEY E. Mail: [email protected]

REFERENCES

Ames, C. (1990). Motivation: What Teachers Need to Know. Teachers College Record, 91 (3), 409-421. Accessed 29/11/2012-http://www.tcrecord.org/Content.asp?ContentId=401.

Aral, N.- Gürsoy Ve F.- Yaşar, M. C. İlköğretim Beşinci Sınıf Çocuklarının Öğrenmelerinde Yapboz Eğitim Materyalleriyle Yapılan Uygulamanın Etkisinin İncelenmesi, Ankara Sağlık Bilimleri Dergisi, 2012.

Bıçakcı, K. – Abul, O. Ve Çaplı, B. Siber Güvenlik Eğitimi için Oyunlaştırma, Bilgisayar Mühendisliği Bölümü, TOBB Ekonomi ve Teknoloji Üniversitesi, Ankara 2 4S Bilgi Teknolojileri A.Ş., Ankara.

Bozkurt, A. Ve Gençkumtepe, E. Oyunlaştırma, Oyun Felsefesi ve Eğitim: Gamification, Akademik Bilişim 2014, 5-7 Şubat 2014, Mersin Üniversitesi, Mersin.

Cansever, Z. – Avsar Z. Ve Tastan K. (2015) Tıp Fakültesi Üçüncü Sınıf Öğrencilerinin Oyunlaştırma Yöntemi ile Tıbbi Öykü Alma Deneyimleri, Department of Medical Education, Ataturk University Faculty of Medicine, Erzurum, Turkey.

C. Cheong, F. Cheong & J. Filippou, Quick quizz: A gamified approach for enhancing learning, PACIS, (2013). 46 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 04 ISSN 1309-6249

Çatak, G. Derleme Makalesi / Review Paper Oynarken Tasarlamak: Dijital Tasarım Oyunları, Sigma 3385- 391,2011(özel sayı),Yıldız Teknik Üniversitesi, Fen Bilimleri Enstitüsü, Mimarlık Anabilim dalı, Yıldız-İstanbul

Emekçi Ve M- Fidan, Ş. (2012) Oyunun Tasarım Platformları: Oyunun Eğitim Ve Kültüre Etkisi, Batman Üniversitesi, Teknik Eğitim Fakültesi, Elektrik Eğitimi, 72100 Batman, Türkiye

K. M. Kapp, The Gamification of Learning and Instruction: Game-based Methods and Strategies for Training and Education, Pfeiffer, 2012.

Klopfer, E., Osterweil, S. & Salen, K. (2009). Moving learning games forward: Obstacles, opportunities, and openness. The Education Arcade: Massachusetts Institute of Technology Lowendahl, J.M. (2011, July 29). Hype Cycle for Education.

Özer, B. Oyunlaştırmanın beşinci sınıf matematik dersinde problem çözme becerisi ve derse karşı tutum üzerindeki etkisi, ISSN:1306-3111 e-Journal of New World Sciences Academy 2010, Volume: 5, Number: 1, Article Number: 1C0115.

Rubin-Vaughan, R., Pepler, D., Brown, S., & Craig, W. (2011). Quest for the Golden Rule: An effective social skills promotion and bullying prevention program. Computers & Education, 56, 166-175.

S. Martin, G. Diaz, E. Sanchristobal, R. Gil, M. Castro & J. Peire, New technology trends in Education: Seven years of forecasts and convergence, Computers and education, 57 (2011), 1893 - 1906. http://dx.doi.org/10.1016/j.compedu.2011.04.003

Surendeleg, G. (2015). The Role of Gamification in Education- A Literature Review The Role of Gamification in Education – A Literature Review, (August).

Torun, F. Ve Duran, H. Çocuk Hakları Öğretiminde Oyun Yönteminin Başarıya, Kalıcılığa Ve Tutuma Etkisi, Adıyaman Üniversitesi Sosyal Bilimler Enstitüsü Dergisi Issn: 1308–9196, Yıl : 7 Sayı : 16 Nisan 2014.

Türksever H. (2011) Çizgi İle İlgili Temel Konuların Öğretiminde Oyunlaştırılmış Yaratıcı Etkinliklerin Öğrenme Erişisine Etkisi, Mehmet Akif Ersoy Üniversitesi Sosyal Bilimler Enstitüsü Güzel Sanatlar Anabilim Dalı Yüksek Lisans Tezi, Burdur.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

THE EVALUATION OF LEARNING ENVIRONMENT DESIGNED FOR USING THRE DIMENSIONAL DYNAMIC GEOMETRY SOFTWARE: TEACHER VIEWS

Hilal KALAY Ministry of National Education Acısu Secondary School Trabzon – TURKEY

Assist. Prof. Dr. Temel KÖSA Karadeniz Technical University Fatih Faculty of Education Trabzon – TURKEY

ABSTRACT

It is an expected situation that education is influenced by the advancement of technology rapidly and we feel it at every stage of life. Thanks to the advancement of technology, three-dimensional dynamic geometry software has emerged and it is thought that they will provide great convenience to math education. Some features of three-dimensional dynamic geometry software like being dynamic, allowing for constructing geometrical structures and looking at them from every aspect, dragging, measuring are very useful. However, some researchers find that teachers have some problems with using this software in spite of all these advantages. The purpose of this study is to find out teachers’ views about learning environment which designed with a three-dimensional dynamic geometry software called Cabri 3D. This study was carried out with case study. The sample of the study consisted of two mathematics teachers. One of the teachers works in town center and the other one works in the village. Descriptive analysis was used to investigate the data obtained from the research. Research results show that the teachers have different viewpoints about the computer- aided learning environment although they have similar competence. Based on the results obtained from this study, it can be suggested that more specific in-service training should be organized for the teachers in order to adapt the computer-aided instruction in mathematics education.

Key Words: Three Dimensional Dynamic Geometry Software, Learning Environment, Teachers’ Views.

INTRODUCTION

Nowadays technology is progressing rapidly and it makes its presence felt in every aspect of our lives. Education is also inevitably impressed in such a case and technology. Moreover, technology dramatically got into activities of the education and hit it hard (Tutkun, Öztürk and Demirtaş, 2011). One of the most significant effects of the technology on mathematical researches is computer algebra systems and dynamic geometry software developed recently. The number of the computer software, which will enable visual and efficient learning environment to student increased thanks to the development of technology (Zengin and Kutluca, 48 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

2011). It is thought that this software will provide great convenience to geometry teaching because three- dimensional geometry software has some important features such as being dynamic, dragging, measuring, leaving a mark, allowing for constructing geometrical structures and looking at them from every aspect. In addition, it is certain that all of these features are very useful in theory.

Cabri 3D being three-dimensional geometry software is one of the computer software used in learning environment. It makes available to teachers and students the all advantages of such dynamic geometry software. The most significant advantages of Cabri 3D are visualization and dynamically dragging geometric objects. Thanks to these advantages, it enables the students to manipulate the structures in a dynamic way and to look geometric structures in the most correct way. At this point, the students require necessary instructions in order to use effectively this software. The teachers who are practitioners of the system play a key role in order that the students can make the most of this software. To provide effective learning by using the software correctly by the students who just encounter with the software is closely related to the attitudes, opinions of the teachers about the software and their guidance to students. In this case, it becomes crucial to reveal the teachers’ views about the dynamic geometry software.

It is generally accepted that teacher is the most critical factor of an education period. All kinds of innovation like content, method or technology inserted to education system can be effective to the extent that they can help to teacher (Tutkun ve diğ, 2011). Teachers must use a lot of materials such as blackboard, smart board and dynamic software during their lessons. Being eager about using these materials is essential to set the effective learning environment by teachers.

It is very normal that teachers encounter some problems in period of accepting the changes in education just as the transition from blackboard to smart board (Baki, Aydın, Özpınar, Çalık, 2009). It can be utilized the aid of technology to overcome these problems. Actually, technology enhances the strength of teacher and the quality of education, minimizes the effort and time of the teachers and students in the lessons, reduces the cost without affecting the quality of the education, and dynamises the students in the learning environment (Öğüt, Altun ve Koçer 2003 transferred by Baki and others 2009). The teachers can be successful inasmuch as they believe features of the system. It is not sufficient that they just use the technology in an effective way. At the same time, they must correctly integrate technology into the teaching-learning environment. Baki (2001) has pointed out in his study that the using computers in mathematical study proceeds slowly by reason of poorly training teachers who adopt technology, and being unwilling about computer usage in teachers’ lessons although they are enthusiastic about using it in their daily lives. It must be essential to teach their own roles to teachers and teacher candidates during their education so that they can effectually carry out technology utilization in mathematical study.

Some studies which analyze attitudes and views of the teachers, teacher candidates and students about technology are available in literature (Güven and Karataş, 2003; Baki and others, 2009; Kösa, Baki and Karakuş, 2008; Tatar, Akkaya and Kağızmanlı, 2011). It was seen generally to be studied with the teachers who have different learning platform and experience when it was investigated the studies conducted with teachers. The aim of this study is found out whether teachers having same learning platform, computer usage and similar occupational experience have different views about computer-aided learning, and they are different in what aspects if any.

The Purpose of the Study The advantages of three dimensional dynamic geometry softwares for teachers and students in learning environments were revealed in various studies. Nevertheless, these softwares have some disadvantages in different usage contrary to theory. Teachers being executives of the system confronted problem as using the software due to various reasons. Numerous factors such as teachers’ work environments, their technological infrastructure, and experiences of the teachers and students affected adversely computer-aided learning environment. Managing the computer-aided learning environment and directing their students, teachers’ views about the matter are crucial. Therefore, the purpose of the study is to reveal teachers’ views about

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

learning environment that three dimensional dynamic geometry software is designed by enriched with Cabri 3D.

METHOD

The main purpose of the study was to reveal the teachers’ opinion about the learning environment which designed with using a three-dimensional dynamic geometry software Cabri 3D. Therefore, to achieve this purpose, the research was conducted using the case study method. Creswell (2002) defined the case study as “A case study is a problem to be studied, which will reveal an in-depth understanding of a “case” or bounded system, which involves understanding an event, activity, process, or one or more individuals”. It is possible to say that case study is based on “How” and “Why” questions (Yıldırım ve Şimşek, 2013). Case study is one of the most frequently used qualitative research methodologiesin educational researches. The main advantage of the method is to give researchers a chance to focus on an issue or a situation, deeply (Çepni, 2009).

Sample The sample of the study consists of two elementary school mathematics teachers who have been teaching in different state schools from each other in Trabzon. Teacher 1 (coded as T1) has a 2 years professional experience and teaching at a state school in a town center. Teacher 2 (coded as T2) has a 3 years professional experience and teaching at a state school in a village. Both T1 and T2 took Basic Computer Science and Computer-Aided Mathematics Teaching courses during pre-service training. Both teachers have been using computers actively in their daily life. Data Collection Within the scope of the study, interviews with teachers are made after they used Cabri 3D in their lessons. Semi-structured interview forms were used during the interviews. The interview form is a document which has been developed in order to ensure that all aspects related to the research problem and the inclusion of the question. The interviewer can change the structure of the sentence, order of questions during the interview or enter the details of some of the issue (Yıldırım ve Şimşek, 2013). The questions asked during the interviews in this study have been developed by researchers.Interviews were recorded with a digital voice recorder during the interviews.

Procedure Before the beginning of the study, the worksheets and learning environment (the desire of researchers) were introduced to the teachers. Because the teachers got a course for using Cabri 3D in mathematics education during their pre-service training, both of them knew how to use Cabri 3D. Therefore, an introductory course for Cabri 3D was not organized to teach the software for teachers. After the introduction of the worksheets and desired learning environment, both of the teachers completed the lessons by using the same activities in their classes. There were 5 worksheets. The front page of the first worksheet is shown as an example (see Figure 1). Worksheets were related with to draw two-dimensional views from different directions of three-dimensional objects and to construct the structures which were given the drawings of three-dimensional objects from different aspects. However, students do not need any advanced information to use Cabri 3D to complete the worksheets. Students only used some basic features such as rotating figures on the screen and to view the figures from different aspects. Both teachers have completed worksheets with their students by creating two- person groups in their classes. After implementations semi-structured interviews with teachers were done.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

Figure 1: One of the examples of worksheets

Analyzing Data In the analysis of data, interview records were converted into writing, firstly. This recording has been made in writing by the researchers. Then, a descriptive analysis of the recordings was done. In the finding section, descriptive analysis results are presented under predetermined sub-themes.

FINDINGS

Teachers performed an application in the learning environment which was designed as enriching with Cabri 3D. In this section, findings acquired from the teachers’ views about the application are presented in subtitles.

Teachers’ Views about Computer-aided Instruction conducted by Using Cabri 3D Both of the teachers think that Cabri 3D makes easier instruction since the students can correctly look at the structures that they will draw at the computer and the software makes the subject more understandable for them. The teachers’ views (T1 and T2) in respect to this are as follows:

T1….Whereas the students could directly look at the structures that they would draw at the computer, they had great difficulty in isometric drawing that was taken a printout. However, they got bored because drawing took a

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

while. Nevertheless, it made easier the instruction since drawing by looking from the computer was more comfortable. T2….Cabri 3D made the subject more understandable for students. On the other hand their learning became superficial without using Cabri 3D. Even if I used three dimensional materials in the lesson, I could not waggle the objects, which was resulted in backwardness. However, they were enthusiastic about learning since they constructed structures on their own at the computer.

Both of the teachers think that Cabri 3D dynamizes the students and enables to them to visualize the structures. So, teachers agree that it affects positively the lessons. Their views in respect to this are as follows:

T1….Students could only make some drawing in the normal classroom environment and so they could disremember later, but they had a mental picture of drawings which they had drew at the computer. In this way, they could comprehend the image when the object was rotated. That’s way; I could say that studies with computer made difference positively. T2….Cabri 3D did not make monotonous the lesson. The students showed great interest to the software that was new for them. They tried to learn and practice. So, I thought this practice brought different experience to the students. They tried to make out following my clues as well as they listened to me. They appeared like solving puzzle. I observed that they were so curious, interested in the new atmosphere and the lesson was more fun and different for them.

According to the interviews, whereas teachers agree to lean towards to computer-aided instruction, their opinions about the topic differentiate. While T1 mentions that guiding to students in a crowded classroom was not difficult for her, T2 had many problems to usual lesson in spite of having fewer students. It was understood that T1 set free students in comparison to T2, and T2 got involved personally with students. The teachers’ views in respect to this are as follows:

T1.… I just showed students to cube’s place and how they could rotate it since Cabri is Turkish. I lead to students and they completed by themselves. This was better for me because they lightened my load at the lesson. Ordinary lecturing was more troubled because I thought continuously how I would lecture and how they would comprehend better. Moreover, why do we waste our breath in the lesson? The students carried off since they were computer worm. There was no necessary to teacher since the students rotated and saw the objects on their own.

T2…. I felt safer myself in the usual learning environment because I could estimate what it would be there. I hesitated to use this software in spite of my proficiency for computer usage and my knowledge about dynamic software to a certain extent. Taking the lead to students became more difficult when they asked something at the same time, and then I had to run around. Nevertheless, I observed that students learned effectively in the computer-aided learning environment. It cannot be ignored its advantages on the students even if it is tiring for the teacher. Therefore, I want to use computer in my geometry lessons.

Teachers’ Views about Classroom Management in Computer-Aided Platform Both teachers state that they do not have any problems about classroom management in this new platform. The teachers’ views in respect to this are as follows:

T1….Classroom management was easier. After children, computer worm, finished their studies, I had a break for their motivation. They listened to me carefully during the lesson since they knew that they could play with computer in the break time. However, I was bored with their complaints since the students did not want to draw. Moreover, they secretly tried to play computer games, and so I had to close the games as controlling on the main computer. The students got bored quickly.

T2....It was not confronted by a problem in classroom management because half the battle won was not to prevent noise or nothing else. To clarify the subject to the students and conduct activities properly was more difficult thing. Since computer-aided instruction enables to individualization, the students was more active in

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

the lesson. However, they caused to lose time in the lesson owing to their different wishes when the students listen quietly to the teacher normally. Apart from this, it was not anything which affect adversely to classroom management because my all students tried their best.

Teachers’ Views about Teamwork in Computer-Aided Platform Teachers hold similar views about lecturing with teamwork. According to them, teamwork provides to learn from each other. The students get for effort within this period and so they are in unity in the classroom. The teachers’ views in respect to this are as follows:

T1….My guidance did not influence to lesson. Students could sit with their close friend and they supported each other when they had problem. They learned each other in this way, but they called me when they could not solve it. They learned by experience and arguing. Therefore, I did not confront problem with lead to the group. I only helped them when they conflicted.

T2….Teamwork in lesson was beautiful in terms of learning each other. I thought it affected positively to learning environment. The students tried to assist each other, which influenced positively with regard to social aspects. They got satisfied when they overcame problem. The students being capable tried to show the others how to solve the problem. The class turned into a big group as well as small groups. It was progressed unity in the classroom.

Teachers’ Views about Positive Sides of Computer-Aided Platform Teachers hold both similar and different views about positive sides of the studies according to the interview. While T1 thinks that the study opens a few doors for the teacher, T2 focuses to acquisitions that the students achieve without struggling. On the other hand, both teachers find useful the study in terms of making drawing easy. The teachers’ views in respect to this are as follows:

T1….Since the students drew themselves, it was only necessary to teachers’ guidance. The teacher was only assistant, but not a leading role, which was more comfortable for the teacher. My drawing was not good and so I did not lecture by drawing to my students last year. I had got three dimensional materials. I put them on the table and I had students draw objects to their notebooks in every aspect.

T2….It was fine that this study enabled to deal with the students one by one for their personal development. Everyone consulted me their problems and they tried to do activities together. So, I can say that they learned on their own. The software did not cause to mislearn arising from drawing, which is a terrific feature. In addition to this, it enabled that students could construct the structures easily and could look at the objects in every aspect. I think this is a particular importance factor. Teamwork was also beneficial to strengthen friendly relations.

Teachers’ Views about Negative Sides of Computer-Aided Instruction Both teachers complain similar problems about negative sides of the learning environment. They stated that they got tired of some problems with related to technical infrastructure of the school. They confronted problems because of fewer and old computers. The teachers’ views in respect to this are as follows:

T1…. I had trouble due to mouse. They locked and turned continuously when the students were rotating the objects. So, they had to reconstruct shapes by opening a new file. The school did not have sufficient equipment and the number of computers was inadequate. I wanted to take my students to computer laboratory, but we coincidenced with the other lessons. In short, most of the problems resulted from technical infrastructure…. When I thought in terms of the students, uninterested students tried to play game. However, they had to listen to me as I lectured in the class. They could not play game but they did otherwise since they got bored. It was so bad that the students did not have the program because permanent learning could not occur without revising at their home.

T2…. The problems encountered in the learning environment exhausted us. There was no computer teacher in our school, and also our computers were out of repair and corrupted. I could use computer in my way but I was

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

not capable of solving the technical problem and treating the program. But I had to re-establish Cabri every morning. I coped with the computers that shut off themselves. All these problems occupied my time in the lesson. In the matter of Cabri, since my students met with a new program, the problems encountered resulted from my students. They did not have full knowledge of Cabri and so they made minor mistakes such as deleting all construction. These problems retarded the students’ learning. Nevertheless, the problems reduced when my students got used to the software.

As is seen from the findings, teachers’ views about computer-aided instruction can differentiate in spite of their similar professional and technical competence. Both teachers attending the study got same training and had similar proficiency in the use of computers. The numbers of students differed by type of the school. T2 had an advantage over T1 because T2 had slightly fewer students, but it was stated that computer-aided instruction was more difficult work. The teachers think different about the guide role of them in learning environment. T1 supposed that lecturing with prepared worksheets in advance was easier in terms of being planned lesson. Being guide to students was defined by T1 as waiting to develop their learning after the teacher shows what they would do. On the other hand, T2 indicated that she made so effort in her lesson considering traditional lecturing although she had fewer students and tried to answer the questions of each student. As far as T2 was concerned, guiding to the students was more difficult and laborious task than lecturing directly. It caused teachers to overwork when students were more active in computer-aided platform. Nevertheless, both teachers were pleased with computer-aided instruction for all intents and purposes even tough they were affected negatively by inadequate technical infrastructure of the schools.

DISCUSSION AND RESULTS

In this study, it is aimed to reveal views of the teachers having similar professional and technical competence about performed applications in learning environment enriched with Cabri 3D. It is emerged after performed applications that the teachers consider the study from a different angle whereas they agree in some places. It is thematically clarified the results from similarities and distinctness in teacher views in this section.

Both teachers think that the use of Cabri 3D affects positively to instruction, makes easier students’ learning, activates the students, and enables them to visualize the structures. Kösa, Baki and Karakuş (2008) obtained similar results when in their studies, they found out teacher views related to the usage of three-dimensional geometry software in solid geometry instruction. Kösa, Baki and Karakuş (2008) pointed out that their comprehension would get easy if the teachers instructed via the software in the sections which the students had difficulty in visualizing. Yeşilyurt (2006) stated in his study that teachers agreed with regards to being beneficial to use instructional technology. At the same time, they leaned towards computer-aided instruction. However, the teachers’ views about it differ in some respects. This distinctness results from their point of view to computer-aided instruction. Their viewpoint can take shape to instruction platform. For this reason, it is necessary an ideal classroom platform so that the teachers can lean towards to computer-aided instruction and use this platform in the most correct way.

Both teachers did not have difficulty in classroom management in general although they did not actively lecture in computer-aided platform. This situation can be connected that the numbers of students is available to computer-aided instruction. Nevertheless, it is seen the teachers’ viewpoint about classroom management differ. The teacher tried to make available to silence in the classroom in case that it was given the students their heads in lesson activities and the teacher was passive in the lesson. It was expected that classroom management made easier in this case according to the other case which teacher and students were more active and students asked questions continuously.

The teachers approved teamwork in computer-aided learning environment because by this means, students learned each other and put together their learning by trial and error. Tutak (2008) inferred from in his study that using materials of computer-aided instruction affected positively the students’ attitudes towards geometry. Moreover, he stated that putting into practice with the teamwork developed the sense of

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

responsibility, strengthened solidarity among the students; appreciating fulfilled the study boosted their self- confidence and made them feel sense of achievement.

The teachers agree with positive sides of the study since incorrectness resulted from drawings of the teachers and the students decreases. Indeed, drawing in geometry lesson is a difficult matter for both teachers and students. It was stated by the teacher that Cabri 3D prevented mislearning resulted from wrong drawings. Furthermore, whereas one of the teachers found useful computer-aided instruction in terms of the teacher, the other considered it significant for the students as well as finding tiring it for teacher. This distinctness resulted from the teachers’ viewpoint about computer-aided instruction and the applications which teachers performed during the instruction. The former teacher gave the students all responsibility during computer- aided instruction and so teacher remained passive with regards to leading the students. The other teacher did the opposite. From this point of view, even if the teachers have similar technical competence, their different opinions about the applications can be based on their attitudes and viewpoints, environmental conditions, feasibilities of the school, students’ behaviors and some other factors.

The teachers agreed with negative sides of the study. Both teachers had difficulty in similar technical infrastructures although they were at different locations. Technological incompetence of the schools forced both the teachers in town center and the teachers in village. In both schools, the teachers lost time because of insufficient, out of order and fewer computers, and so instruction was unsatisfactory. Çağıltay and Çakıroğlu (2001) indicated that the most crucial problem of computer-aided learning environment was inadequate materials. These problems could cause to lose the teachers’ desires with the usage of technology. It was revealed by Genç (2010) that these negative thoughts distracted the teachers from using computer in their lesson.

RECOMMENDATIONS

In accordance with the results obtained from this study, it is recommended to prepare computer aided learning environment where they can move comfortably so that teachers can look at the new platform in a positive light. Also it is suggested that the physical conditions of the classroom and some conditions like classroom size must be suitable for computer aided learning environment. Teachers, the most important factor of the learning environment, must get the facts straight for their management of the learning environment efficiently. Teachers who passed similar education levels basically have very different opinions from each other. So this discrepancy is originated from incapable of comprehending the new system sufficiently by either or both the teachers. That’s why; the essence of the subject must be comprehended to the teachers theoretically and practically. It is not only taught to the teachers “how” they will use computers in lessons, but also showed “why” it must be used and “what” the students will gain with this approach by way of pre-service training when they study university. Thus, they can understand the benefits of proper use of dynamic geometry software in their lessons and use it correctly when they become a teacher. In addition, being provided special in-service training activities for teachers is recommended in order to put into practice computer aided instruction and perform their application in this direction.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

BIODATA AND CONTACT ADDRESSES OF AUTHORS

Dr. Temel KÖSA is an Assistant Professor of Mathematics Education at Karadeniz Technical University in Trabzon, Turkey. His areas of interest in research are using technology in mathematics education, spatial ability, geometry education and problem solving.

Assist. Prof. Dr. Temel KÖSA Karadeniz Technical University Fatih Faculty of Education Department of Secondary Science and Mathematics Education 61335 Sogutlu,Trabzon-TURKEY E. Mail: [email protected]

Hilal KALAY is a mathematics teacher at Ministry of National Education since 2012. She was graduated from Karadeniz Technical University as a mathematics teacher. She has not only a master degree but also she is doctoral student in Department of Secondary Science and Mathematics Education of Karadeniz Technical University. She is specifically interested in geometry education, spatial ability and Dynamic Geometry Softwares.

Hilal KALAY Acısu Secondary School Ministry of National Education Akçaabat, Trabzon-TURKEY E. Mail: [email protected]

PREFERENCES

Baki, A. (2001). Bilişim Teknolojisi Işığı Altında Matematik Eğitiminin Değerlendirilmesi, Milli Eğitim Dergisi, 149, 26-31

Baki, A., Kösa, T. ve Karakuş F. (2008). Uzay geometri öğretiminde 3D dinamik geometri yazılımı kullanımı: öğretmen görüşleri. İntenational Educational Technology Conference (IETC), 6-9 Mayıs 2008, Eskişehir, Turkey.

Baki, A., Yalçınkaya, H., Özpınar, İ. ve Uzun, S. (2009). İlköğretim Matematik Öğretmenleri ve Öğretmen Adaylarının Öğretim Teknolojilerine Bakışlarının Karşılaştırılması. Turkish Journal of Computer and Mathematics Education, Vol.1 No.1, 65-83

Can, R.(2010). Cabri Geometri ile Hazırlanan Bir Ders Tasarımının Öğretmen Adaylarının Gelişimine Etkisinin İncelenmesi. Yüksek Lisans Tezi, Marmara Üniversitesi, Eğitim Bilimleri Enstitüsü, İstanbul.

Creswell, J. (2002). Research design: Qualitative, quantitative and mixed method approaches. London: Sage.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 05 ISSN 1309-6249

Çağıltay, K., Çakıroğlu, J., Çağıltay, N. ve Çakıroğlu, E. (2001). Öğretimde Bilgisayar Kullanımına İlişkin Öğretmen Görüşleri, Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 21: 19-28.

Çepni, S. (2009). Araştırma ve proje çalışmalarına giriş. Trabzon: Üçyol Kültür Merkezi.

Genç, G. (2010). Dinamik geometri yazılımı ile 5. sınıf çokgenler ve dörtgenler konularının kavratılması. Yayımlanmamış yüksek lisans tezi, Adnan Menderes Üniversitesi.

Güven, B. ve Karataş, İ. (2002). Dinamik geometri yazılımı Cabri ile geometri öğrenme: öğrenci görüşleri. The Turkish Online Journal of Educational Technology, 2(2), 67-78.

Kutluca, T. ve Zengin, Y. (2011). Ortaöğretim matematik dersinde geogebra kullanımı üzerine öğretmen adaylarının görüşleri. 5th International Computer & Instructional Technologies Symposium, 22-24 September 2011, Fırat University, ELAZIĞ- TURKEY

Tatar, E., Akkaya, A. ve Kağızmanlı, T. (2011). İlköğretim Matematik Öğretmeni Adaylarının geogebra ile Oluşturdukları Materyallerin ve Dinamik Matematik Yazılımı Hakkındaki Görüşlerinin Analizi. Turkish Journal of Computer and Mathematics Education, Vol.2 No.3, 181-197

Tutak, T. (2008). Somut nesneler ve dinamik geometri yazılımı kullanımının öğrencilerin bilişsel öğrenmelerine, tutumlarına ve van Hiele geometri anlama düzeylerine etkisi. Yayımlanmamış doktora tezi, Karadeniz Teknik Üniversitesi. Trabzon.

Tutkun, Ö., Öztürk, B. ve Demirtaş, Z. (2011). Matematik öğretiminde bilgisayar yazılımları ve etkililiği. Journal Of Educatıonal And Instructıonal Studıes In The World, Volume 1 Issue 1 Article 17

Yeşilyurt, E. (2006). Öğretmenlerin Öğretim Araç ve Gereçlerini Kullanma Durumlarını Etkileyen Faktörler. Yayınlanmamış Yüksek Lisans Tezi, Fırat Üniversitesi Sosyal Bilimler Enstitüsü, Elazığ.

Yıldırım, A. ve Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

USING ICE-BREAKERS IN IMPROVING EVERY FACTOR WHICH CONSIDERED IN TESTING LEARNERS SPEAKING ABILITY

Parisa YEGANEHPOUR Ağrı İbrahim Çeçen University Faculty of Science and Letters Department of English Language and Literature Ağrı-TURKEY

Prof.Dr. Mehmet TAKKAÇ Erzurum Atatürk University Kazim Karabakır Faculty of Education Department of English Language Teaching Erzurum- TURKEY

ABSTRACT

The objective of this paper is to demonstrate a suitable integration of ice-breaker activities into upper- intermediate EFL learners to test their speaking ability. Ice-breaking activities require students to practice speaking English as a foreign language in more enjoyable ways and get positive result. However four factors of grammar, pronunciation, fluency and vocabulary are considered simultaneously. The actual classroom research was performed while teaching speaking through ice-breakers to 20-27 year-old-students of the American culture Institution of Erzurum Branch in Turkey in upper-intermediate level. According to the result of factor analysis and information gained from a descriptive analysis of each factor in pre-test and post-test, using ice- breaker activities has a positive effect in improving all four factors, but this effect for pronunciation and fluency is more than the effect for vocabulary and grammar. According to the results the most improved factor is pronunciation and the least improved factor is grammar.

Keywords: Speaking skill, Ice-breakers, Testing speaking, factors, English as a Foreign Language.

INTRODUCTION

Speaking is the most demanding skill among English learners and over the past decades, increasing interest in different aspects of improving speaking ability has triggered a variety of investigations and theoretical discussions that have shed light on improving this ability. Icebrekars will be used in this study to improve speaking ability in adult upper-intermediate EFL learners. Ice breaking means breaking the ice among learners and using ice breakers encourages students to interact all together.

It is the time of internet and information technology, so speaking English has become so important and many EFL instructors and supervisors understand the essence of the speaking process. Learning to speak English fluently is important to most of the students. Thus, there are lots of demands from teachers to help students in

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

developing speaking ability. Using an appropriate ice breaker is important in an English language lesson because it organizes the students for being successful on many different levels.

According to Flanigan (2011), performing ice breaking activities in English class will direct students to the good mood of learning. Also appropriate kind of ice breaking activities will make students sure to get the most from their lesson and also, they will have fun.

This study will highlight different positive dimensions of using ice breaker activities and their effects in improving adult Turkish EFL learners' oral ability. It also will consider positive contributions of ice breakers in fluency, pronunciation, vocabulary and grammar.

There are several empirical studies related to the beneficial effects of effective classroom activities on language acquisition (Busch, 1982; Day, 1984; Ely, 1986; Spada, 1986; Ellis, 1993; Pica, Lincoln- Porter, Paninos, and Linnell, 1996) and all of them proved the existence of a definite direct relationship between language learning and activities which result in successful oral interactions. Elly (1986) also, confirmed the direct relation between class participation and oral correctness. A major problem that language teachers face in the classroom is the difficulty in encouraging students to join the conversation (Beeb, 1983; White and Lightbown, 1984; Katz, 1996; Tsui, 1996). Research studies that have been done (Satto, 1982; Pica, Young, and Daughty, 1987; Chaudron, 1988; Tomizawa, 1990; Song, 1994; Flowerdew and Miller, 1995) pointed out that the problem of students’ reticence in East Asian countries was more serious than their western counterparts. John and Hymes (1972), Sato (1982) confirmed cultural parameters as a factor in students’ passiveness. Peregoy and Boyle (2001) by considering these problems stated that speaking like the other language skills has the same importance. They said that despite traditional methods that each skill was taught separately, now all four skills (reading, writing, speaking and listening) appear simultaneously in every English class and EFL context.

Shumin (1997) explained that knowing grammar and vocabulary of a language is not enough for being able to speak that language. He claimed that language acquisition will be possible if learners interact with each other in a class environment. However, English has limited use in learners' real life and, it is difficult for them to speak English in the classroom appropriately. So, it is the task of language teachers to persuade students to use English for social interaction in classroom. For creating motivation in EFL context, teacher should maintain different kinds of strategies and activities for attracting students' attention and making them interested in the lesson. By this way, s/he can support and help language learners. Krashen and Terrel (as cited in Lightbown & Spada, 1999) mentioned that through interaction, students will be able to make their own easy and meaningful conversation. Then, communication and interaction lead students to use the language instead of focusing and talking about its grammar.

Celce-Murcia (2001) stated that activities must be student-centered and communication should be authentic, that means students must do an activity because it is interesting for them, not because teacher asks them to do. In addition, Peck (1978) summarized some factors that teachers must take into consideration. When the teacher chooses the communication activities, s/he must focus on meaning, collaboration and social interaction. An effective teacher encourages students to speak English inside and outside of the classroom.

Krashen and Terrel (1983) emphasized that rather than teaching and talking about the structure of language, we should focus on language use. Therefore, topics and activities in the classroom should capture students’ attention and encourage them for making meaning and more interaction with each other. Brown (1994) confirmed that if interaction strategies play important role in intrinsic motivation of students and when they are closely connected to students’ goals and interests, they would have a positive effect on students' speaking ability.

Evaluation of Speaking Researchers (Burns & Joyce, 1997; Kayi, 2006; Richards & Renandya, 2002) believe that speaking is an interactive process of making meaning and, for speaking successfully, learner must be successful in linguistic and sociolinguistic competence. Henning (1987), Brown (2004), Farhadi (2003), Kitao and Kitao (1996), Spolsky

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

(1992), Nambiar and Goon (1993), Upshur and Turner (1995), Messerklinger (1997), and MacGregor (2000) said that assessing oral ability of learners' is difficult and time-consuming. They also agreed that reliability of subjective measure is very low. They all considered grammar, pronunciation, fluency, and vocabulary as evaluation scale.

Another group of researchers Harris (1997), Rolheiser and Ross (1998), Brindley &Scoffield (1989), Saito (2003), Nunan (1988), Benson (2001), Rolheiser and Ross (1998), Blue (1994), Coombe and Canning (2002), Cassidy (2007), Chamot and O’Malley (1994), Bachman and Palmer, (1989), Ariafar and Fatemipour (2013), thought that this formal kind of assessment is traditional and students cannot monitor their progress critically, so they suggested that learners' self-assessment is much better than that kind of linguistic assessment. Learners will be trained for self-assessment for this condition. This kind of assessment is carried out by learners. When students are able to assess themselves accurately then, they would be able to inform teachers about their own needs. Figure 1 was adopted from Rolheiser and Ross (1998) theory about self-assessment.

Figure 1: How Self-Evaluation Contributes to Learning

According to Rolheiser and Ross' (1998) theoretical model, students set higher goals and as a result commit more personal efforts. Blue (1994) believed that when learners would like more independence and autonomous learning, then they will be interested in self-assessment.

Another kind of assessment which was considered by some researchers is peer-assessment (Johnson & Rose, 1997; O’Malley & Pierce, 1996; Brown, 1998; Yurdabakan, 2011; Anderson, 1998; Yoshida, 2001; Stefanakis, 2002). In this kind of assessment, students judge the language performance of other student or students. All mentioned researchers agree that the most important advantage of this assessments is that students learn to

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

collaborate with each other. Anderson (1998) said that providing different perspectives for students is the most striking advantage of peer-assessment. Brown (1998), Johnson & Rose (1997), O’Malley & Pierce (1996), and Özdemir (2012) pointed out that peer-assessment causes development of metacognitive abilities, communication skills, student's confidence, and collaborative environment. O’Malley and Pierce (1996), and Yoshida (2001) claimed that application of this method also will create some problems such as unreliability and subjectivity. But, teachers should set criteria with students so that they could be more involved in activities. According to Stefanakis (2002), teachers must draw students' attention in multiple intelligence. Then students by promoting collaboration between themselves will be able to understand potential differences among themselves. Yurdabakan (2011) also noted a very important point. He said that students for doing peer- judgment at first must be able to do self-judgment.

In this study the researcher used formal assessment and sample IELTS test questions were used, but, it does not mean that she does not agree with other kinds of assessment.

METHODOLOGY

This study aimed at answering the following questions: 1. What factors can be considered in testing speaking ability of EFL learners? 2. What is the effect of using ice-breakers in improving every factor, vocabulary, grammar, pronunciation and fluency that considered in testing learners' speaking ability?

Since real random selection of the subjects is impossible, the researcher made use of intact groups based on the results of students' previous general English test scores. Therefore, the design which can fit this research is the quasi-experimental design, besides pre-test and post-test pattern.

In the current study, ice breakers are independent variables and speaking is the dependent variable. Thus, the ice breakers' effectiveness, the amount of improvement, factors that can be considered in testing speaking ability, and effect of using icebreakers in each factor will be analyzed quantitatively by data analysis of pre-test and post-test.

Setting and Participants After administering the sample speaking IELTS test, on the basis of the result, 100 students, whose homogeneity was confirmed-were selected and considered as the experimental group. Coming from different departments such as Science, History, Literature, Computer Science and Civil Engineering, this group would attend English classes two times a week throughout the semester (about 18 sessions, 3 hours each session).

As it was mentioned earlier, there is a two fold purpose that will promote the present study. The main reason of this study is (a) to investigate factors that are considered in testing speaking (b) to study the effect of using ice-breakers in improving every factor; vocabulary, grammar, pronunciation, and fluency. Data for this study was obtained from pre-test and post-test. Then in order to do statistical analysis, the Lizrel software was used.

Scoring Technique The sample IELTS speaking test was given to the students to analyze their abilities on pronunciation, grammar, vocabulary, and fluency. Analytical scoring of speaking which was based on “Language Assessment: Principles and Classroom Practices”, (Brown, 2004) can be seen in table 1.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

Table 1: Language Assessment Aspects score Description Vocabulary 1 Speaking vocabulary inadequate to express anything but the most elementary needs. 2 Has speaking vocabulary sufficient to express him/ herself simply with some circumlocutions. 3 Able to speak language with sufficient vocabulary. 4 Can understand and participate with a high degree of precision of vocabulary. 5 Speech on all levels is fully accepted.

Grammar 1 Errors in grammar are frequent but can be understood 2 Can usually handle elementary construction quite accurately but does not have through or confident control of grammar 3 Control of grammar is good 4 Able to use language accurately and errors in grammar are quite rare. 5 Equivalent.

Pronunciation 1 Errors in pronunciation are frequent but can be understood.

2 Accent is intelligible though often quite faulty. 3 Errors never interfere with understanding and rarely disturb. 4 Errors in pronunciation are rare. 5 Equivalent to and fully accepted. Fluency 1 No specific fluency description. 2 Can handle with confidence but not with social situation. 3 Rarely has to group words. 4 Able to use the language fluently on all levels. 5 Has complete fluency in the language. Analytical scoring of speaking has four items and per item scores 5. So, the final maximum score can be 100.

Data Analysis The first class of data in this research comprised of one group of scores which were got from l00 learners who took part in the study. These scores showed their general English proficiency level and were used for calculating homogeneity of data. Second set of data comprised of a group of scores which showed speaking ability of learners. In order to do statistical analysis, the researcher used the LIZREL statistical software. Scores of pre-test exposed that students in the experimental group statistically were almost in the same level and they had homogenous English speaking proficiency.

Then paired t-test showed the correlation between four factors considered in testing speaking ability (vocabulary, grammar, pronunciation, and fluency).

Homogeneity Test Homogeneity test is a test for equality of variances and in LIZREL it can be measured by Levene's test. Löfgren (2013), pointed out that equality of variances can be computed for parametric and nonparametric statistical methods: Analysis of variance, ANOVA can be used for a parametric method and, Kruskal-Wallis one-way analysis can be used for a nonparametric method.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

Data of this study are normally distributed, therefore parametric Levene's test was applied for testing equality of variances.

In LIZREL, the parametric Levene's test (for normally distributed data) is built into the ANOVA procedure. So, the researcher ran the ANOVA. Tables, 2 and 3 show the results of one way ANOVA test.

Table 2: Oneway: Test of Homogeneity of Variance between Learners PREVIOUS TEST SCORE Levene Statistic df1 df2 Sig. .790 1 98 .376

Table 3: ANOVA: Previous Test Scores of Learners Sum of Squares Df Mean Square F Sig. Between Learners 67.240 1 67.240 1.362 .246

According to the parametric Levene's test, there must be an equality of variance. In this case, if the p-value was below 0.05, we could say that there is not equality of variances between learners, but according to Table 3, the p-value or sig is 0.246> 0.05. So, there is equality of variances between learners. As a result, a Levene's test verified the equality of variances in the samples of this study (homogeneity of variance) (p>0.05) (Martin and Bridgmon, 2012).

Factor Analysis: Vocabulary, Grammar, Pronunciation, and Fluency For measuring speaking ability, different factors have been considered by different researchers, but as test questions in this study were chosen from sample IELTS speaking test questions, the researcher applied four factors of vocabulary, grammar, pronunciation, and fluency for scoring which was based on “Language Assessment: Principles and Classroom Practices”, (Brown, 2004).

In this part, researcher used paired sample t-test to measure the effect of using ice-breakers on each factor, before and after treatment. It is used to detect the difference between four dependent variables. So, Table .4, shows the correlation of each factor for experimental group in pre-test and post-test.

Table 4: Paired Samples Statistics: Difference between Four Dependent Variables Mean N Std. Deviation Std. Error Mean Pre-test-vocabulary 10.7000 100 2.02283 .28607 Pair 1 Post-test-vocabulary 16.6000 100 2.35606 .33320 Pre-test-grammar 12.3000 100 2.51729 .35600 Pair 2 Post-test-grammar 16.8000 100 2.42437 .34286 Pre-test-pronunciation 11.9000 100 2.45157 .34670 Pair 3 Post-test-pronunciation 20.0000 100 3.35030 .47380 Pre-test-fluency 9.8000 100 2.66497 .37688 Pair 4 Post-test-fluency 17.7000 100 3.06561 .43354 Pre-test 44.7000 100 6.88165 .97321 Pair 5 Post-tests 71.1000 100 7.51122 1.06225

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

Table 5: Paired Samples Test of Four Dependent Variables Paired Differences t df Sig. (2- Mean Std. Std. Error 95% Confidence tailed) Deviation Mean Interval of the Difference Lower Upper Pre-test-vocabulary-post- Pair 1 -5.90000 3.45378 .48844 -6.88155 -4.91845 -12.079 49 .000 test-vocabulary Pre-test-grammar-post- Pair 2 -4.50000 1.82108 .25754 -5.01754 -3.98246 -17.473 49 .000 test-grammar Pre-test- pronunciation - Pair 3 -8.10000 2.65153 .37498 -8.85356 -7.34644 -21.601 49 .000 post-test-pronunciation Pre-test- fluency -post- Pair 4 -7.90000 2.49285 .35254 -8.60846 -7.19154 -22.409 49 .000 test-fluency Pair 5 Pre-test-post-test -26.40000 5.89361 .83348 -28.07495 -24.72505 -31.674 49 .000

According to the result of mean scores on Table 4. and 5., using ice-breaker activities had positive effect in improving all four factors, but the amount of improved scores for pronunciation and fluency were more than vocabulary and grammar. According to the results the most improved factor was pronunciation and the less improved factor was grammar. Vocabulary mean= 5.90 Grammar mean= 4.50 Pronunciation mean= 8.1 Fluency mean= 7.9

The results of paired sample t-test were significant; p<0.05, and Vocabulary: t=-12.079, df=49, p=.000 Grammar: t=-17.473, df=49, p=.000 Pronunciation: t=-21.601, df=49, p=.000 Fluency: t=-22.409, df=49, p=.000

According to the above mentioned statistical information, it could be concluded that there is significant increase in all four factors of experimental groups' post-test scores. So, in this part again, the positive effect of using ice-breaker activities in improving upper-intermediate level students' speaking ability was proved.

DISCUSSION AND CONCLUSION

There have been a few studies in Turkey about the effect of some kinds of ice- breakers on learning skills of children. But, there has been no research done, at least in Turkey, to examine the effect of ice-breaker activities on EFL adult learners. The reason, maybe, is related to teachers' or students' character and/or teaching or other local restrictions.

The main objective of this research was to learn the effect of ice-breaking activities on four factors, i.e. vocabulary, grammar, pronunciation, and fluency. To verify this and to answer the submitted research questions, participants, after homogenization, were selected and ice-breaker activities were applied in the group during the semester. The results indicated considerable difference between the mean scores of the participants in pre-test and post-test. So, according to the results, performance and the amount of improvement of speaking ability of students are better and it may answer the research questions positively.

According to the result of factor analysis and information gained from a descriptive analysis of each factor in pre-test and post-test, using ice-breaker activities had a positive effect in improving all four factors, but this 64 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

effect for pronunciation and fluency was more than the effect for vocabulary and grammar. According to the results the most improved factor was pronunciation and the least improved factor was grammar.

According to the results of this study, it can be put in forward that using ice-breakers facilitates the communication among learners and is a good way for skipping from language barriers. As a communication strategy use of ice-breakers makes oral communication among students more easily and by suppressing the problem of linguistic knowledge of silent learners supports their attention and develops the communication among them.

BIODATA AND CONTACT ADDRESSES OF AUTHORS

Dr. Parisa YEGANEHOUR completed her BA studies on English Language Translation and her MA on English Language Teaching in Iran. She also completed her PhD on English Language Teaching in Turkey. She, currently has employed as a teaching assistant in Ağrı İbrahim Çeçen University, Faculty of Science and Letters, Department of English Language and Literature. She is specially interested in different methods of teaching and learning language.

Dr.Parisa YEGANEHPOUR Ağrı İbrahim Çeçen University Faculty of Science and Letters Department of English Language and Literature 04100, Ağrı-TURKEY E. Mail: [email protected]

Prof. Dr. Mehmet TAKKAÇ is currently vice chanceller in Erzurum Atatürk University. He has his PhD, MA, and BA on English Literature and Language Department. He also,had been the chairman of ELT Department of Atatürk University since 2007. He had been the manager of School of Foreign Languages of the same university since 2008. His main interests are language teaching and learning, applied linguistics and drama.

Prof.Dr. Mehmet TAKKAÇ Erzurum Atatürk University Kazim Karabakır Faculty of Education Department of English Language Teaching Erzurum-Turkey E. Mail: [email protected]

REFERENCES Anderson, S. R. (1998). Why talk about different ways to grade? The shift from traditional assessment to alternative assessment. New Directions for Teaching and Learning, 74, 10.1002/tl.7401.

Ariafar, M., & Fatemipour, H.R. (2013). The effect of self- assessment on Iranian EFL learners' speaking skill. Applied Linguistics & English Literature. 2(4). Retrieved May30, 2015 from www.ijalel.org/pdf/287.pdf.

Bachman, L., & Palmer, A. S. (1989). The construct validation of self-ratings of communicative language ability. Language Testing, 6, 14-25.

Beebe, L. (1983). Risk-taking and the language learner. In H. Seliger & M.H. Long, (Eds), Classroom oriented research in second language acquisition. Rowely, MA: Newbury House. 65 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

Benson, P. (2001). Teaching and Researching Autonomy in Language Learning. London: Longman.

Blue, G. M. (1994). Self-assessment of foreign language skills: Does it work? CLE Working Papers, 3, 18-35. Retrieved Aug 23, 2014 from http://www.eric.ed.gov.

Brindley, C., & Scoffield, S. (1998). Peer assessment in undergraduate programs. Teaching in Higher Education, 3(1), 79-89.

Brown, H. D. (1994). Teaching by principles. New Jersey: Prentice Hall.

Brown, J. D. (1998). New ways of classroom assessment. Bloomington, Illinois, USA: TESOL.

Brown, H. D. (2004). Language assessment: principles and classroom practices. New York: Pearson Education.

Burns, A., & Joyce, H. (1997). Focus on speaking. North Ryde, N.S.W.: National Center for English Language Teaching and Research.

Busch, D. (1982). Introversion-extroversion and the ESL proficiency of Japanese students. Language Learning, 32, 109-132.

Cassidy, S. (2007). Assessing “inexperienced” students’ ability to self-assess: Exploring links with learning style and academic personal control. Assessment and Evaluation in Higher Education, 32(3), 313–330.

Chamot, A.U., & O’ Malley, J. M. (1994). The CALLA handbook: Implementing the Cognitive Academic Language Learning Approach. White Plains, NY: Addison Wesley Longman.

Chaudron, C. (1988). Second language classroom: Research on teaching and learning. New York: Cambridge University Press.

Coombe, C., & Canning C. (2002). Using self-assessment in the classroom: Rationale and suggested techniques. Karen’s Linguistics Issues. Retrieved November 28, 2014, from http://www3.telus.net/linguisticsissues/selfassess2.html.

Day, R. (1984). Student participation in the ESL classroom or some imperfections in practice. Language Learning. 34, 69-100. Retrieved on 12 june, 2014 from links. jstor.org/sici?sici=00398322(198006)14:2<175:TCDOLP>2.0.CO;2-Z

Eliss, R. (1993). Japanese students abroad: Relating language ability in class and in the community. Thought Current in English Literature.

Ely, C. (1986). An analysis of discomfort, risk-taking, sociability and motivation in the second language classroom. Language Learning, 36, 1-25.

Farhady, H. (2003). Classroom Assessment: A Plea for Change. Paper presented at the 2nd conference on issues in English language teaching in Iran, Tehran, Iran. Retrieved July 3rd, 2014, from http://65.54.113.26/Publication/6146097/classroom-assessment-a-plea- for-change

Flanigan, E. (2011). The importance of warm up activities in English class. Retrieved May 24, 2014 from http://www.ehow.com

Flowerdew, J., & Miller, L. (1995). On the notion of culture in L2 lectures. TESOL Quarterly , 29(2), 345-373.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

Harris, M. (1997). Self-assessment of language learning in formal settings. ELT Journal, 51(1), 12-20.

Henning, G. (1987). A guide to language testing: Development, evaluation, research. Boston: Heinle & Heinle Publishers.

Johnson, N. J., & Rose, L. M. (1997). Portfolios: Clarifying, constructing and enhancing. Pennsylvannia: Technomic Publishing Company.

Katz, A. (1996). Teaching style: A way to understand instruction in language classrooms. In K. M. Bailey, & D. Nunan, (Eds.), Voices from the Language Classroom (pp. 145-167). New York: Cambridge University.

Kayi, H. (2006). Teaching speaking: Activities to promote speaking in a second language, The Internet TESL Journal, Vo. XII, No. 11. Retrieved June 15, 2014 from http://iteslj.org/Articles/Kayi-Teaching Speaking.html.

Kitao, K.S., & Kitao, K. (1996). Testing Speaking. (ERIC Document Reproduction Service No: ED 398261).

Krashen, S.D. & Terrell, T. (1983). The Natural Approach. New York: Pergamon.

Lightbown, P. & Spada, N. (1999). How language are learned. Oxford: Oxford University Press.

Löfgren, K. (2013). Normality test using SPSS: How to check whether data are normally distributed. Retrieved February 12, 2014, from https://www.youtube.com/watch?v=IiedOyglLn0.

MacGregor, D. (2000). Second language proficiency assessment. Retrieved from: www.cal.org/resources/archive/rgos/assessment.html.

Martin, W. E., & Bridgmon, K. D. (2012). Quantitative and Statistical Research Methods: From Hypothesis to Results. somerset, NJ: Wiley.

Messerklinger, J. (1997). Evaluating oral ability. The Language Teacher Online. Retrieved 14 June, 2014 from http://www.jalt-publications.org/

Murcia,C.(2001). Teaching English as a second or foreign language. Boston: Heinle & Heinle.

Nambiar, M. K., & Goon, C. (1993). Assessment of oral skills: A comparison of scores obtained through audio recording to those obtained through face-to-face evaluation, RELC Journal, 24 (1), 15-31.

Nunan, D. (1988). The Learner-centered Curriculum: A Study in Second Language Teaching. Cambridge: Cambridge University Press.

O' Malley, M., & Pierce, L. V. (1996). Authentic assessment for English language learners: Practical approaches for teachers. USA: Addison- Wesley.

Özdemir, S. (2012). Speaking portfolios as an alternative way of assessment in an EFL context. Retrieved June 8, 2014 from www.thesis.bilkent.edu.tr/0006043.pdf

Peck, S. (1978). Developing Children’s Listening and Speaking in ESL. In C. Murcia, (Ed). Teaching English as a second or foreign language. (3rd ed). (Pp. 139-149). Boston: Heinle & Heinle.

Peregoy, S. & Boyle, O. (2001). Reading, writing and learning in ESL: A resource book for K-12 teachers. New York: Longman.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 06 ISSN 1309-6249

Pica, T., Young, R., & Doughty, C. (1987). The impact of interaction on comprehension. TESOL Quaterly, 21, 37- 58.

Pica, T., Lincoln, P,F., Paninos, D., & Linnell, J. (1996). Language learners' interaction: How does it address the input, output, and feedback needs of L2 learners? TESOL Quarterly, 30, 1, 59-48.

Richards, J., & Renandya, W. (2002). Methodology in language teaching. Cambridge: Cambridge University Press.

Saito, Y. (2003). The use of self-assessment in second language assessment. Working paper in TESOL and Applied Linguistics (Online). Retrieved August 2nd, 2014, from http://www.tc.columbia.edu/academic/tesol/WJFiles/pdf/Saito_Forum .pdf.

Satto, C. (1982). Ethnic styles in classroom discourse. In M. Hines, and W. Rutherford, (Eds.), TESOL. 81( pp.11- 24). Washington, DC; TESOL.

Shumin K. (1997). Factors to consider: Developing adult EFL students’ speaking abilities. English Teaching Forum 25(3). Retrieved May 29, 2014 from http://exchanges.state.gov/forum/vols/vol35/no3/p8.html.

Song, M. J. (1994). Ethnic background and classroom participation: A study in adult intermediate ESL classes. Language research, 30(2), 435-448.

Spada, N. (1986). The interaction between types of contact and types of instruction: Some effects on the second language proficiency of adult learners. SSLA, 181-199.

Spolsky, B. (1992). Diagnostic testing revisited. In E. Shohamy, & R.A. Walton, (Eds.), "Language assessment and feedback: Testing and other strategies" (p.29-39). National Foreign Language Center. Dubuque, IA: Kendall/Hunt Publishing Co.

Stefanakis, E. H. (2002). Multiple intelligences and portfolios. USA: Heinemann.

Tomizawa, S. (1990). Psychological and social-cultural factors affecting the Japanese adult ESL learners' inactiveness in oral interaction in English. Dissertation Abstracts International, 51, A2669.

Tsui, B. M. (1996). Reticence and anxiety in second language learning. In Bailey, K. M. & Nunan, D. (Eds.), Voices from the language classroom (pp. 145- 167). New York: Cambridge University.

Upshur, J.A., & Turner, C.E. (1995) Constructing rating scales for second language tests. ELT Journal, 49 (1), 3- 12.

White, J., & Lightbown, P. (1984). Asking and answering in ESL classes. The Canadian Modern Language Review, 40(2), 228-244.

Yoshida, Y. (2001). Authentic Progress Assessment of Oral Language: Oral Portfolios. Retrieved November, 18, 2014 from http://eric.ed.gov/PDFS/ED453674.pdf.

Yurdabakan, İ. (2011). The view of constructivist theory on assessment: Alternative assessment methods in education. Ankara University, Journal of Faculty of Educational Sciences, 44(1), 51-57.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 07 ISSN 1309-6249

A MODEL PROPOSAL FOR THE IMPROVEMENT OF INTERNSHIP ACTIVITY IN OFFERING GASTRONOMY EDUCATION PROGRAMS AT THE HIGHER EDUCATION INSTITUTIONS

Assist Prof. Dr. Mehmet SARIOĞLAN Balıkesir University Balıkesir- TURKEY

ABSTRACT

Recently, gastronomy education has begun to take its place in international literature within educational sciences and as a major type of education notably has been living a development process. Even in the case that the most important reason for the failure to gain Professional training as gastronomy, absolutely the acquisition of basic gastronomy education attainment is factoran indispensable for an effective and quality of life. But, gastronomy education qualitative and quantitative of qualificationon the increase is designed different researchareas. One of thet his research is gastronomic Professional training internship phenomenon. In this study, the effectiveness of internship phenomen on which is an important part of offering gastronomy education programs at higher education institutions in Turkey, has been measured by a quantitative study. As a result of study, different problem shave been identified during the internship. Also in consequence of literature survey, obtained data showed paralellisim with previous study. The result of the study, a model proposal is improved for solving the problems and gearing up effectiveness of internship.

Keywords: Gastronomy Education, Internship in Gastronomy Education.

INTRODUCTION

We can say clearly ; the countries which are dominant in the world have strong economies from past to present. The reason for this ; it is proceed from integrating the education which is required to train qualified work force, especially undertaken role of vocational technical education with the technologhy of 21th century. Vocational education to be given individuals so as to be qualified; it needs to be used as a process which helps them improve their talents ambidextrously by the means of considering business as an aim and grooming them to work. The foremost task of Vocational Education Foundations is to train students productively in terms of both theoritical and practical. In this context ; Internships are quite important that enables business spaces to students in order to make their learnings improved and strenghtened which are gained in schools as theoritically (Dionisius et al., 2008; Fersterer et al., 2008; Ryan et al., 2007).

Gained experiences during internship is a significant fact upon moving thoughts to another areas of students after graduation. Likewise Internships is a period which students make contact with their working area for the first time in the future. On the other hand Internship reveals its supportive role by habituating students to sectors fractionally with the aim of reaching specified purposes in education.Besides internship, brings valuable informations such as recognizing the issues about working life and dealing with them, making good contacts with coworkers and superiors, identfying guests, reconing their expectations and how to make healthy communications with them (Parey, 2009; Zwick, 2007; Beckmann, 2002; Mohrenweiser&Backes-Gellner, 2010). Internship education; due to being an adaptation process in the matter of converting theoritical knowledge to practical knowledge, elapsed times during internships can be described as an significant processes that grooms potential personells to future businesses within education terms. The whole conducted researchs relating internships remarks the crucial advantages with regards to improve skills of problem solving, gaining experience, getting to know working life. In the direction of obtained datas, the internship phenomenon can be described as that students who have theoritical vocational knowledge using their academical knowledges in real life, in other words; converting acquired knowledges to behaviour by learning through experience. Internship is a conducted activity in an attempt to gain experience and implement educations related to field of 69 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 07 ISSN 1309-6249

and art or an occupation. As it is understood from the definition, Internship is a significant phase for the business life of individuals because they are the conducive working area which helps individuals to have preunderstandings for future businesses (Dustmann&Schönberg, 2007Smits, 2006; Hofer&Lietz, 2004).

Internship; can be expressed as a remarkable entire education process that includes understanding how to apply the acquired knowledge from theorotical lessons in practice and adapting to working life (Hays, Rardin, Jarvis, Taylor, Moormsan & Armstead, 2002; Narayan, Olk & Fukami, 2010). Stated in other words; Internship is a period that interns who receive theorotical education spend time by working temporarily at one or more than one departments of Institutions in an attempt to increase their practical knowledge in business life (Petrillose & Montgomery, 1997; Studer, 2015). Interns can obtain information at first hand during their internship and carreer oppurtunities can be provided in the meantime of educational process (Riva & Erickson, 2008). Internship has an essential role for interns to see working conditions and their carreer developments. By the means of supporting theorotical features with practical training; provides interns bunch of advantages consisting of occuppational environment (Korthagen, Loughran & Russell,2006; Masters, France & Thorn, 2009; Patel, 2015).

Internship education which helps to gain the real life and business experiences where information, skill and experiences that students acquire in academical environment has taken place in the media of production and service delivery by converting to practical training has been taken from different aspects by gastronomical education system (Ko & Chung, 2015; Cullen, 2010; Cullen, 2012). Internship is a fact that constitutes a significant phase of the occupational gastronomy education and because of the vocational features, it has to be evaluated in multidimensial approach. Just because Tourism sector has dynamical pattern; either the education in that field is required to be the same. In other saying, the gastronomical education has to be not only theorotical but also practical to be successful (Hegarty,2014; Hyun-Ju, Kyoung-Sook, & Yu-Kyeong, 2006).

The main goal of the gastronomy education is to gain experiences about the programmes which interns have been trained on, searching out the daily applications at catering enterprises, gaining experiences for their carreers by applying their talents and learnings in different methods (Ruhanen, Breakery & Robinson, 2012;Yu & Pang, 2007; Cullen, 2010). Interns must be equipped with practical skills and learnings during their each stage of gastronomy training, and regardless of how and which part of stage it is used on, internship is a significant educational method in the sense of theory and practice must be carried out obligatorily from part to whole (Bourelle, 2015; Cullen, 2014).

Model Proposal for Increasing the Efficiency of Training Case for Education of Gastronomy in Higher Education Institutions

Strategical action plan has been made up aimed at increasing the effectiveness of internship that is an indispensable key fact of gastronomy programmes which exist within the structure of Higher Education Institutions in Turkey. This action plan consists of three stages and the most important feature is to be an applicable method. It has been predicted that if the method is applied in an effective way, it would maximize the efficiency of the gastronomical education.

Stage-I: Collaboration between Relevant Higher Education Institution amd Culture / Tourism Ministry; Gastronomical education programmes within Higher Education Institutions i.e Universities, in order that enhancing the effectiveness of internship of gastronomy educational programmes within universities, before educational internship activities commence; collaboration protocol with the Culture and Tourism Ministry is required to be realize in all conscience. This protocol supposed to focus on subjects such as referring interns who will receive internship training in near future to enterprises, analysis of the need for he qualified personnel in enterprises, the general scope of internship, rules and requirements of the internship. In case of providing cooperation within the frame of this protocol; positioning the internship training fact in a legal form will be provided. By this way; the effectiveness of the internship training should have been able to groww by means of enterprises and interns realize their responsibilities and competencies.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 07 ISSN 1309-6249

Stage-II: A Seperate Allocation of Fund for the Internship; Interns who take educational gastronomy programme, receive low wages in exchange for working at enterprises; as a consequence of that it affects adversely both enterprise’s financial position and intern’s motivations. In order to obviate this situation, The Government should assist them with subsistence wages. In case the Government assistance is provided to them in exchange for the internship training, it would increase both the financial means of enterprises and the intern’s motivation. Thus; the activities of internship training will reach to a level of intended conditions.

Stage-III: Analysis Of The Achievements In Internship Completion; There is no control mechanism to measure the achievements of the internship at the end of the programme. Since the control mechanism would be formed effectively, the internship control mechanism would be formed effectively, the internship exams just as ordinary lectures must be regulated to interns immediatly afterwards their internship programme in the very beginning of the academic year. Students who fail to pass the exam have to repeat the internship programme. Thus; students who are conscious of being subjected to an exam with their achievements during internship programme, interns would likely take part in various training activities.

RESULT AND SUGGESTION

Together with an extensive literature search; it has been concluded that internship is the most significant factor in order to improve the efficiency of gastronomical education. As a result; three staged model proposal has been developed concerning how as it should be so that improving and sustaining the efficiency of gastronomical education. Relevant Higher Education and Central Organization Institutions, Cultural/Tourism Ministry should have to make legislative regulations so as to employ this method.

As a result of this study constitute proposal of model has applicable feature. If this studies proposal accept and applicable, it will estimated that internship student increase qualification. From now on studies must be internship for different kitchen department as well as content.

IJONTE’s Note: This article was presented at 4th World Conference on Educational and Instructional Studies - WCEIS, 5-7 November, 2015, Antalya-Turkey and was selected for publication for Volume 7 Number 1 of IJONTE 2016 by IJONTE Scientific Committee.

BIODATA AND CONTACT ADDRESS OF AUTHOR

Mehmet SARIOĞLAN is a assistant professor (PhD) at Tourism Faculty at Balıkesir University in Turkey. He graduated from the department of Hospitality Management at Balıkesir University in 2004. He gets her M.S degree in 2007 at the department of Tourism & Hospitality Management and PhD degree in 2011 at the department of Tourism & Hospitality Management. He is interested with food&beverage management, gastronomy, gastronomy tourism and gastronomy education.

Mehmet SARIOĞLAN Balıkesir University Tourism Faculty Gastronomy and Kitchen Arts Department Balıkesir- TURKEY E. Mail: [email protected]

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 07 ISSN 1309-6249

REFERENCES

Beckmann, M. (2002). Firm-Sponsored Apprenticeship Training in Germany: Empirical Evidence from Establishment Data, Labour, 16(2), 287-310.

Bourelle, T. (2015). Writing in the Professions An Internship for Interdisciplinary Students, Business and Professional Communication Quarterly, 7 (1).

Cullen, F. (2014). Culinary Internship and the European Mobility Action Plan: Part One, School of Culinary Arts and Food Technology.

Cullen, F. (2012). An Investigation in Culinary Life and Professional Identity in Practice during Internship, School of Culinary Arts and Food Technology.

Cullen, F. (2010). Phenomenologıcal Vıews’ And Analysıs Of The Student ‘Self’ Usıng Mıxed Methods Research To Investıgate The Nuances Of Culınary Academıc Issues Related To Students On Internatıonal Internship, 4th International Technology, Education and Development Conference (8-10 March 2010-Spain), INTED2010 Proceedings, 4899-4907.

Cullen, F. (2010). Phenomenological Views and Analysis of Culinary Arts Students' International Internships: “The Educational Psychology and Nature of Being” Before, During, and After International Culinary Internship, Journal of Culinary Science & Technology, 8 (2), 106-126.

Dionisius, R., Muehlemann, S. Pfeifer, H. Walden, G. Wnzelmann, F. Wolter, S. (2008). Cost and Benefit of Apprenticeship Training-A Comprison of Germany and Switzerland, Social Science Research Network.

Dustman, C. Schönberg, U. (2007). Apprenticeship Training and Commitment to Training Provision, The Swiss Leading House on Economics of Education, Firm Behavior and Training Policies is a Research Programme of the Swiss Federal Office for Professional Education and Technology (OPET).

Fersterer, J. Pischke, J-S. Winter-Ebmer, R. (2008). Returns to Apprenticeship Trainin in Austria: Evidence Form Failed Firms, The Scandinavian Journal of Economics, 110 (4), 733-753.

Göggel, K. Zwick T. (2012). Heterogeneous Wage Effects of Apprenticeship Training, The Scandinavian Journal of Economics, 114(3), 756-779.

Hays, Kimberly A., Rardin, David K.; Jarvis, Paul A.; Taylor, Nicole M.; Moorman, Annorah S. & Armstead Catherine D. (2002). An Exploratory Survey On Empirically Supported Treatments: Implications For İnternship Training, Professional Psychology: Research and Practice, 33(2), 207-211.

Hegarty, J.A. (2014). Standing The Heat-Assuring Curriculum Quality in Culinary Arts and Gastronomy, Routledge Taylor&Francis Group, Newyork.

Hofer, H. Liets, C. (2004). Labour Market Effects of Apprenticeship Training in Austria, International Journal of Manpower, 25(1), 104-122.

Hyun-Ju, H., Kyoung-Sook, H. & Yu-Kyeong, C. (2006). The Effects of Internship Program Satisfaction on the Career Decisions of Culinary Major Students, Korean Journal of Food And Cookery Science, 22(5), 702-711.

Ko, W.H. & Chung, F.M. (2015). Learning satisfaction for culinary students: The effect of teaching quality and professional experience, International Journal of Vocational and Technical Education, 7 (1), 1-13. 72 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 07 ISSN 1309-6249

Korthagen, F., Loughran, J. & Russell, T. (2006). Developing Fundamental Principles For Teacher Education Programs And Practices, Teaching and Teacher Education, 22(8), 1020-1041.

Masters, Kevin S.; France, Christopher R. & Thorn, Beverly E. (2009). Enhancing Preparation Among Entry-Level Clinical Health Psychologists: Recommendations For “Best Practices” From The First Meeting Of The Council Of Clinical Health Psychology Training Programs (CCHPTP), Training and Education in Professional Psychology, 3(4), 193-201.

Mohrenweiser, J. Backes-Gellner, U. (2010). Apprenticeship Training: For Investment or Substitution? International Journal of Manpower, 31(5), 545-562.

Narayan, V.K., Olk, P.M. & Fukami C.V. (2010). Determinants of Internship Effectiveness: An Exploratory Model, Academy of Learning & Education Management, 9(1), 61-80.

Parey, M. (2009). Vocational Schooling Versus Apprenticeship Training-Evidence From Vacancy Data, University of Essex and Institute for Fiscal Studies.

Patel, H.N. (2015). Undergraduate Internship Program Structures for Effective Postgraduation Employability: A Case Study of a Mass Media Arts Internship Program, Dissertation Theses, Atlanta University, USA.

Petrillose, M.J. & Montgomery, R. (1997). An Exploratory Study of Internship Practices in Hospitality Education and Industry's Perception of the Importance of Internships in Hospitality Curriculum, Journal of Hospitality & Tourism Education, 9 (4), 46-51.

Riva, Maria T., Erickson Cornish, & Jennifer A. (2008). Group Supervision Practices At Psychology Predoctoral İnternship Programs: 15 Years Later, Training and Education in Professional Psychology, 2(1), 18-25.

Ruhanen, L. Breakery, N. & Robinson, R. (2012). Knowledge exchange and networks: a new destination for tourism internships? Current Issues in Tourism, 15 (3), 183-196.

Ryan, P. Gospel, H. Lewis, P. (2007). Large Employers and Apprenticeship Training in Britain, An International Journal of Employmenyt Relations, 45(1), 127-153.

Smits, W. (2006). The Quality of Apprenticeship Training, Education Economics, 14(3), 329-344.

Studer, J.R. (2015). A Guide to Practicum and Internship for School Counselors in Traning, Routledge Taylor&Francis Group, Newyork.

Yu, S.S. & Pang, H.-W. (2007). The Contribution of Hotel Brand Image on Expectation and Satisfaction for Internship and Job Preference of Students Majoring in Culinary Art, Korean Journal of Food And Cookery Science, 23(1), 9-18.

Zwick, T. (2007). Apprenticeship Training in Germany-Investment or Productivity Driven?, Social Science Research Network.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 08 ISSN 1309-6249

THE IMPACT OF CHARTER SCHOOLS ON STUDENT ACHIEVEMENT IN THE UNITED STATES

PhDc. Sajid Ali Yousuf ZAI University of Arkansas Arkansas -USA

ABSTRACT

The purpose of this paper is to discuss charter schools in the United States and how it is different from the traditional public schools in terms of student performance in math and reading subjects. Several empirical studies have been discussed in this paper to provide support for charter schools in the United States. There are currently more than 6000 charter schools that represents about six percent of the U.S. public school system. Charter schools focus on personalized approach including smaller class sizes, more individual attention to and strong parental involvement. Out of 41 areas from 22 states, 26 areas’ post learning gains for charter schools is more than traditional public schools. In reading, 23 regions have larger learning gains than traditional public schools. Charter school students outperform traditional public school students in state standardized tests. The charter schools produce 40 percent better results in both math and reading scores per dollar spent.

Keywords: Charter schools, traditional public schools, United States, student performance.

INTRODUCTION

Charter school is defined as a school providing free public elementary and/or secondary education to eligible students under a specific charter granted by the state legislature or other appropriate authority (U.S. Department of Education, 2013). A brief overview of charter schools would be important before a discussion of these types of schools and the advantages of expanding charter school options in the United States. Chartering provides an alternative to public schools and is usually supported by non-profit groups, universities, and some government entities. Charter schools can be founded by teachers, parents, or other supporters who feel that public schools are not the only options. Charter schools can be run by public school systems, by nonprofit organizations, by private schools, or by religious organizations (Tschampl-Diesing, 2010). Charter schools receive public funding but are allowed more flexibility in curricular decision than public schools (Holmes, Desimone, & Rupp, 2003).

TYPES OF CHARTER SCHOOLS IN THE UNITED STATES

There are two types of Charters school operate in the United States: conversion charter schools and open- enrollment charter schools. Conversion charter schools have some flexibilities in terms of operation, it is administered by school leadership and conversion charter schools only allow students in their boundary lines of district while open-enrollment charter schools are administered independently (Office for Education Policy, 2012). A main difference between conversion charter and open-enrollment charter schools is, an existing public school that has been converted into charter schools is known as conversion charter schools while an open- enrollment charter school is a newly-developed public school run by a non-government organization (Arkansas Public School Resource Center, 2015).

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 08 ISSN 1309-6249

CHARTER SCHOOLS IN THE USA

Charter schools are rapidly growing since their first legislation in the 1990s. Charter schools are unevenly spread throughout the United States. California is a leading charter schools with more than one thousand charter schools, followed by Texas with more than 600 and Florida with more than 500 charter schools (U.S. Department of Education, 2013)

Nu m be r of Ch art er Sc

Figure 1: Growth in the number of the US Charter Schools Data Source: National Center for Education Statistics (NCES)

Currently, there are total 6,079 charters schools that represents only six percent of the U.S. public school system of 98,454 elementary, middle and high schools. A majority of charter schools have been established as elementary public schools. Whereas, less than 20% these schools have been established as either middle or secondary charter schools. 55% of the charter schools are located in urban areas and cities, while about 16% charter schools are located in rural areas.

Numb er of stude nts enroll ed (in thous ands)

Figure 2: Growth of Enrollments in Charter Schools Data Source: National Center for Education Statistics (NCES)

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 08 ISSN 1309-6249

From year 1999–2000 to 2011–12, the number of students enrolled in public charter schools increased from 0.3 million to 2.3 million students and the percentage of public school students who attended charter schools increased from 0.7 to 4.2 percent (U.S. Department of Education, 2013).

REASONS TO CHOOSE CHARTER SCHOOL

A study conducted by the National Study of Charter Schools of the U.S. Department of Education (1997) stated that three most cited reasons for creating a charter school are to 1) realize an educational vision, 2) gain autonomy, and 3) serve a special population. Parents and teachers choose charter schools because of the school’s academic standards, relatively small class size, and innovative approaches to education. Charter schools focus on personalized approach including smaller class sizes, more individual attention to and strong parental involvement.

EVIDENCE TO SUPPORT CHARTER SCHOOL SYSTEM

Holmes et al. (2003) argue that charter schools increase competition by “… an infusion of competition into the public education system that provides an incentive for traditional schools to increase quality. This follows the standard economic argument that competition forces firms to increase quality and/or lower price. When a charter school opens, the traditional public school, which previously held a monopoly on public education in a feeder district, faces the prospect of losing students to the new competitor. To the extent that the school's agent (ostensibly a principal) experiences disutility from a decline in enrollment, this might lead to an increase in the traditional school's quality in order to retain students. Such disutility might result from a decline in stature of the school in the community, lessened prospects for career advancement, a loss of personnel and budget provided by the funding agency, or a decrease in job satisfaction.” (p.2). That is, charter schools increase competition by allowing more choices for parents and students to choose the type of school system they prefer.

Holmes et al. (2003) found that having a choice between charter schools and traditional schools improve the performance of the traditional public schools in the surrounding area by a one percent increase. Therefore, there is support that charter schools also increase traditional school performance. Solmon, Paark, and Garcia (2001) found no statistical significance within the first year of students attending a charter school when compared to traditional public schools. However, students who do attend charter schools for two or three years do experience gains in reading and math that are significantly greater than those students enrolled in traditional public schools.

Hanushek, Kain, and Rivkin (2002) analyzed student achievement gains for Texas cohorts of students in grades 4-7 from 1996-2001. The sample includes over 6,600 students in charter schools and more than 800,000 students in total from traditional public schools and charters. In Texas academic achievement is measured annually using a criterion referenced test titled the Texas Assessment of Academic Skills (TAAS). Their longitudinal data model contained controls for how long the charter school has been in operation and student mobility. Hanushek, et al. (2002) found similar results to Solmon, et al. (2001) that students who are in charter schools for the first year have lower math and reading scores, but these effects shrink quickly. Similar findings were revealed by Mills (2013) when examining 10 years of achievement scores from grades three to grade eight in Arkansas State. Mills (2013) study concluded that charter schools have small negative impacts on student achievement in both math and reading scores. However, such negative effect tend to gradually decline over the years of charter schools operation.

That is, as charter schools mature the differences between math and reading scores for traditional public schools and charter schools disappear. Hanushek, et al. (2002) also found that higher-quality charter schools are usually just as good as or better than traditional public schools.

Sass (2006) found that new charter schools initially tend to have lower achievement, but the long-run performance of charters is important. By their fifth year, charters become even with traditional public schools

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 08 ISSN 1309-6249

in math and begin to produce reading scores that are better than traditional public schools by 10 percent based on annual achievement gains. Sass (2006) states "Charter schools are quite diverse; some are similar to traditional public schools while others seek to serve niches by targeting particular types of students (e.g., special education or at-risk students) or emphasizing particular programs (e.g., music, art, and languages). They also vary in their management structure, where most run as nonprofit entities but a significant number operated by for-profit management companies. Charter schools that target special education and at-risk students tend to have lower student achievement in math than non-targeted charters or the average traditional public school (holding student characteristics constant). The fact that parents willingly place their children in these schools (and keep them there) suggests that special education and at-risk charters may provide other valuable services beyond the core math and reading instruction tested on standardized exams, such as behavior management, development of social skills or oral communication skills” (p. 119). Many research findings suggest that charter schools have a positive impact on student achievement (Abdulkadiroglu et al., 2009; Dobbie & Fryer, 2009; Tuttle et al., 2010).

META-ANALYSIS ON VALUE-ADDED EFFECT OF CHARTER SCHOOLS

Meta-analysis study was also conduct on the effectiveness of charter schooling. The first meta-analysis conducted by Betts and Tang (2011) investigated the value-added effects of charter schools by analyzing 25 empirical studies. The research concluded that overall effect sizes ranging from.020 to .055 in favor of charter school students’ mathematics and reading achievement scores.

Another meta-analysis study was conducted by Center for Research on Education Outcomes (CREDO) in 2013 using student achievement data from Charter schools and traditional public schools in 25 states. The researchers found statistically positive effect in favor of charter schools. Based on the above mentioned meta- analysis studies, the researcher concluded that charter schools are showing small but positive effect on student performance. In one of the most recent study conducted by Stanford University’s Center for Research on Education Outcomes (CREDO) found that urban charter schools perform better than traditional public schools in urban areas (CREDO, 2015). The study was conducted at 41 urban areas in 22 states. According to CREDO’s (2015) report, in mathematics, 26 region post learning gains for charter schools students that is more than their traditional public schools counterparts. In reading, 23 regions have larger learning gains than traditional public schools.

Charters schools produces about 40 percent better results in both math and readings scores per dollar spent (Wolf, et al. 2014). In their study, Wolf, et al (2014) found that Charter schools tend to show more productivity than traditional public schools. Charter schools are cost effectively and produces better student results. Across 30 states and the DC, charter schools receive 28.4 percent less funding than other public schools, a gap of more than $3,814 per pupil. (Batdorff et al., 2014).

CHARTER SCHOOL AS MARKET-BASED REFORM

Charter schools are usually referred as market-based reforms because they introduce competition into the traditional public school system. Thus traditional public schools have to enhance their educational system to keep students from going to other schools, in which the traditional public schools would lose funding for that student. A market-based reform creates competition among schools. However, this competition can lead to negative consequences. Such that, traditional public schools losing students and funding to reform schools and not being able to provide an adequate education to other students. That is, successful schools may become more selective in which students they enroll and less-successful schools may lose resources when competing with the more elite schools. This would cause more tension between the schools.

CHARTER SCHOOL ACCOUNTABILITY

Charter schools have more autonomy in school-based decisions with compare to traditional public school system. The extra autonomy in charter schools also demand more accountability. If charter schools do not

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 08 ISSN 1309-6249

perform well or cannot enroll enough students to stay open, then the school faces being shut down. Therefore, charters do have more accountability than traditional public schools, because charter schools have more to lose than the other traditional public school. Also, charters are held to higher standards for student performance than traditional public schools.

PRACTICAL PLAN

Given these previously mentioned studies and the positive impact that charters can have on students, not only in achievement scores, but also socially and behaviorally. It is recommended that expanding the charter schooling in the United States is a good idea and should be implemented. However, before policy and legislatures are enacted, there should be more research about proper implementation of charter schools. Empirical evidences should be considered before implementing charter schools to make it more effective schooling. Garrison and Holifield (2005) state that the effectiveness of charter schools starts with a strong charter school law that is developed by the state. The Center for Education Reform states that the each state should "(a) permit an unlimited or substantial number of charter schools; (b) allow a number of entities in addition to the local school board to authorize charter schools; (c) permit a variety of individuals and groups both inside and outside the existing public school system to start charter schools; (d) permit new schools to start up from scratch; (e) permit charter schools to be started without proving specified levels of local support; (f) provide automatic blanket waivers from most or all state education laws and regulations; (g) permit charter schools to be independent legal entities; (h) guarantee 100 percent of per-pupil state funding to charter schools; (i) permit charter schools to control their funds; and (j) give charter schools complete control over personnel decisions." (Garrison and Holifield, 2005:90).

CONCLUSION

Given the empirical evidence in this policy brief, it is recommended to implement the expansion of charter school options in the United States. This brief provided supporting evidence for the use of charter schools, by using empirical research and looking at different states that have implemented and studied the effectiveness of charters. Based on different research designs and performance assessments between charter and traditional public schools, it is not possible to get an accurate comparison (Tschampl-Diesing, 2010). Because there is no common Charter law across the states. Each state is independent to plan their own charter rules and regulations. In addition, charter schools have a higher number of disadvantaged students than the traditional public schools, this diversion in two forms of schooling also makes it difficult to yield precise comparison. However, considering the evidence presented, expanding charter options in the United States seems to be an effective way for teaching students, not only in academics, but also socially and behaviorally. Also this policy brief provided documentation on how to implement state policy effectively, so charter schools have the greater chances of success.

BIODATA AND CONTACT ADDRESS OF AUTHOR

Sajid Ali Yousuf ZAI, PhDc. from University of Arkansas in the major of Educational Statistics and Research Methods. He is interested in international studies and polices to improve students’ math, science, and reading scores at secondary level education. He has more than 10 years of teaching experience and adequate relevant national and international research experience. He has been working as a teacher, principal, and teacher-trainer in different reputable government and non-government organizations in Pakistan. He has also been working as a teaching assistant in college of education and health professions in the University of Arkansas, USA for three years where he has taught statistics to undergraduate and graduate level students. He also engages in several teacher-training programs in Pakistan and the United States. His primary interest lies in quantitative research specially dealing with a large-scale data and analyzing mathematics standardized scores across countries.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 08 ISSN 1309-6249

Sajid Ali Yousuf ZAI Educational Statistics and Research Methods College of Education and Health Professions, University of Arkansas Arkansas - USA E. Mail: [email protected] , [email protected]

REFERENCES

Abdulkadiroglu, A., Angrist, J., Cohodes, S., Dynarski, S., Fullerton, J., Kane, T., et al. (2009). Informing the Debate: Comparing Boston’s Charter, Pilot and Traditional Schools. The Boston Foundation. Retrieved from http://scholar.harvard.edu/files/cohodes/files/informingthedebate_final.pdf

Arkansas Public School Resource Center | Charter School FAQs. (2015, January 1). Retrieved March 31, 2015, from http://www.apsrc.net/charterschoolfaqs

Batdorff, M., Maloney, L., May, F.J., Speakman, T. S., & Wolf, J. P. (2014).Charter School Funding: Inequity Expands. School Choice Demonstration Project. Department of Education report, University of Arkansas. Retrieved on January 21, 2016, from http://www.uaedreform.org/wp-content/uploads/charter-funding- inequity-expands.pdf

Betts, J.R., & Tang, Y.E. (2011). The Effects of Charter Schools on Student Achievement: A Meta—Analysis of the Literature. Seattle, WA: National Charter Research Project, University of Washington.

Center for Research on Education Outcomes (2013) “Charter School Growth and Replication,” Stanford, CA: CREDO, Stanford University.

CREDO (Center for Research on Education Outcomes, 2015). Urban Charter School Study Report on 41 Regions. Retrieved January 20, 2016, from http://urbancharters.stanford.edu/download/Urban%20Charter%20School%20Study%20Report%20on%2041% 20Regions.pdf

Dobbie, W., & Fryer, R. G., Jr., (2009). Are high-quality schools enough to close the achievement gap? Evidence from a social experiment in Harlem. (NBER Working Paper No. 15473). Cambridge, MA: National Bureau of Economic Research.

Garrison, L. F., & Holifield, M. (2005). Are Charter Schools Effective? Planning and Changing 36(1&2), 90-103. Retrieved on Jan 20, 2016 from http://files.eric.ed.gov/fulltext/EJ737644.pdf

Hanushek, E. A., Kain, J. F., & Rivkin, S. G. (2002). The impact of charter schools on academic achievement. Unpublished manuscript. Retrieved January 25, 2016, from http://users.nber.org/~confer/2002/hiedf02/KAIN.pdf

Holmes G, DeSimone J, Rupp N. (2003). Does School Choice Increase School Quality? Working Paper no. 9683, National Bureau for Economic Research. Available from: EconLit, Ipswich, MA. Accessed January 26, 2016.

Mills, J. N. (2013). The Achievement Impacts of Arkansas Open-Enrollment Charter Schools. Journal of Education Finance, 38(4), 320-342.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 08 ISSN 1309-6249

Office for Education Policy. (2012). Traditional and Charter School Funding in Arkansas. (2012). Office for Education Policy, 9(3), 1-5. Retrieved March 30, 2015, from http://www.officeforeducationpolicy.org/downloads/2012/05/traditional-and-charter-school-funding-in- arkansas.pdf

Sass, T. R. (2006). Charter schools and student achievement in Florida. Education Finance and Policy, 1(1), 91- 122.

Solmon, L., Paark, K., & Garcia, D. (2001). Does charter school attendance improve test scores? The Arizona results. Phoenix, AZ: Goldwater Institute Center for Market Based Education.

Tschampl-Diesing, C. (2010). Charter schools as an effective choice for increasing student achievement. (Doctoral dissertation). Available from Faculty Research & Creative Activity. (Charter Schools) Retrieved from http://coe.unomaha.edu/moec/briefs/charterschools.pdf

Tuttle, C. C., Teh, B., Nichols-Barrer, I., Gill, B. P., Gleason, P., & Mathematica Policy Research, I. (2010). Student Characteristics and Achievement in 22 KIPP Middle Schools: Final Report. Mathematica Policy Research, Inc.

U.S. Department of Education, National Center for Education Statistics, Common Core of Data (CCD), "Public Elementary/Secondary School Universe Survey," 1999–2000 through 2011–12. See Digest of Education Statistics 2013.

U.S. Department of Education. (1997). A study of charter schools: First year report (Executive Summary).

Wolf, J. P., Cheng, A., Batdorff, M., Maloney, L., May, F. J., & Speakman, T. S., (2014, April). The Productivity of Public Charter Schools. School Choice Demonstration Project. Department of Education Reform, University of Arkansas. Retrieved March 30, 2015, from http://www.uaedreform.org/downloads/2014/07/the-productivity- of-public-charter-schools.pdf

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

TECHNOLOGY EDUCATION IN PRESCHOOL: AN APPLIED SAMPLE LESSON

Gökben TURGUT Public Education Center Bornova, İzmir- TURKEY

Res. Assist. Yeliz TUNGA Computer Education& Instructional Technology Department Ege University İzmir- TURKEY

Assist. Prof. Dr. Tarık KIŞLA Computer Education & Instructional Technology Department Ege University İzmir- TURKEY

ABSTRACT

Science and technology is rapidly changing and developing in our ages. Human knowledge is being renewed and changed every day. This situation makes technology integration which accelerates accessing information into educational systems inevitable. Developing ICT skills of children starting from early ages gains importance considering the fact that those skills support the ability and attitude to use electronic media their future lives. For this reason, European Union gave a significant place to education of information technologies as naming “Technical Skills” in 111th European Youth Program in order to meet changing trends in both education and labor market in 1993(TEİAŞ, 2010). In the same manner, State Planning Organization of Turkey declared goal as “information and communication technologies will be one of main tools of education process and it will be provided that both teachers and students use those technologies effectively” in the Strategy of Information Society (2006 -2010). Then, Movement of Enhancing Opportunities and Improving Technology”, known as FATIH project was started(MEB, 2012). Researches related to FATIH project shows that teachers complain the most the lack of suitable e-content for interactive boards and tablets (Özkan and Deniz, 2014; Gürol, Donmuş and Arslan, 2012; Ayvacı, Bakırcı and Başak, 2014). In this study, it is aimed to present suggestions and experiences for researchers and early childhood educators by showing a sample lesson with various instructional materials based on those gaps in the literature. For this reason, a sample technology education lesson was developed for preschool students. First of all, an e-content which is compatible with interactive boards is developed by using Adobe Flash software considering preschool children’s needs and characteristics. Furthermore, various instructional materials is prepared to gain objectives of the lesson. Then, the lesson was applied in a private school with 16 preschool students. At the end of study, suggestions and experiences is reported for future researches.

Keywords: Preschool, Information Technologies, Smart Board, E- Content, Technology Education.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

INTRODUCTION

Science and technology has changed and developed rapidly these days. Human knowledge is being renewed and changed every day. Academic studies related to educational research which provide renewable information source for both educators and students for educational process have been conducted since 1980. In addition to increasing importance technology integration into the education, technological development also shapes professions of today and future apparently. Professions are being changed by focusing technological development. For example, according to statistics, 58 percent of companies prefer individuals who has taken technology training and 73 percent of newly opened companies are technologies based companies in England(Özbayoğlu, 2014). Strandberg(2002) establish a relationship between diffusions of high technology and technological levels of individuals in productive society. Abilities to use technology of individuals and whether they have taken technological training before are closely related to society high technology production, according to him.

In this context, countries that want to high quality labor and strong economy need to give place to technology education in their education policies. Dugger(1997) stated that technology literacy efforts must begin in kindergarten and continue each year through high school in all school across the country. Similarly, technology education is given to children starting at age 6 in developed countries such as Finland, Australia, France, and Estonia(Rasinen, Virtanen, Endepohls-Ulpe, Ikonen, Ebach, & Stahl-von Zabern, 2009). Developing ICT skills of children starting from early ages gains importance considering the fact that those skills support the ability and attitude to use electronic media their future lives. For this reason, European Union gave a significant place to education of information technologies as naming “Technical Skills” in 111th European Youth Program in order to meet changing trends in both education and labor market in 1993(TEİAŞ, 2010). In the same manner, State Planning Organization of Turkey declared goal as “information and communication technologies will be one of main tools of education process and it will be provided that both teachers and students use those technologies effectively” in the Strategy of Information Society (2006 -2010). Then, Movement of Enhancing Opportunities and Improving Technology”, known as FATIH was started(MEB, 2012).

Technology education refers a designed process which includes improve problem-solving skills and self esteem by understanding and using available technological facilities(Şenel and Gençoğlu, 2003). Similarly, International Technology Education Association - ITEA(1999) defines technological knowledge as nature and evolution of technology and technological concepts, principles and contextual relationships.

The definition of technology education and standards vary according to cultures and society needs. Dugger and Gilberti(2000) separate technology education into two categories as students’ understanding about technology and students’ capabilities in technology field. The first category contains cognitive processes such as definitions of fundamental concepts and technological knowledge – how technology works- what is an importance and position of technology in the/our world- ethical issues and terminology related to IT/technology. The second category includes students’ technological skills and productivity abilities in information technology field. These two different approach toward to technology education complements each other. Dugger and Gilberti (2000) list 20 standards of the combination of these two approaches as follows.

Nature of Technology  Students develop a notion related to technology and its scope.  Students develop a notion related to the fundamental concepts of the technology.  Students develop a notions related to relationships between both technology and other disciplines and varied technologies.

Technology and Society  Students develop a notion related to impacts of technology on the culture, economy, social life and politics.  Students develop a notion related to impacts of technology on the nature.  Students develop a notion related to society role about development and usage of the technology.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

 Students develop a notion related to impacts of technology on the history Students develop a notion related to impacts of technology on the nature.

Design  Students develop a notion related to a/the design (process)  Students develop a notion related to the engineering design.  Students develop a notion related to roles in the problem- solving process such as problem analysis, research, development, inquiry and invention

Proficiency for Technological World  Students develop their skills to participate to design process.  Students develop their skills to sustain (maintain) technological devices and systems.  Students develop their skills to evaluate effects of technological systems and devices.

Designed World  Students develop a notion related to choose and use medical technology  Students develop a notion related to agricultural technology usage and selection.  Students develop a notion related to energy and power technologies usage and selection.  Students develop a notion related to BİT usage and selection.  Students develop a notion related to industrial technologies usage and selection.  Students develop a notion related to transformation technologies usage and selection.  Students develop a notion related to constructional technologies usage and selection.

In 1997, “computer” course have included as an elective course to the primary education curriculum for the first time in Turkey. According to availability of computer laboratory, schools offered an computer course for graders from 4th to 8th and duration of this course was limited to one or two hours per week. However, those days computers was new technological devices and cost of building computer laboratory was excessively high that’s why computer courses wasn’t widespread all over the country. In 2005, importance of technology education was realized and to meet increasing need of individuals efficiently use technology, computer course was included both primary and elementary school curriculum by Ministry of Education. Similarly, duration of this course was limited an hour per week. In 2007, name of computer course was changed to “Information Technologies” course and duration of the course was increased in primary education curriculum for 4th and 5 the graders. Constructivist educational approach was adopted and information technology course curriculum and instructional materials such as workbooks, students books etc. were rearranged by Ministry of Education in the same year. In addition, Media Literacy course was offered as an elective course for primary school students for the first time in 2007. However, Ministry of Education removed the computer courses from primary school curriculum and it was offered as an elective course for only elementary school students in 2010. Duration of this course was reduced to one hour as well. By the year 2012, educational system was changed and a new educational system called as 4+4+4 have been started. Computer courses offered as an elective course for only elementary school students in Turkey with this new educational system. The latest program is differ from others. In previously, school managements decided to whether information technology course offer for students or not. However, there is a need parent request to open computer course for their children in 4+4+4 system. If there is sufficient request from parents, computer course can open for the elementary school students. Programming subjects was increased and course name was again changed to Information Technology and Software in 2012. Courses have been compulsory course for 5th and 6th graders for the first time and it was offered as an elective course 7th and 8th graders in 2013. Computer course was also graded for the first time in the same year, before 2013 computer courses were elective courses and students didn’t graded by ICT teachers.

Current unity title list of students’ workbooks available on the Information in Educational Network (EBA) portal are given below.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

5th Grade  Importance of ICT in daily life  Social and cultural contributions of ICT  Fundamental concepts of ICT  Usage and management of ICT  Privacy and security dimensions of ICT  Ethical and social values in ICT usage

6th Grade  Internet and Communication  Communication Devices  Information Sharing and Tools  Project Development and Management

7th Grade  Ten fingers typing  Electronic Spreadsheets (MS Excel)  Databases  Making Web Site (Adobe Dreamweaver)

8th grade  Information Systems  I am making a website  I am making a computer program

ICT (technology) courses are included in only graders from 5th to 8th curriculum and there is no technology course in preschool and first four year of the primary school in our country, as seen above. Exceptionally, some private schools and colleges offer coding and ICT courses from preschool to high school.

Researches related to computer usage in preschool education show that children needs to learn technological skills and how to use them with basic sciences effectively in addition to basic sciences education. It is seen that e-skills or ability to use technological devices are necessary for children to integrate their knowledge with other disciplines (Kaçar and Doğan, 2007). Recently, importance of technology education in preschool has realized and related studies about this subject has also started in our country. In contrary to common belief about using technology in early years at child education harm children in preoperational ages – between 4 and 7 ages- , studies state that computer usage in preschool education with the proper time, content, context and guidance helps children critical, analytical thinking, socializing ability and ability to working collaboratively especially for those who need to special education (Dodge and Colker, 1995; Akkoyunlu and Tuğrul, 2002; Healy, 1998, Papert, 1998). Kartal and Güven(2006) list points that need to pay attention to computer usage in preschool education in their study. These points can be summarized as follows.  Duration: Duration of the time spent on computer should be limited.  Purpose: Computer should seen as an device not a goal by children  Context: Collaborative learning environment and well designed ergonomic working area should be provided such as well lighting, roominess etc.  Computer should be used for proper and relevant purposes.  Social Environment: Computer based activities should provide children an opportunity for socializing. For example; child can improve his/her social and democratic skills such as respect the right of others, solving a conflict, making friends.  Guidance: It should be provided teacher guidance to help students in social, pedagogical and cognitive aspect of teaching activities such as helping focus on subjects, encouraging students, improving children’s’ verbal abilities, asking discussion questions, keeping distance between computer screen and children, preventing demotivation feeling resulting from failure.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

Teaching activities enriched by the use of information and communication technologies does not prevent child’s physical activities, verbal communication and socializing opportunities. In contrast, well designed lesson enriched with technology usage improve child’s verbal and linguistic communication abilities, problem solving skills, critical thinking abilities and ability to work collaboratively and it provides some other meta-cognitive learnings such as discrimination, establishing pattern, organizing etc.

Likewise Kartal and Güven(2005) suggestions for computer education in preschool, Clements (1999) presents advises related to increasing social interaction in classes where computers are used for educational purposes in preschool. According to Clement (1999), social interaction can be encouraged by placing two seats in front of the computer and one at side of the teacher. Computers can be placed to close each other to facilitate the sharing opinions among children. He also suggests that centrally located computers can increase participation to computer activity by inviting all children near to the computers. Muller and Perlmutter (1985) observed that children who involves computer based activities spent nine times as much time talking to peers during activities than while doing puzzles. Similarly, Elkind(1999) gave some suggestions to teachers related to technology education. He said that teachers need to observe how children themselves overcome the technology and he added that some initial instructions is necessary and certain limits need to be set yet children should be allowed make their choices. Dugger and Gilberti(2000) suggest some example subject for technology education from preschool to K2 level;  Natural World and human made World  People and technology  Systems, sources, process  Technologies and relationships between technologies and other fields  Pros and cons of technology usage

Davis and Shade (1999) list concepts could be taught to children in early ages- preschool students as follows;  Computer peripherals (processor, hard disc, mouse, keyboard, printer etc.)  Working principles of computers ( input units, processor, output units)  How a computer program works? Coding structure  Communication between computers  Advantages of using computers  Limitations and powerful sides of computers  History of computer technologies and the fact that computers was a product of human intelligence and they were invented by human being.

The aim of this study to apply an example lesson about technology education in preschool by using various instructional materials and flash based educational games in light of literature. Flash based educational games are designed for smart boards. Characteristics and needs of preschool students are taken into consideration in design phase of flash based educational games. In addition to flash based educational games, various instructional materials designed for this lesson with the help of preschool educators. It is tried to all instructional materials of the study are enriched by reinforce. Finally, the another aim of this study to contribute children socializing, verbal and motor skills and making suggestions for both researchers and teachers with this study.

An Applied Sample Lesson As it is mentioned in introduction, computer peripherals subject is chosen from suggested subject list by Davis and Shade(1999) for technology education for preschool students. First of all objective of lesson is chosen. Then strategies, method and techniques are selected to gain this objective. Detailed information about lesson is given Table 1.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

Table 1: Lesson Plan of Applied Sample Lesson

PRIVATE ………. PRIMARY SCHOOL DATE: 26/11/2014 PART 1 Course Name Information Technologies Unity Title Introduction to the Information technologies Subject Computer peripherals Duration 2 hours (40 + 40 minutes) PART II Objectives Learners will be able to tell name of computer peripherals Learners will be able to tell functions of computer peripherals. Precautions (If Exists) ------Methods and Techniques Presentation, gamification, drill and practice Smart board, hardware models, leaderboards, flash Instructional materials cards, flash based e-content, PowerPoint

presentation Activities

It will be asked to children that what they know about computers and peripherals. Hardware cardboard model will be showed to children and necessary time will be given for children to examine the hardware cardboard models. Then it will be announced that they will learn peripheral of computers and functions of them at the end of lesson. PowerPoint presentation consist of computer hardware photos will be showed and and functions of peripherals will explained by using this presentation. Flashcards will be given to children and it will be asked them to examine the peripherals images on flashcards. The interface of flash based e-content designed for smart board will be introduced to children and rules of games will be announced. Games will be played and scores of the children will be marked to the leaderboards. At the end of lesson, free/necessary time will be given for students to draw an image/picture of peripherals.

Researcher: ICT Teacher: .…….. .………......

Study process is separated into two main parts namely lesson preparation and implementation of the lesson. Preparation process involves subject (unity) selection, preparing lesson plan, developing e-contents and choosing instructional materials. Lesson is consist of motivating learners, recalling prior knowledge of them, lecturing and evaluation phases. Study process is given below as figure 1.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

Figure 1: Structure of the process

Development of the Flash Based E- Content Elkind (1999) argues that there is a significant relationship between children learning and motivation, if a child does not have the learning motivation which results from feeling of curious, inquiry, desire and competition, learning process cannot be efficient or proper. Therefore, Motivational ARCS Model is used in the design of this material. Motivational ARCS model aims to design motivational aspect of learning environments to stimulate and maintain students’ motivation toward learning process. The model consists of two major parts. The first part represents components of motivation while the second part is a systematic design process which assists educators in making motivational improvements in given set of learners (Keller, 1987).

Needs and characteristics of preschool students such as illiterate, difficulty at understanding abstract concepts are taken into the consideration in design phase of this material. Flash based module is a kind of drill and practice software and the aim of this material is to provide children to make a practice related to objectives of this lesson.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

Flash based module is consist of two educational games. There are 15 questions in the first game of the module. Questions are related to peripherals and their functions. It is expected from children to select an image of the correct answer of questions. It is also planned that game is supported with flash cards. That is, children need to show flash cards of correct answers. Questions of this game are enriched with examples usage of peripherals in daily life and there is a vocalization and various animations for each question. An example screenshots of the first game is given below.

Figure 2: Main Page of Module

Figure 3: “OYUN 1” Screenshot

The second is a drag and drop style matching game. Game screen is divided into the two sections. There are shadows of peripherals on the top section and images of peripherals are in the bottom section of the screen(Figure 3). Children need to match shadows with corresponding peripherals in the game.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

Figure 4: “OYUN 2” Screenshot

Other Instructional Materials 1- Cardboard models of peripherals are prepared by prospective early childhood education teachers to concrete the subject. 2- Flash cards are prepared by using Adobe Photoshop program. Peripheral images are putted on flash cards. 3- PowerPoint presentation is prepared by using photos of peripherals. Since target group of instruction are illiterate, text or written expression isn’t used in the presentation. 4- Leaderboard is prepared to mark scores of students. Children’s’ photos and colorful pins are used for leaderboard to create attractive instructional material.

Figure 5: Hardware Cardboard Models

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

Figure 6: Flash Cards Figure 7: Leaderboard

IMPLEMENTATION

The implementation of this lesson made in a private elementary school in the spring semester of 2014-2015 academic years. Participants of this study 16 preschool students. The lesson was lasted 3 hours and the lesson was conducted with the teacher of children since researchers weren’t familiar with students. Before the lesson researchers prepared various instructional material and obtained information about students such as number of students, name and photos of students and their favorite activities from their children.

The whole lesson is divided into three part namely, introduction, development, evaluation. Each part is explained in detailed below.

Introduction  At the beginning of the lesson, researchers tried to draw attentions of children by asking questions. For example, do you have a computer in your home and if they have, what are the kinds of their computers, how do they describe their computer.  In order to motivate children, it is announced that a game would be played during the lesson.  Rules of lesson such as speaking in order, asking permission to talk vs. are explained to children.

Development  Peripherals and functions of them were explained to the children by using PowerPoint presentation. It is provided that children observed 3D visual model of peripherals by using cardboard models of peripherals since children need to concrete materials and examples in early ages.  It is asked to children to compose a desktop computer by using cardboard peripheral model.  Example scenarios were given to children. For example, your father goes to abroad for business purposes and you want to send a pictures of a toy to your father so can you use a camera?  Flash cards were distributed to children and necessary time was given children to examine flash cards.  Flash based material was used to reinforce to new knowledge of children. First of all, material was introduced to children and brief information about rules of games was given. o As mentioned earlier, the first game consists of questions related to peripherals and functions of them. Before the starting game, children saw the photo of their teacher on game (figure ) screen and they reacted positively. For example; “Hey, look at the screen, our teacher are there”. “She looks well”. Then, students answered all questions by using previously given flash cards. One of researchers took a note and 87 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

inserted a pin for each correct answer of students on the leaderboard. Colors of pins were selected by children. For each question, one student was selected to come the board and mark correct answer on the smartboard. Researchers and teachers gave feedback during the game. o Students play the second game of the module. The second game is a shadow matching game. Children matched peripherals shadows with corresponding peripheral by drag and drop. All students played the game successfully. o Children wanted to play again the second game. Each child played one more time the game.

Evaluation  Questions related to peripherals were asked to children by using flashcard. Collaborative working chance is given to children and children answer questions collaboratively. A pin was added to the leaderboard for each correct answer.  Lesson was closed with a drawing activity and homework. Children draw their favorite peripheral and color them(Figure 8, 9).  The homework was given to children. It was asked to the children tell the functions of their favorite peripheral to their parents and friends by using their drawings as a flash card like their researcher did.

Figure 8: Photos from the class

Figure 9: Students' drawings

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

RESULTS AND SUGGESTIONS

There is a common belief regarding as technology usage in preschool education can cause negative effects on children. However, recent studies shows that information technology education usage in preschool with proper guidance in relevant activities can help children to improve their problem-solving, verbal, linguistic and even physical skills without feeling isolated and inactive by sharing their ideas with their classmates. On account of these reasons, it is obvious that there is need to more research about both technology education and technology usage in preschool.

In this study, it is aimed to provide a sample technology education lesson for preschool students. Computer peripherals is selected subject of this lesson and the lesson was applied in a private elementary school in the spring semester of 2014-2015 academic years. 16 preschool students participated to this study. For the lesson, flash based e- content compatible for interactive boards and various instructional materials were developed. Lesson plan and scheme of the lesson is given previous part of this article. Furthermore, an implementation of the lesson is explained in detailed. Researchers observed that children were willing to participate the instructional activities during the lesson.

The following suggestions are offered based on researchers’ observation related to technology education and information technology usage in preschool.  Animations can be used in multimedia materials for preschool students.  Guidance and necessary supports should be provided to students during technology based activities.  Collaborative learning environment should be provided. Children should be encouraged to group working.  New trends in educational technologies such as gamification can be used in preschool.  Quantity and quality of the educational software for preschool students should be increased.  Preschool teachers and preservice preschool teachers should be encouraged to use technology for educational activities and purposes. In-service trainings for preschool teachers can be served.

BIODATA AND CONTACT ADDRESS OF AUTHORS

Gökben TURGUT completed her BS studies on Computer Education and Instructional Technology, her MS in Computer Education and Instructional Technology at Ege University in Turkey. She has been working as a computer teacher for 10 years in MEB. She is scholarly interested in technology education, pre-school education, digital storytelling, programming education in early-learning ages, developing mobile instructional applications and qualitative research methods.

Gökben TURGUT Public Education Center Bornova, İzmir- TURKEY E. Mail: [email protected]

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

Yeliz TUNGA received B.S. degree in Computer Education and Instructional Technology from the Middle East Technical University in 2013. Currently, she is a graduate student and she is working as a research assistant Computer Education and Instructional Technology department at Ege University. She is interested in gamification, game- based learning, teacher- education, serious games

Res. Assist. Yeliz TUNGA Computer Education & Instructional Technology Department Ege University İzmir- TURKEY E. Mail: [email protected]

Tarık KIŞLA has taken his B.S. degree from Mathematics, Ege University, and M.S and Phd. degrees from International Computer Institute. He is currently working as an Asist. Prof. in Department of Computer and Instructional Technologies, Ege University. He gives lectures on information technologies, algorithms, programming language, technology integration in education, mobile learning and distance education. Further information about his publications and projects can be found from http://egitim.ege.edu.tr

Assist. Prof. Dr. Tarık KIŞLA Department of Computer and Instructional Technologies Faculty of Education Ege University E. Mail: [email protected]

REFERENCES

Akkoyunlu, B. & Tuğrul, B. (2002). The Impact of Technological Interaction at Home Environment on Pre-School Childrens' Computer Literacy Skills. Hacettepe Eğitim Fakültesi Dergisi, 2(2), s. 13-21.

Ayvacı, H. Ş., Bakırcı, A. G. H. & Başak, M. H. (2014). Fatih projesinin uygulama sürecinde ortaya çıkan sorunların idareciler, öğretmenler ve öğrenciler tarafından değerlendirilmesi. Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi, 11(1).

Clements, D. H. (1999). Young children and technology. In Nelson, G. D. (Ed.). Dialogue On Early Childhood Science, Mathematics, and Technology Education. (pp. 92-105). Washington, DC: American Association for the Advancement of Science.

Davis, B. C. & Shade, D. D. (1999). Integrating technology into the early childhood classroom: The case of literacy learning. Information Technology In Childhood Education, 221-254.

Dodge, D. T. & Colker, L. J. (1995). (3rd. [''AI.).The creative curriculum for early childhood educaton. Teaching Staker. Ine. Washington. D.C.

Dugger, W. E. & Gilberti, A. F. (2000). Standards for technological literacy: Content for the study of technology. Technology Teacher, 59(5), 8-13.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

EBA. Retrived November 20, 2015 from Eba Web site: http://www.eba.gov.tr/ekitap#!/ekitap/ders,bilgi-ve- iletisim-teknolojileri.

Elkind, D. (1999). Dialogue on early childhood science, mathematics, and technology education: A context for learning. In American Association for the Advancement of Science.

Gürol, M., Donmuş, V. & Arslan, M. (2012). İlköğretim kademesinde görev yapan sınıf öğretmenlerinin fatih projesi ile ilgili görüşleri. Eğitim Teknolojileri Araştırmaları Dergisi, 3(3).

Healy, J. M. (1998). Understanding TV's effect on dcveloping brain. AAP News: The Officia! News Magazine of the American Academy of Pediatrics

Kaçar, A. Ö. & Doğan, N. (2007). Okulöncesi Eğitimde Bilgisayar Destekli Eğitimin Rolü. Akademik Bilişim (s. 1- 11). Kütahya: Dumlupınar University.

Kartal, G. & Güven, D. (2006). Okulöncesi eğitimde bilgisayarın yeri ve rolü. Boğaziçi Üniversitesi Eğitim Dergisi, 23(1).

Keller, J. M. (1987). Development and use of the ARCS model of instructional design. Journal of instructional development , 10 (2), s. 2-10.

MEB. (2012). Fatih Projesi. Retrieved November 20, 2015 from http://fatihprojesi.meb.gov.tr/tr/icerikincele.php?id=6

Muller, A. A. & Perlmutter, M. (1985). Preschool children's problem-solving interactions at computers and jigsaw puzzles.Journal of Applied Developmental Psychology, 6:173-186.

Özbayoğlu, G. (2014). Meslek Seçimi Ve Geleceğin Meslekleri.

Özkan, A. & Deniz, D. (2014). Orta öğretimde görev yapan öğretmenlerin Fatih projesine ilişkin görüşleri. Ege Eğitim Dergisi, 15(1), 161-175.

Papert, S. (1980). Mindstorms: Children, rnicrocomputers and powerful ideas. New York: Basic Books.

Rasinen, A., Virtanen, S., Endepohls-Ulpe, M., Ikonen, P., Ebach, J. & Stahl-von Zabern, J. (2009). Technology education for children in primary schools in Finland and Germany: Different school systems, similar problems and how to overcome them. International Journal of Technology and Design Education,19(4), 367-379.

Strandberg, G. (2002). Technology, economics, and politics. Journal of Industrial Technology, 18(2), http://www.nait.org

Şenel, A. & Gençoğlu, S. (2003). Küreselleşen dünyada teknoloji eğitimi. Gazi Üniversitesi Endüstriyel Sanatlar Eğitim Fakültesi Dergisi, 11(12), 45-65.

Keller, J. M. (1987). Development and use of the ARCS model of instructional design. Journal of instructional development, 10(2), s. 2-10.

Technology for All Americans Project & International Technology Education Association. (1996). Technology for all Americans: A rationale and structure for the study of technology. International Technology Education Association.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 09 ISSN 1309-6249

TEİAŞ. (2010). TEİAŞ. Retrieved November 20, 2015 from TEIAŞ Web site: http://www.teias.gov.tr/eBulten/makaleler/2010/avrupa_b%C4%B0rl%C4%B0%C4%9F%C4%B0_e%C4%9F%C4 %B0t%C4%B0m_pol%C4%B0t%C4%B0kasi.htm

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

THE RELATIONSHIP BETWEEN 7th AND 8th GRADE STUDENTS' CONCEPTUAL LEARNING AND MATHEMATICS SELF-EFFICACY LEVELS OF SUBJECT OF “ALGEBRAIC EXPRESSIONS AND EQUATIONS”

Assoc. Prof. Dr. Sare ŞENGÜL Marmara University Atatürk Education Faculty İstanbul- TURKEY

Assist. Prof. Dr. Yasemin KABA Kocaeli University Education Faculty Kocaeli- TURKEY

Prof. Dr. Yusuf AYDIN İstanbul Commerce University Faculty of Arts and Sciences İstanbul- TURKEY

ABSTRACT

The aim of this research is to determine the correlation between 7th and 8th grade students’ conceptual learning and mathematics self-efficacy in ‘Algebraic Expressions and Equations’ subject. The study was carried out in a public school on the Anatolian side of the city of Istanbul in 2011-2012 academic years. The study was conducted with 97 students in total and 47 of them are 8th grade and 50 of them are 7th grade students. The research model of the study is screening model. The data of the study was collected through ‘Conceptual Understanding Test regarding Algebraic Expressions and Equations [CUTAEE]’ and ‘Self-efficacy Perceptions towards Mathematics Scale [SPMS]’. The data of the study was analyzed by using qualitative and quantitative methods. Frequency (f) and percentages (%) were used for quantitative methods. The data obtained through CUTAEE was evaluated with content analysis. According to the obtained findings, it was determined that there was a significant and positive correlation between the mathematics self-efficacy levels of the students and the concepts regarding ‘Algebraic Expressions and Equations’ subject of the 7th and 8th grade students. Besides, while a significant difference was found in favor of 8th grade students in terms of students’ conceptual understanding, there was not a significant difference between the mathematics self-efficacy levels of the 8th students. In terms of genders, it was determined that there was a positive and significant correlation in favor of male students between both mathematics self-efficacy and conceptual understanding levels of 7th and 8th grade students. The suggestions were made in accordance with the obtained findings.

Keywords: Conceptual learning, mathematics self-efficacy, algebraic expressions, equations.

INTRODUCTION

The primary and middle schools have great importance since they have preparatory roles in terms of constructing the basic scientific information for the higher levels of education. Starting from the first years, well-constructed mathematics information is among the subjects that are needed to be carefully considered since it is the pioneer of the students’ future academic achievements. According to Hung (2000), mathematics is a whole of systems which is based on thinking skills which are composed of conceptual structures and is a thinking style which uses intuition and mental presentation of the information. In order to understand mathematics, it is necessary not only to apply algorithmic rules but also to acquire the conceptual learning dimension by discussing the information (Davis, 1992).

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

Concepts are mental tools which ensure people to classify and organize the things they have learnt by constructing the basics of information. Kaptan (1998) defines concept as the common name which is given to the group of ideas, objects and events which have similar features and Senemoğlu (2005) defines it as a category which is used in grouping similar objects, people, events, ideas and processes. In other words, concepts provide individuals to classify and organize the things they learnt. Individuals starting from their childhood years classify the concepts by actively learning them, constantly organize them by giving new meaning to learnt information and even produce new information and concepts (Cansüngü Koray & Bal, 2002). For this reason, concepts have an important place in understanding and sensing the meaning of the world, concepts constitute the basic units of information and the conceptual relationships create the scientific structures.

It is not enough to make definitions and to give examples for creating and learning concepts. In addition to that, it is necessary to be able to determine the critical points regarding the concept, to state the main characteristics, to relate concepts with everyday life, to make connections with other concepts and sub- concepts and to specify clearly the common and different features between various concepts (Alkan & Uğurel, 2004), as the knowledge of a concept is chained to one another with the relations of a wide variety of different concepts. If we associate the knowledge of a concept to a chain’s ring, then each ring will contain some information. As the inter-connected knowledge expands, the ring of the chain to which the concept is bounded will also expand so that the information piece to which it is connected will become stronger (Baki & Kartal, 2002). On the contrary, if we consider the fact that mathematics subjects are in the form of a helical structure, the lack of information in the pre-concepts will hinder the students’ meaningful structuring processes on the next levels. It can be said that this case will be effective on the perceptions of students as ‘I do not understand mathematics and I cannot do it’. Besides, it is thought that it can have negative reflections on the points of students’ self-confidence and organizing an activity which is necessary for students to display a performance regarding mathematics and successfully accomplished it. The findings of the study which was carried out by Randhawa, Beamer and Lundberg in 1993 also show that mathematics self-efficacy is an important variable between the attitudes towards mathematics and mathematics achievements.

When students engage into a certain learning process, the source of their efforts will be composed of their interests, attitudes and beliefs to become successful in this process. According to Bloom (1998) affective domain components (interest, attitudes etc.) have power to explain the 25% of the change in learning products. This shows the fact that one fourth of the difference between the learning of individuals is derived from these affective features. In addition to this, the belief of self-efficacy is an effective precursor on the mathematics achievements of the individuals (Kiemanesh, Hejazi & Esfahani, 2004). According to Zimmerman, Bandura and Martinez-Pons (1992), self-efficacy and using strategies explain the 30% of the variability in academic achievement.

Hackett and Betz (1989) define self-efficacy towards mathematics as ‘believing your own skills to successfully accomplish the tasks regarding mathematics’. In the studies about this subject, many researchers have analyzed the correlation between mathematics self-efficacy and various variables (mathematics achievement, mathematics attitude, mathematics concerns, interests to lessons related with mathematics and choosing occupation related with mathematics). In many studies which searched the mathematics self-efficacies, it was found that there was a significant correlation between students’ mathematics achievements and their self- efficacies (Chen, 2002; Hackett & Betz, 1989; Migray, 2002; Moore, 2005). When the direction of this correlation was examined, it was presented that it was a negative correlation with concerns regarding mathematics and a positive one with mathematical performances (Cooper & Robinson; 1991) and also it was found out that mathematics self-efficacy was an important variable between attitudes towards mathematics and mathematics achievement (Hackett & Betz, 1989; Randhawa, Beamer & Lundberg, 1993), besides mathematics self-efficacy had an important intermediary role in the process of choosing an occupation regarding mathematics (Betz & Hackett, 1983; Hackett, 1985).

The mathematical concepts are abstract and it is not easy to learn and to construct them properly. It is especially important in this point to present the level of mathematics self-efficacies of students and

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

mathematical subjects in which the students have a lot of misconceptions. The ‘Algebraic Expressions and Equations’ subject in ‘Algebra’ sub-learning field stated in the 7th and 8th grades of the middle school mathematics program has an important place in terms of making students develop a positive attitude towards mathematics. Because algebra is an important learning field which has an important role in improving mathematical thinking and is a mathematical language which expresses itself with symbols, tables, words and graphics (Stacey & MacGregor, 2000). Accepting algebra as a language shows how important is to teach algebra for understanding mathematics (Williams & Molina, 1997). Students should understand the letters which are used in different situations in algebra, the structural features of the algebraic equations, symbols for interpreting the equations given in case of equation and solving the equations and operations carried out symbols (Kieran, 2007). Kieran (2007) puts understanding and using symbols and mathematical understanding into the centre of the algebraic thinking. For this reason, the purpose of this study to determine whether there is a correlation between 7th and 8th grade students’ conceptual learning and mathematics self-efficacy in ‘Algebraic Expressions and Equations’ subject and to present this correlation after analyzing it according to different variables and also the answers of the following questions are searched; 1. Is there a significant difference between the conceptual learning levels of 7th and 8th grade students? 2. Is there a significant difference between the mathematics self-efficacy levels of 7th and 8th grade students? 3. Is there a significant correlation between students’ mathematics self-efficacies and their conceptual learning together with sub-dimensions of the self-efficacy scale? 4. Are mathematics self-efficacies of students a significant predictor of their conceptual learning? 5. Is there a significant difference between students’ conceptual learning and their mathematics self- efficacies by their genders?

METHOD

Research Design This research is a descriptive study which was carried out with relational screening model. The relational screening models are research models that are trying to determine the presence of the change or the degree of change between two or more variables. The purpose of description in this model is to determine the discriminations between cases such as individuals and objects rather than finding the size of something present which fits to certain standards. The correlations found through screening cannot be interpreted as a real cause and effect relationship; but they can give useful results in predicting the other one by giving some clues towards that direction if the case in a variable is determined (Karasar, 2003).

Study Group The study group of the research is consisted of a class of 7th grade and a class of 8th grade students who were randomly selected from a public middle school in the Anatolian side of Istanbul in 2011-2012 academic years. In the study group there 20 female and 27 female in total 47 8th grade students and 22 female and 28 male in total 50 7th grade students. In this sense, this study was carried out with 97 students.

Data Collection Tools and Collecting Data Two assessment tools were used in this study. The first one was ‘Conceptual Understanding Test regarding Algebraic Expressions and Equations [CUTAEE]’ which was prepared about ‘Algebraic Expressions and Equations’ subject. CUTAEE is a test which is consisting of 13 open-ended questions which was created as result of the classification of the concepts selected according to the objectives related with the ‘Algebraic Expressions and Equations’ subject. It was paid attention to create questions in way to determine whether students have misconceptions, whether they created correlations between concepts and whether they learnt the concepts meaningfully. For the items used in the assessment tool, opinions of the 2 experts in the subject area and 2 academicians were taken before the implementation. First of all, in order to specify the content validity, it was asked to experts whether the questions used in the assessment tool represent the considered objectives in the different types of ‘Algebraic Expressions and Equations’ subject defined in related literature. Besides, the items in the assessment tool was analyzed by experts for understanding whether they were expressed properly, their level of difficulty, whether they could cause misunderstandings and to what extent they test the thing that they wanted to assess.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

The consensus in the evaluations of the expert and academician was calculated by using the following formula stated in Miles and Huberman (1994): ‘Agreement Percentage=Agreement/(Agreement+Disagreement) x 100’. As a result of this calculation, the consensus percentage was found as ,91. In addition to that, a pilot study was carried out to guarantee that the time allocated for the test was suitable and whether the items of the test were clear or not with 15 8th grade and 10 7th grade students who can be compared with the general academic backgrounds of the participants in a broader study. The test was taken its final form by making the necessary editions as a result of the opinions of the experts and the pilot study.

The second assessment tool was ‘Self-efficacy Perceptions towards Mathematics Scale [SPMS]’ which was developed by Umay (2002) in order to test the students’ self-efficacy perceptions towards mathematics. In likert type scale there are 8 positive (1, 2, 4, 5, 8, 9, 13, 14) and 6 negative (3, 6, 7, 10, 11, 12) in total 14 items. The items of the scale were scored as; never (1), rarely (2), sometimes (3), generally (4) and always (5). Besides, the scoring was conducted in reverse for the negative items. The scale is consisted of three factors. These factors were defined as 1) mathematics self-esteem, 2) the awareness at the behaviors in mathematics subjects and 3) the ability to convert mathematics into life skills. The first factor is installed in the 3rd, 10th, 11th, 12th, and 13th items; the second factor in 4th, 5th, 6th,7th, 8th and 9th items; the third factor in 1st, 2nd, and 14th items. The alpha reliability coefficient of the scale was calculated as = 0,88 for the total. The alpha reliability coefficient of the scale was determined as = 0,70 for this study, the alpha reliability coefficient for the sub-factors was found respectively for the first factor as = 0,58; for the second factor as = 0,59 and for the third factor as = 0,61.

The implementation was carried out in different days with 7th and 8th grades. First of all, CUTAEE was conducted with 7th grades in two lessons. Later on, they were asked to fill in SPMS. 25 minutes were given to students for this. The same procedure was repeated with the 8th grade students.

Data Analysis The answers of the each student that they gave for the question in CUTAEE were analyzed one by one and classified under five categories. Furthermore, each of these categories was evaluated in four different ways by dividing into sub-units. The evaluation form can be seen Table 1.

Table 1: Categories and Sub-units The definition of equation and knowing the definitions of the types of equations and giving example There is a definition and there is an example 3 points There is a definition but there is not an example 2 points There is not a definition but there is an example 1 point There is not a definition and there is not an example 0 point Explaining the correlation between equality and inequality with its reasons Know the correlation between concepts, know the reason 3 points Know the correlation between concepts but do not know the reason 2 points Do not know the correlation between concepts but know the reason 1 point Do not know the correlation between concepts and do not know the 0 point reason Be able to express the given problems on figures mathematically There is visualization and interpretation 3 points There is visualization without interpretation 2 points There is no visualization but there is interpretation 1 point There is no visualization and interpretation 0 point Analyzing the direct correlation between two variables by using tables and graphics and interpreting the figure There are tables and graphic with reasons 3 points 96 Copyright © International Journal on New Trends in Education and Their Implications / www.ijonte.org

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

There are tables and graphics without reasons 2 points There are no tables and graphics but there is a reason 1 point There are no table and graphics and there is no reason either 0 point Making calculations with algebraic expressions and interpreting that operations There is a calculation with an interpretation 3 points There is a calculation without an interpretation 2 points There is no calculation but there is an interpretation 1 point There is not calculation and interpretation 0 point

The maximum score one can get from CUTAEE is 39. On the other hand, necessary analyses were carried out by evaluating the data obtained from the assessment tools through statistical analysis method. During the data analysis, correlation, regression and t-test statistical operations were used.

FINDINGS AND COMMENTS

In this part, findings obtained from research questions for the 7th and 8th grade students’ conceptual learning and mathematics self-efficacies are presented respectively. The results appeared as result of the data analysis regarding the first sub-problem of the study are given in Table 2.

Table 2: t-test Results Regarding the CUTAEE Scores of the 7th and 8th Grade Students Grade Level N sd df t p 7th grade 50 23,23 4,983 th 95 2,259 0,026 8 grade 47 25,62 5,394

When Table 2 is analyzed, it is seen that 7th grades’ conceptual learning arithmetic mean is 23,23, standard deviation is 4,983; 8th grades’ conceptual learning arithmetic mean is 25,62 and standard deviation is 5,394. As a result of the t-test carried out for the conceptual learning of the 7th and 8th grades, a significant difference at ,05 significance level was found. It was seen that in t–test conducted for 7th and 8th grade students, there was a statistically significant difference between conceptual learning of the students at ,05 level in favour of 8th grade students [t(95)= 2,259; p < ,05]. According to this finding, it can be said that 8th grade students structured the concepts related with the ‘Algebraic Expressions and Equations’ subject better. It can be said that this is a result of the teaching in 8th grade level which is based on the concepts learnt in 7th grade and 8th grade students’ effort to correlate that concepts with new ones by re-questioning the same concepts. The results appeared as result of the data analysis regarding the second sub-problem of the study are presented in Table 3.

Table 3: t-test Results Regarding Mathematics Self-efficacy Scores of 7th and 8th Grade Students Grade Level N sd df t p 7th grade 50 50,446 9,131 95 0,327 0,744 8th grade 47 51,020 8,112

When Table 3 is analyzed, it is seen that 7th grades’ mathematics self-efficacy arithmetic mean is 50,446, standard deviation is 9,131; 8th grades’ mathematics self-efficacy arithmetic mean is 51,020 and standard deviation is 8,112. As a result of the t-test carried out for the mathematics self-efficacy of the 7th and 8th grades, a significant difference at ,05 significance level was not found. It can be said that 7th and 8th grade students are equal to each other in terms of their mathematics self-efficacies [t(95)= 0,327; p > ,05]. Although there was not a significant correlation here, when their mathematics self-efficacy averages are considered, it can be said that 8th grade students’ mathematics self-efficacy average score is higher that 7th grades. The results appeared as result of the data analysis regarding the third sub-problem of the study are presented in Table 4.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

Table 4: The Correlation between Students’ Self-efficacy Scores and Conceptual Learning R p N Value Slf-Ef./ CUTAEE 0,767 ,000 97 p < ,05 st Slf-Ef. 1 Dimension / CUTAEE 0,538 ,000 97 p < ,05 nd Slf-Ef. 2 Dimension / CUTAEE 0,520 ,000 97 p < ,05 Slf-Ef. 3rd Dimension / CUTAEE 0,417 ,000 97 p < ,05

When Table 4 is analyzed, a high level, significant and positive correlation is seen between the students’ self- efficacies and their conceptual learning (R= ,767; p < ,05). According to this, it can be said that students who have high level mathematics self-efficacies have also high level conceptual learning. Büyüköztürk (2012), defines the case as a high level correlation when the correlation coefficient is between 0,70-1,00 as an absolute value and when it is between 0,70-0,30 as a middle level correlation. The results appeared as result of the data analysis regarding the fourth sub-problem of the study are presented in Table 5.

Table 5: The Regression Analysis about Predicting Students’ Conceptual Learning according to Their Self- efficacies Slf-Ef./ CUTAEE B St. Error B Beta t p Fixed 20,425 2,664 --- 7,677 ,000 CUTAEE 1,239 0,106 0,767 11,643 ,000 R = 0,767 R2 = 0,588 F(1-95) = 135,557 p = ,000 p < 0,05 Slf-Ef. 1st Dimension / CUTAEE B St. Error B Beta t p Fixed 0,987 1,563 --- 6,275 ,000 CUTAEE 0,388 0,062 0,538 6,220 ,000 R = 0,538 R2 = 0,289 F(1-95) = 38,688 p = ,000 p < 0,05 Slf-Ef. 2nd Dimension / CUTAEE B St. Error B Beta t p Fixed 9,980 1,806 --- 5,527 ,000 CUTAEE 0,428 0,072 0,520 5,935 ,000 R = 0,520 R2 = 0,270 F(1-95) = 35,219 p = ,000 p < 0,05 Slf-Ef. 3rd Dimension / CUTAEE B St. Error B Beta t p Fixed 5,838 1,159 --- 5,037 ,000 CUTAEE 0,207 0,046 0,417 4,466 ,000 R = 0,417 R2 = 0,174 F(1-95) = 19,946 p = ,000 p < 0,05 According to the results of the regression analysis given in Table 5, it is seen that students’ mathematics self- efficacies are important predicators of their conceptual learning (R = 0,767; R2 = 0,588; F(1-95) = 135,557; p < ,05). On the other hand, when an analysis is carried out in terms of sub-dimensions of the self-efficacy scale, it can be said that the self-efficacies of the students that they developed for the so-called lesson is an important predicator of both ‘mathematics self-esteem’, ‘the awareness at behaviors in mathematics subjects’ and ‘the ability to convert mathematics into life skills’. The results appeared as result of the data analysis regarding the fifth sub-problem of the study are presented in Table 6.

Table 6: t-test Results for the Difference between Students’ Self-efficacy Scores and Their Conceptual Learning Scores by Gender Gender & Self-Efficacy N sd df t p Male 55 55,33 7,418 95 7,595 ,000 Female 42 47,74 5,897 Gender & Concept N sd df t p Male 55 26,84 4,633 95 5,840 ,000 Female 42 21,36 4,503

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

According to Table 6, there is significant difference between students’ mathematics self-efficacy levels (t(97)= 7,595; p < ,05) and their conceptual learning (t(97)= 5,840; p < ,05) by their genders and this difference is in favor of male students. In addition to that the effect sizes were also calculated together with all the relational analysis results. Because with the conducted t-test whether there is a significant difference or not is presented but it does not inform us about the size of the difference (Şengül & Dereli, 2013). For this reason, it is important to know the effect size as well as the statistical significance (Morgan, Leech, Gloeckner & Barrett, 2004). According to Cohen (1988) if ,01< ç2 < ,06 then the effect is small, if ,06≤ ç2 < ,14 then the effect is average, if ,14≤ ç2 then the effect is big. The effect size is 0,37 for the gender and mathematics self-efficacy so the effect size is big. According to this, it can be said that 37% of the variance observed in mathematics self- efficacy score depends on the gender. The effect size is 0,26 for the gender and conceptual learning so the effect size is big. According to this, it can be said that 26% of the variance observed in conceptual learning score depends on the gender.

CONCLUSION, DISCUSSION AND IMPLICATIONS

According to the research finding, it was appeared that the conceptual learning of 8th grade students is higher than 7th grade students. This finding shows us that as the grade level of students goes up, their conceptual learning also increases. It can be said that this result supports the opinion of Ausubel (1968) that knowledge is a cumulative process. It is also important in terms of showing the fact that pre-information should be properly constructed in conceptual learning.

A significant and positive correlation was found between students’ mathematics self-efficacy belief scores and their conceptual learning scores. In addition to that it was determined that students’ self-efficacy is an important predicator of their conceptual learning. This finding shows parallelism with the dimensions such as ‘mathematical self-esteem’, ‘the awareness at the behaviors in mathematics subjects’ and ‘the ability to convert mathematics into life skills’ which are the components of the conceptual achievement self-efficacy scale. This finding of the study supports the opinions of Kiemanesh, Hejazi and Esfahani (2004) that the belief of self-efficacy is also an effective precursor of the people’s mathematical achievements. Thus it is important to have students see mathematics as ‘perceivable, useful and worth dealing with’ and to provide them learning environments which will help them to study carefully and diligently. As conceptual learning and communicating by using mathematical knowledge are supported at the program of teaching mathematics in middle schools (MEB, 2012), it is also thought that it is effective to give importance to let students abstract, make correlations and infer mathematical understandings with the help of concrete experiences and to create learning environments in accordance with this purpose.

Although self-efficacy levels of 8th grade students were higher, a statistically significant difference could not be found between the self-efficacy levels of 7th grade students and theirs. This finding shows parallelism with the opinion of Israel (2007, pp. 38) that ‘ the students who perceive themselves as insufficient on certain occasions can get success by setting goals for themselves and putting more efforts even though they do not have self- confidence. Although self-efficacy, which is a belief, is directly related with the idea of ‘I am going to be successful’, it is not exactly related with having skills, experiences, understandings and information which are necessary for being successful’.

The study presents that the levels of both conceptual learning and mathematics self-efficacy of male students are higher than female students. It is thought that male students have more tendencies to choose a profession which depends on numerical studies then female students as a result of the effective role of mathematics self- efficacy in choosing a profession and the level of mathematics self-efficacy to predict mathematical concepts is effective in obtaining these findings (Şengül, 2011). This finding of the study support the results of the studies carried out by Betz and Hackett (1983) and Taşdemir (2012).

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

BIODATA AND CONTACT ADDRESSESS OF AUTHOR

Sare ŞENGÜL is an associate professor at department of Primary Mathematics Education, Atatürk Education Faculty, Marmara University, İstanbul, Turkey. Her research interests are mathematic attitude, conceptual learning, metacognition, concept cartoons, number sense and differential equations.

Assoc. Prof. Dr. Sare ŞENGÜL Department of Primary Mathematics Education Atatürk Education Faculty Marmara University İstanbu- TURKEY E. Mail: [email protected]

Yasemin KABA is an assistant professor at department of Primary Mathematics Education, Education Faculty, Kocaeli University, Kocaeli, Turkey. Her research interests are problem posing, problem solving, mathematical understanding, metacognition, RBC theory and cryptology.

Assist. Prof. Dr. Yasemin KABA Department of Primary Mathematics Education Education Faculty Kocaeli University 41380 Kocaeli- TURKEY E. Mail: [email protected] / [email protected]

Yusuf AYDIN is a professor at Faculty of Arts and Sciences, İstanbul Commerce University, İstanbul, Turkey. His research interests are problem based learning, conceptual understanding and concept cartoons.

Prof. Dr. Yusuf AYDIN Faculty of Arts and Science İstanbul Commerce University İstanbul- TURKEY E. Mail: [email protected]

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

REFERENCES

Alkan H., & Uğurel, I. (2004). Kavramsal öğrenme yaklaşımına, günümüz öğrenme araçlarını kullanarak örnek oluşturma: Fonksiyon kavramı. VI. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi: İstanbul.

Ausubel, D. (1968). The psychology of meaningful verbal learning. New York: Grane and Stratton.

Baki, A., & Kartal, T. (2002). Kavramsal ve işlemsel bilgi bağlamında lise öğrencilerinin cebir bilgilerinin değerlendirilmesi [The evaluation high school students’ algebraic knowledge with regards to conceptual and operational information]. V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi: Ankara. http://www.fedu.metu.edu.tr/UFBMEK-5/b_kitabi/PDF/Matematik/Bildiri/t211d.pdf adresinden 19.03.2008 tarihinde edinilmiştir.

Betz, N. E., & Hackett, G. (1983). The relationship of mathematics self efficacy expectations to the selection of science-based college majors. Journal of Vocational Behavior, 23, 329–345.

Bloom, S. B. (1998). İnsan nitelikleri ve okulda öğrenme [Learning at school and the qualities of human]. Çev. D. A. Özçelik, İstanbul: Milli Eğitim Yayınları.

Büyüköztürk, Ş. (2012). Sosyal bilimler için veri analizi el kitabı. Ankara: Pegem Akademi.

Cansüngü Koray, Ö., & Bal, Ş. (2002). Fen öğretiminde kavram yanılgıları ve kavramsal değişim stratejisi. G.Ü. Kastamonu Eğitim Fakültesi Dergisi, 10(1), 83-90.

Chen, P. (2002). Mathematics self-efficacy calibration of seventh graders. Unpublished doctoral dissertation, City University of New York, New York: USA.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Erlbaum.

Cooper, S. E., & Robinson, D. A. G. (1991). The relationship of mathematics self-efficacy beliefs to mathematics anxiety and performance. Measurement and Evaluation in Counseling and Development, 24(1), 4-11.

Davis, R. B. (1992). Understanding understanding. The Journal of Mathematical Behavior, 11, 225-241.

Hackett, G. (1985). The role of mathematics self-efficacy in the choice of math-related majors of college women and men: A path model. Journal of Counseling Psychology, 32, 47-56.

Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self efficacy, mathematics performance correspondence. Journal for Research in Mathematics Education, 20, 261-273.

Hung, D. (2000). Some insights into the generalizing of mathematical meanings. Journal of Mathematical Behavior, 19(1), 63–82.

İsrael, E. (2007). Özdüzenleme eğitimi, fen başarısı ve özyeterlilik. Yayınlanmamış doktora tezi, Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü: İzmir.

Kaptan, F. (1998). Fen öğretiminde kavram haritası yönteminin kullanılması. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 14, 95-99.

Karasar, N. (2003). Bilimsel araştırma yöntemi - kavramlar, ilkeler ve teknikler. Ankara: Nobel Yayınları.

International Journal on New Trends in Education and Their Implications January 2016 Volume: 7 Issue: 1 Article: 10 ISSN 1309-6249

Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In Proceedings of the Second Handbook of Research on Teaching and Learning Mathematics (pp.707–762). Charlotte: Information Age.

Kiemanesh, A. R., Hejazi, E., & Esfahani, Z. N. (2004). The role of math self-efficacy, math self-concept, perceived usefulness of mathematics and math anxiety in math achievement. Proceedings of the 3rd International Biennial SELF Research Conference, Self-Concept, Motivation and Identity: Where to from here? Berlin, Germany.

MEB. (2012). Ortaokul ve imam hatip ortaokulu matematik uygulamaları dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Ankara: Talim ve Terbiye Kurulu Başkanlığı.

Migray, K. (2002). The relationships among math self-efficacy, academic self-concept and math achievement. Unpublished doctoral dissertation, Arizona State University, Arizona,:USA.

Miles, M. B., & Huberman, M. A. (1994). An expanded sourcebook qualitative data analysis. London: Sage Publication.

Moore, N. M. (2005). Constructivism using group work and the impact on self-efficacy, intrinsic motivation and group work skills on middle-school mathematics students. Unpublished doctoral dissertation. Arizona State University, Arizona: USA.

Morgan, G. A., Leech, N. L., Gloeckner, G. W., & Barrett, K. C. (2004). SPSS for introductory statistics: use and interpretation. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. Publishers.

Randhawa, S. B., Beamer, E. J., & Lundberg, I. (1993). Role of mathematics self-efficacy in the structural model of mathematics achievement. Journal of Educational Psychology, 85, 41-48.

Stacey, K., & MacGregor, M. (2000). Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18(2), 149-167.

Senemoğlu, N. (2005). Kuramdan uygulamaya gelişim ve öğrenme. Ankara: Gazi Kitabevi.

Şengül, S. (2011). Effects of concept cartoons on mathematics self-efficacy of 7th grade students. Educational Sciences: Theory & Practice, 11(4), 2291-2313.

Şengül, S., & Dereli, M. (2013). The effect of learning integers using cartoons on 7th grade students’ attitude to mathematics. Educational Sciences: Theory & Practice, 13(4), 2509-2534.

Taşdemir, C. (2012). Lise son sınıf öğrencilerinin matematik öz-yeterlik düzeylerinin bazı değişkenler açısından incelenmesi (Bitlis ili örneği). Karadeniz Fen Bilimleri Dergisi, 2(6), 39-50.

Umay, A. (2002). İlköğretim matematik öğretmenliği programının matematiğe karşı öz-yeterlik algısına etkisi. Journal of Qafqaz University, 8. http://journal.qu.edu.az/article_pdf/1027_328.pdf adresinden 13.11.2014 tarihinde edinilmiştir.

Williams, S.E., & Molina, D. (1997). Algebra: What all students can learn. the nature and role of algebra in the k- 14 curriculum: Proceedings of a National Symposium (pp. 41-44), Washington: National Academy Press.

Zimmerman, B. J., Bandura, A., & Martinez-Pons, M. (1992). Self-motivation for academic attainment: The role of self-efficacy beliefs and personal goal setting. American Educational Research Journal, 29, 663-676.