Papers by Mustafa Cevikbas
Augmented and Virtual Reality in Mathematics Education, 2024
The use of technology in mathematics education is becoming more common, and innovative technology... more The use of technology in mathematics education is becoming more common, and innovative technology applications are gaining attention. Augmented reality (AR), virtual reality (VR) and mixed reality (MR) offer attractive and novel instructional opportunities in a variety of subjects, including mathematics. As pre- and in-service teachers play a vital role in adapting innovative and futuristic technologies for mathematics education, we analyzed the current state-of-the-art scientific developments regarding the inclusion of AR, VR and MR in mathematics education, based on the last five years of relevant research results, to identify the most prevalent developments. We examined 12 papers on the use of AR, VR and MR in mathematics education published in international peer reviewed journals, focusing on the study characteristics, research methodologies and instructional tools used studies, interventions in technology-rich environments, and the advantages and disadvantages of using AR, VR, and/or MR in teaching mathematics. The literature was systematically reviewed based on the Web of Science and SCOPUS databases. The findings showed that the analyzed papers focused mainly on AR technologies. The analysis revealed that the most frequently used software tools were Unity and Vuforia, and the most prominent digital devices were smartphones. The majority of research studies were on geometry, followed by algebra. The most prominent advantages reported were advanced visualization and increased teaching motivation, whereas the most frequently reported disadvantages were the lack of infrastructure and equipment and the need to create instructional materials. The utilization of 3D technologies in teaching mathematics facilitates enhanced visualization, heightened teacher engagement, enhanced collaborative and teamwork dynamics in mathematics instruction, and offers a versatile teaching milieu. This review reveals that positive and negative elements associated with the utilization of AR, VR, and MR technologies in the context of teaching mathematics with promising results on the improvement of the mathematics instruction. The current review also advocates for scholarly exploration within the domains of VR, MR, and XR.
Educational Studies in Mathematics, 2024
Teaching methods to promote cooperative learning may shape mathematics teachers’ roles in the cla... more Teaching methods to promote cooperative learning may shape mathematics teachers’ roles in the classroom, requiring a shift from direct supervision to delegating authority to small groups of students. While it is widely acknowledged that mathematics teachers’ beliefs play a crucial role in shaping their instructional practices and behaviors, there is limited research on how mathematics teachers’ beliefs about their professional roles influence their scaffolding behaviors in cooperative learning environments. The aim of this qualitative study is to investigate mathematics teachers’ beliefs about their roles in cooperative learning and the relationships between their beliefs and instructional scaffolding practices, which are highly important in cooperative learning environments. In this study, we investigate the teaching practices of four middle school mathematics teachers in Beijing, China, through videotaping of their teaching and semi-structured in-depth interviews. The results show that the participating in-service mathematics teachers held conflicting beliefs about their roles, oscillating between direct supervision (as specialist and controller) and delegation of authority (as observer and facilitator). These beliefs could be identified in different patterns of teacher–student interaction, including unidirectional interactions, non-scaffolding interactions, and scaffolding interactions. In this paper, we critically examine these findings and conclude with a reflection on the limitations of this study and its implications for future research and practice.
International perspectives on the teaching and learning of mathematical modelling, 2024
Researching Mathematical Modelling Education in Disruptive Times, 2024
Modelling plays a central role in various curricula, enhancing students’ real-world problem-solvi... more Modelling plays a central role in various curricula, enhancing students’ real-world problem-solving skills in mathematics education. Innovative methods, such as the flipped classroom approach, effectively boost modelling competencies, aligning with curriculum requirements. Explanatory videos, integral to the flipped classroom, enable self-paced learning in non-traditional settings. This study explores pre-service teachers’ perspectives on using explanatory videos in flipped modelling classrooms to teach modelling. It also analyses the attributes of modelling-focused videos using a self-developed framework. The results highlight pre-service teachers’ recognition of the value of videos and the effectiveness of flipped instruction in mathematical modelling. Additionally, their proficiency in creating high-quality videos indicates their adeptness in this educational context.
Modelling plays a central role in various curricula, enhancing students' real-world problem-solvi... more Modelling plays a central role in various curricula, enhancing students' real-world problem-solving skills in mathematics education. Innovative methods, such as the flipped classroom approach, effectively boost modelling competencies, aligning with curriculum requirements. Explanatory videos, integral to the flipped classroom, enable self-paced learning in non-traditional settings. This study explores pre-service teachers' perspectives on using explanatory videos in flipped modelling classrooms to teach modelling. It also analyses the attributes of modelling-focused videos using a self-developed framework. The results highlight pre-service teachers' recognition of the value of videos and the effectiveness of flipped instruction in mathematical modelling. Additionally, their proficiency in creating high-quality videos indicates their adeptness in this educational context.
ZDM-Mathematics Education, 2024
Review studies are vital for advancing knowledge in many scientific fields, including mathematics... more Review studies are vital for advancing knowledge in many scientific fields, including mathematics education, amid burgeoning publications. Based on an extensive consideration of existing review typologies, we conducted a meta-review and bibliometric analysis to provide a comprehensive overview of and deeper insights into review studies within mathematics education. After searching Web of Science, we identified 259 review studies, revealing a significant increase in such studies over the last five years. Systematic reviews were the most prevalent type, followed by meta-analyses, generic literature reviews, and scoping reviews. On average, the review studies had a sample size of 99, with the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines commonly employed. Despite certain studies offering nuanced distinctions among review types, ambiguity persisted. Only about a quarter of the studies explicitly reported employing specific theoretical frameworks (particularly, technology, knowledge, and competence models). Co-authored publications were most common within American institutions and the leading countries are the United States, Germany, China, Australia, and England in publishing most review studies. Educational review journals, educational psychology journals, special education journals, educational technology journals, and mathematics education journals provided platforms for review studies, and prominent research topics included digital technologies, teacher education, mathematics achievement, and learning disabilities. In this study, we synthesised a range of reviews to facilitate readers' comprehension of conceptual congruities and disparities across various review types, as well as to track current research trends. The results suggest that there is a need for discipline-specific standards and guidelines for different types of mathematics education reviews, which may lead to more high-quality review studies to enhance progress in mathematics education.
Systems
Despite the growing interest in the field, the overall impact of augmented reality (AR) and virtu... more Despite the growing interest in the field, the overall impact of augmented reality (AR) and virtual reality (VR) on mathematics learning remains unclear, with previous studies reporting mixed results. Moreover, to date, no systematic review has evaluated the potential of AR/VR in mathematics education, including its benefits and drawbacks for learners. To address this gap, the present systematic literature review aims to identify research trends, determine characteristics and methodologies, and explore the potential benefits and drawbacks of AR/VR technologies in mathematics learning based on existing empirical studies. In accordance with the PRISMA guidelines, we analyzed 59 peer-reviewed journal articles published in English that focused on AR/VR implementation in mathematics education. The review determined that geometry was the most widely studied topic of mathematics, with several studies focusing on the use of AR/VR to assist students with learning disabilities. The present re...
Springer eBooks, 2022
This systematic review study aims to describe the current state of the art with respect to foster... more This systematic review study aims to describe the current state of the art with respect to fostering mathematical modelling competencies. The modelling literature was searched using six reputable electronic databases and a hand-search strategy. An in-depth analysis of 44 studies demonstrated that researchers have developed, applied, or recommended multiple strategies for fostering students’ and pre-service teachers’ modelling competencies. The study’s results indicate that the following aspects were of particular importance: 1) conducting training strategies and exposing students to modelling tasks, 2) supporting students’ and pre-service teachers’ metacognitive and psychological development, 3) using digital technologies, and 4) taking advantage of the strengths of different theoretical and conceptual constructs of modelling that were supportive for modelling competency development. The majority of the reviewed studies reported that the intervention strategies used to foster modelling competencies were encouraging but not fully satisfactory, since most participants were far from attaining expertise in modelling, even after the interventions. Future research should include more databases and different competency constructs in the literature search to overcome the survey’s shortcomings.
ZDM – Mathematics Education
Lesson planning is of central importance to the teaching of all subjects in school. However, desp... more Lesson planning is of central importance to the teaching of all subjects in school. However, despite its high relevance, there is still a substantial need for a comprehensive review of factors affecting lesson planning. Empirical evidence on how teachers’ competence in lesson planning can be developed, what challenges may be encountered during the lesson planning process, and successful lesson planning designs and practices should come to light on. To close this gap the current paper presents the results of a systematic review of 20 empirical research studies on teacher competence in mathematics lesson planning. For detailed insight into the most recent contributions of the reviewed studies on mathematics lesson planning, we analyzed studies conducted during the past decade, adapting the “process model of lesson planning” and the model of “competence as continuum” as a heuristic for approaching lesson planning. We present key results of the studies related to four major themes: (1) ...
Systems, 2023
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
Frontiers in Education
Mathematical modelling is essential for teaching and learning of mathematics aimed at improving s... more Mathematical modelling is essential for teaching and learning of mathematics aimed at improving students’ competence in solving real-world problems with mathematical means. Innovative technology-rich approaches can provide new paradigms for mathematical modelling education, which may produce new opportunities for the learning and teaching of mathematical modelling. On the other hand, there may be a few challenges to the successful use of technology in modelling. Although several studies have focused on the use of digital technologies in modelling education, there is a lack of research on the educational potential of digital technologies in mathematical modelling. To close this research gap, we decided to conduct a descriptive systematic literature review on the advantages and challenges of using digital technologies for learners and instructors in mathematical modelling. The literature on mathematical modelling education was searched via three recognized databases. Literature search...
ZDM - Mathematics Education, 2023
Lesson planning is of central importance to the teaching of all subjects in school. However, desp... more Lesson planning is of central importance to the teaching of all subjects in school. However, despite its high relevance, there is still a substantial need for a comprehensive review of factors affecting lesson planning. Empirical evidence on how teachers' competence in lesson planning can be developed, what challenges may be encountered during the lesson planning process, and successful lesson planning designs and practices should come to light on. To close this gap the current paper presents the results of a systematic review of 20 empirical research studies on teacher competence in mathematics lesson planning. For detailed insight into the most recent contributions of the reviewed studies on mathematics lesson planning, we analyzed studies conducted during the past decade, adapting the "process model of lesson planning" and the model of "competence as continuum" as a heuristic for approaching lesson planning. We present key results of the studies related to four major themes: (1) dispositions and their influence on developing and implementing lesson plans, (2) quality aspects of lesson plans and the development of lesson planning skills, (3) difficulties in lesson planning, and (4) the relationship between lesson planning skills and performance in implementation of lesson plans. The results of our literature review reveal that teachers (especially novice teachers) face difficulties in lesson planning and their overall competence (and knowledge) are not at an expert level. However, as the results of the examined studies pointed out, teachers can acquire such competence and knowledge through training within initial teacher education and professional development. Overall, teachers need support in planning mathematics lessons by delineating their lesson plan to improve their awareness of students' thinking, possible learning trajectories, effective usage of the curriculum and teaching resources, and the potential of innovative pedagogies that incorporate new technology.
Frontiers in Education, 2023
Mathematical modelling is essential for teaching and learning of mathematics aimed at improving s... more Mathematical modelling is essential for teaching and learning of mathematics aimed at improving students' competence in solving real-world problems with mathematical means. Innovative technology-rich approaches can provide new paradigms for mathematical modelling education, which may produce new opportunities for the learning and teaching of mathematical modelling. On the other hand, there may be a few challenges to the successful use of technology in modelling. Although several studies have focused on the use of digital technologies in modelling education, there is a lack of research on the educational potential of digital technologies in mathematical modelling. To close this research gap, we decided to conduct a descriptive systematic literature review on the advantages and challenges of using digital technologies for learners and instructors in mathematical modelling. The literature on mathematical modelling education was searched via three recognized databases. Literature search revealed 38 papers that were eligible for analysis. Based on empirical evidence, this paper describes the educational opportunities offered by digital technologies (e.g., academic, emotional/psychological, cognitive, social, and instructional/ pedagogical enhancements) and challenges to their effectiveness (e.g., learners' and instructors' lack of competence or experience in using technology and "black-box" threats). The results of the study reveal that the advantages of the use of digital technologies in the modelling process outweigh the emerging challenges, which is a promising result discussed in detail.
Sustainability
Flipped classroom (FC) is a widely accepted, innovative pedagogy designated to enhance students’ ... more Flipped classroom (FC) is a widely accepted, innovative pedagogy designated to enhance students’ learning by changing the paradigm of instruction. It has the potential to adapt learning to the students’ needs, interests, and mutual expectations by using the advantages of both online and face-to-face learning, which strengthens the quality of the instruction. The potential of FC to foster personalized learning (PL) has become vital in education, as individuals face different possibilities and difficulties in the learning process. To date, no systematic review study has focused on the ways in which PL occurs in FCs and the role of personalized FCs in education. The present study aims to close this gap by exploring the value of flipping instruction and strategies to support PL. We searched the literature, focusing on peer-reviewed research studies published in English that focus on PL in FCs. The key results include (a) the study characteristics, (b) the approaches developed and used i...
Bu çalışmanın amacı, ters-yüz sınıf modeli uygulamalarına dayalı bir matematik sınıfındaki öğrenc... more Bu çalışmanın amacı, ters-yüz sınıf modeli uygulamalarına dayalı bir matematik sınıfındaki öğrenci katılımının incelenmesidir. Bu amaç çerçevesinde TYSM'nin öğrenci katılımının davranışsal, duyuşsal ve bilişsel boyutları üzerindeki rolü araştırılmıştır. Bunun yanında öğrenci katılımı üzerinde önemli rolü olan TYSM uygulamalarının neler olduğu konusunda bir inceleme yapılmış ve öğrenci katılımının artırılması için TYSM uygulamalarının nasıl geliştirilebileceğine ilişkin katılımcı görüşleri alınmıştır. Çalışma, nitel araştırma yöntemlerine uygun olarak durum çalışması şeklinde tasarlanmıştır. Araştırmanın durumunu, onuncu sınıf kademesinde TYSM'nin uygulandığı tek bir sınıf, analiz birimini ise öğrenci katılımı oluşturmaktadır. Araştırmanın katılımcılarını 2015-2016 eğitim-öğretim yılında Ankara ilindeki bir Anadolu Lisesi'nde öğrenim gören 33 onuncu sınıf öğrencisi oluşturmaktadır. Araştırmanın katılımcılarının belirlenmesinde ölçüt örnekleme yöntemine başvurulmuş ve katı...
ZDM – Mathematics Education
Educators sometimes effect changes in education through the implementation of new ideas, and some... more Educators sometimes effect changes in education through the implementation of new ideas, and sometimes extraordinary circumstances force them to change their educational approaches, as during the COVID-19 crisis. Although we live in a digital age, the limited use of technology in education, particularly prior to the COVID-19 pandemic, and teachers’ insufficient experience with online or hybrid learning and teaching approaches resulted in several countries being unprepared for education during the pandemic. The flipped classroom (FC) is an innovative pedagogy with the potential to engage students in mathematics education using hybrid education combined with online and face-to-face learning, which is especially important during a pandemic. However, despite the high expectations surrounding this innovative approach, to date, no systematic literature review has discussed the opportunities and pitfalls of FCs in mathematics education regarding pandemic-related issues. In the present syst...
International Journal of Science and Mathematics Education, 2021
Many students are becoming increasingly disengaged in school, particularly in mathematics. This i... more Many students are becoming increasingly disengaged in school, particularly in mathematics. This is an important problem as lack of engagement may threaten students’ achievement and performance in mathematics. A flipped learning pedagogy, which encourages students to take an active role in learning mathematics, has become a widely researched topic in recent years. However, few empirical studies to date have focused on the influence of flipped learning on student engagement in secondary mathematics classrooms. This qualitatively oriented study aimed to extend existing research on the role of flipped learning in behavioral, cognitive, and emotional engagement by adopting a social constructivist perspective to examine a secondary mathematics classroom. The participants were 33 high school students and their mathematics teacher, from whom data were gathered using multiple empirical methods. The results indicate that a flipped learning pedagogy has the potential to play a positive role in...
ZDM, 2020
Innovative methods can change the paradigm of teaching mathematics and inspire teachers to espous... more Innovative methods can change the paradigm of teaching mathematics and inspire teachers to espouse new ideas and gain new experiences. The flipped classroom (FC) is currently an innovative pedagogical approach that has high potential to transform the teaching of mathematics. In the case study described in this paper, we investigated one mathematics teacher’s transformation of teaching in two mathematics classrooms through implementing interventions based on FC methods; furthermore, we identified several key points of FC design as well as challenges and opportunities afforded by teaching mathematics in FCs. The results of the study showed that the tasks posed by the teacher, the implemented discourse, teacher feedback and scaffolding, and the teaching–learning environment were changed in FCs, although the approaches used by the teacher to analyze the tasks and students’ learning were similar to those used in non-FCs, which points out the strengths of traditional teaching approaches. ...
Mathematics, 2021
Task design constitutes a growing core of research in mathematics education. In particular, task ... more Task design constitutes a growing core of research in mathematics education. In particular, task design in Dynamic and Interactive Mathematics Learning Environments (DIMLEs) has become very popular, although it remains under-researched. This study aims to systematically analyze the current state of research on task design in DIMLEs. The literature was searched through the Web of Science, and 10 articles were included in the review. Results show that the majority of research studies were undertaken in Asia, with a focus on secondary and higher education. Studies used design-based research, case study, and grounded theory. Most studies were carried out in the domain of geometry, followed by algebra and calculus. Most researchers used GeoGebra as a DIMLE. The studies used different frameworks and contributed to the literature by developing and testing design principles, problematizing task design, and extending existing frameworks. There are also some reported challenges concerning tas...
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Papers by Mustafa Cevikbas
kitabın yeni basımının çıkarılmasındaki en önemli etken ilk versiyonun genişletilmek
istenmesidir. Bununla birlikte, önceki baskıları okuyan okuyucuların birçoğu kitabın
kısa ve öz oluşunu takdir ettiklerini ifade etmişlerdi. Bu basımda, bu avantajı kaybetmek
istemedim. Dolayısıyla bu basımdaki yeniliklerin büyük bölümü ikinci bir tez önerisi
örneğini de (Ek B) kapsayan öğrencilerimin çalışmalarından örnekler içermektedir.
Diğer bir etken, nitel bir araştırmanın1 nasıl yapılacağı ve sunulacağına ilişkin sanat
temelli yaklaşımları da içine alan yeni yaklaşımların gelişim göstermesidir. Bu yaklaşımları
kapsamlı bir şekilde ele almak istemedim, aksi hâlde kitabın hacmi bir hayli
artmış olacaktı. Dolayısıyla kitabın ilk hâlinden daha kapsamlı olmasını fakat fazla da
uzun olmamasını istedim. Bu yeni yaklaşımlara ilişkin gelişmeleri araştırmak isterseniz
Encyclopedia of Qualitative Research (Nitel Araştırma Ansiklopedisi) (Given, 2008),
Handbook of Qualitative Research (Nitel Araştırma El Kitabı), 4. Basım (Denzin & Lincoln,
2011) ve Qualitative Inquiry (Nitel Araştırma) dergisi güzel bir başlangıç olur.
Bölüm 1’de ve Bölüm 3’te tasarım yaklaşımımı bu gelişmelerin bazıları ile özellikle
de postmodernizm unsurları ve brikolaj olarak bilinen yaklaşım ile nasıl uyumlu gördüğümü açıklamaya çalıştım ve Bölüm 2’de araştırma paradigmalarına ilişkin yapılan
tartışmaları önemli ölçüde genişlettim ve yeniden düzenledim. Bununla birlikte, araştırmamızın anlamlandırmaya çalıştığı herhangi bir gerçekliğin varlığını inkâr eden ve çalıştığımız olgu ile araştırma sonuçlarımız arasında bir ilişki olduğuna işaret eden herhangi bir geçerlik kavramını (ya da bağlantılı terimleri) kabul etmeyen yaklaşımları benimseyen bu gelişmelerin bazılarından özellikle de radikal yapılandırmacı
ve göreceli yaklaşımdan kuşku duyuyorum. Nesnel ya da mutlak gerçeklik
iddiasında bulunmamakla birlikte her teori ve sonucun bizim yorumlamamız olduğuna
inandığım için yeterince postmodernist olmama ve Bölüm 2’de hiçbir teorinin çalıştığımız
şeylerin tüm karmaşıklığını yansıtamayacağını ileri sürmeme rağmen, içinde yaşadığımız
fiziksel, sosyal ve kültürel dünyayı daha iyi anlama hedefinden ya da bu olgular
için inandırıcı açıklamalar oluşturma imkânından vazgeçmeyi kabul etmem.
Bu durum, bu kitabı yeniden gözden geçirmemdeki üçüncü uyarana dayanır: nitel
araştırmaya bakış açımın çalıştığım şeylere ilişkin bir felsefi gerçekçilik tarafından nasıl
canlandırıldığı konusunda gittikçe artan farkındalığım. Bu bakış açısını, üstlendiğim
eleştirel ve gerçekçi pozisyonun yalnızca çok sayıdaki nitel araştırmacının esas yaptıkları
uygulamalar ile uyumlu olmadığını aynı zamanda bu araştırmacıların karşılaştıkları
birtakım zor teorik, metodolojik ve politik meselelerde araştırmacılara yardımcı olma
konusunda değerli olduğunu öne süren A Realist Approach for Qualitative Research (Nitel
Araştırmaya Realist Bir Bakış Açısı) (Maxwell, 2011b) isimli kitabımda uzun uzadıya
ele alarak geliştirdim. Bununla birlikte, bu bakış açısını nitel araştırma için tek bir doğru
paradigma olarak değil ama diğer bakış açıları arasında yararlı bir bakış açısı olarak öneririm.
Yazma öğretimi ile uğraşan Peter Elbow’un da (1973, 2006) iddia ettiği gibi hem
avantajları hem de bozuklukları ya da kör noktaları görmeye çalışarak karşılaştığınız
herhangi bir teori ya da durumla birlikte hem “inanma oyununu” hem de “şüphe etme
oyununu” oynamak önemlidir. Bu sebeple, bu kitabın öğrenciler ve ele alınan konulara
ilişkin çeşitli roller üstlenen araştırmacılar için pratik olarak faydalı olmasını istiyorum.
Burada geliştirdiğim nitel araştırma tasarımı modeli bir dizi felsefi bakış açısı ile bağdaşmaktadır ve bunun yaygın olarak pek çok nitel araştırma için uygulanabileceğine
inanıyorum. Eleştirel realist bir bakış açısının olası sonuçları konusunda daha fazla farkındalığa sahip olmam kitabın diğer bölümlerini genişletmeme ya da kitabı tekrar elden geçirmeme neden oldu -özellikle Bölüm 3’te bulunan teori tartışması; Bölüm 4’te bulunan araştırma sorularını geliştirme (ve yeniden gözden geçirme); Bölüm 5’te bulunan araştırma ilişkileri ve araştırma etiği, görüşme sorularını geliştirme ve veri analizi; Bölüm 6’da bulunan geçerlik kavramı ve Bölüm 7’de bulunan bir araştırma önerisindeki alanyazın taramasının içeriği ve uygun işlevleri. Aynı zamanda, ifadelerimi daha açık hâle getirme çabası içerisinde kitabın dilini düzeltmeye çalıştım. Kitabın sizin için nasıl daha faydalı olabileceği konusunda verebileceğiniz dönütler için minnettar olacağım.
Son olarak kitabı gözden geçirirken önceki basımlarda nitel araştırmayı nasıl tanımladığıma dair neredeyse açık açık hiçbir şey söylemediğimin farkına vardım; bu, nitel bir yaklaşım için en gerekli gördüğüm şeydir. Bölüm 2’de, bu konu hakkında daha çok açıklama yaptım. Bununla birlikte nitel araştırma için kısa bir tanım şu şekilde olurdu: 1) Çalıştığınız insanların anlayış ve bakış açılarını fark etmenizi, dünyayı kendi bakış açınız
yerine onların bakış açısından görmenizi sağlayan, 2) bu bakış açılarının onların fiziksel,
sosyal ve kültürel ortamları tarafından nasıl şekillendiğini ve bunların o ortamları nasıl
şekillendirdiğini gösteren ve 3) bu olgu ve ilişkileri değiştirmeye ve sürdürmeye ilişkin
süreçleri daha iyi anlamanıza yardım etmek için yapılan araştırmalardır. Nitel araştırmanın
bu üç yönü, özellikle de sonuncusu, çalışılan olguyu değişkenler açısından görmeye
dayanan çoğu nicel araştırma yaklaşımlarıyla çelişir -çeşitlilik gösteren şeylerin
özellikleri ve bu sebeple bağlamlar üzerinden karşılaştırılır ve ölçülür (değişken ve süreç
düşünme arasındaki farkı Bölüm 2, Bölüm 3 ve Bölüm 4’te ele aldım). Nitel araştırmanın
daha bariz yönlerinin çoğu ile karşılaştım; bunlar, nümerik verilerden ziyade yazımsal
ve görsel verilere dayanır ve tümevarımsal, açık uçlu yaklaşımlardır ve temel hedefi
insanlar ve ortamlar üzerinden genellemelere ulaşmak değil, nitel araştırmanın üç ana
özelliğinden dolayı belirli anlamlardır. (Bu konuların daha detaylı bir tartışması için bk.,
Maxwell, 2011b.)
Kitabın bu basımında emeği geçen herkese teşekkür etmek istiyorum. Bilhassa George
Mason Üniversitesinde bulunan öğrencilerime, özellikle de çalışmalarını kitapta
örnek olarak sunmama katkıda bulunanlara, eserin son hâlinin ortaya çıkmasında bir
hayli katkı sunan SAGE’in editöryal kadrosuna, özellikle de benim editörüm Vicki
Knight ve Kalie Koscielak, Codi Bowman, Libby Larson, Nicole Elliot ve Amanda
Simpson’a ve eseri daha iyi bir hâle getirmek için gözden kaçırdığım hususları
görmem noktasında dönütlerinden yararlandığım bu basım öncesinde hazırlanan taslak
metnin hakemlerine teşekkür ederim:
David Carlone, North Carolina Üniversitesi, Greensboro
Sharon L. Caudle, Texas A&M Üniversitesi
Joseph W. Check, Massachusetts Üniversitesi, Boston
Paula Dawidowicz, Walden Üniversitesi
Mary S. Enright, Capella Üniversitesi
Deborah Gioia, Maryland Üniversitesi, Baltimore
Gaetane Jean-Marie, Oklahoma Üniversitesi
David M. Kleist, Idaho Devlet Üniversitesi
William B. Kline, Mississippi Üniversitesi
Elizabeth Bussman Mahler, EdD, Northeastern Üniversitesi
Eliane Rubinstein, Avila Üniversitesi, Arizona
Anastasia P. Samaras, George Mason Üniversitesi
Ning Jackie Zhang, Florida Merkez Üniversitesi
Not
1. Bazı nitel araştırmacılar, “araştırma (research)” terimi yerine “sorgulama (inquiry)”
terimini kullanmayı tercih ediyorlar ve “araştırma” terimini nicel veya pozitivist
yaklaşımlarla yakından ilişkili olarak görüyorlar. Bu konudaki kaygılarına katılıyorum
(bk. Maxwell, 2004a, 2004b) ve nitel araştırmaların bazı tiplerinin bilimselden daha çok
hümanistik olduğunu anlıyorum fakat ben, bir dizi nitel yaklaşımı içeren “araştırma”
teriminin daha kapsamlı bir tanımını kullanmayı tercih ediyorum.
The purpose of this study was to analyze the preservice mathematics education teachers’ engagement with different representations while they were solving mathematical problems in dyads. We conducted task-based interviews with ten preservice teachers’ who worked in pairs to identify the geometric locus of points in the context of plane geometry. In order to observe preservice teachers’ possible interaction with different representations of mathematical concepts, we provided the pairs with plain papers, pencils, graph papers, geometric tools like ruler, protractor and pair of compasses, and a computer with access to a free Dynamic Geometry Software called Geogebra.
Findings reveal that preservice mathematics education teachers’ had a tendency to use graphical representations, both pencil drawn on paper and constructed by Geogebra, instead of symbolic or notational representations. Their interaction during the interviews showed that they were convinced with the usage of graphical representations while they were analyzing data, making conjectures, constructing arguments, and justifying assertions. They did not need to use algebraic representations encapsulating the formal mathematical language as long as they provided valid warrants based on graphical representations. They had also some difficulties in engaging with algebraic representations when they were intervened with interview questions to do so. We believe that sharing preservice mathematics education teachers’ interaction with both each other and different forms of representations will contribute the research in mathematics education by helping to understand the complex nature of mathematical learning.