Ayhan Kursat Erbas

Ayhan Kursat Erbas
Middle East Technical University | METU · Department of Mathematics and Science Education

Ph.D., Mathematics Education, University of Georgia

About

84
Publications
72,929
Reads
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818
Citations
Additional affiliations
November 2015 - present
Middle East Technical University
Position
  • Professor (Full)
Education
August 1999 - August 2004
University of Georgia
Field of study
  • Mathematics Education
September 1997 - June 1999
Middle East Technical University
Field of study
  • Mathematics Education
September 1995 - June 1997
Middle East Technical University
Field of study
  • Mathematics

Publications

Publications (84)
Article
We investigated and compared sociomathematical norms in secondary mathematics teachers’ classrooms before and after using mathematical modeling activities. Participants were four secondary mathematics teachers. The data included 104 h of videotaped classroom observations and teacher interviews. The data analysis revealed notable changes in sociomat...
Article
This study aimed to investigate secondary mathematics teachers’ noticing of stu- dents’ mathematical thinking in the context of a professional development (PD) program utilizing modeling-based teacher investigations. The PD program was con- ducted with two groups of mathematics teachers from two public high schools. It included seven 1-month-long...
Article
This study investigated pre-service secondary mathematics teachers’ (PSMTs’) anticipation and identification of students’ thinking as they engaged in examining and analyzing student work on four modelling problems. The study comprised four two-week-long cycles. The data were collected through individual reflection papers and written group reports o...
Article
Full-text available
Genc, M., & Erbas, A. K. (2020). Secondary mathematics teachers’ conceptions of the barriers to the development of mathematical literacy. International Journal for Mathematics Teaching and Learning, 21(2), 143-173. The purpose of this study was to investigate secondary mathematics teachers’ conceptions of the barriers to the development of mathema...
Article
Full-text available
Genc, M. & Erbas, A. K. (2019). Secondary Mathematics Teachers‘ Conceptions of Mathematical Literacy. International Journal of Education in Mathematics, Science and Technology, 7(3), 222-237. The purpose of this study was to investigate secondary mathematics teachers‘ conceptions of mathematical literacy, which are important to consider when is es...
Article
Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers’ ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented...
Article
The purpose of this study was to examine the potential interrelationships between teachers’ mathematical knowledge for teaching (MKT) the function concept and their students’ learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers a...
Conference Paper
As part of a larger project aiming to develop a framework of competencies for mathematics teacher educators by utilizing a Delphi approach, the purpose of this study was to investigate what a group of experts think about the competencies that mathematics teacher educators should possess. The data were collected in a workshop with 10 experts coming...
Article
Asking effective questions has been considered to be one of the most important indicators of good teaching since questioning is an important instructional tool and the ability to ask effective questions requires sophisticated pedagogical reasoning. Teachers can facilitate students’ higher-level thinking through effective questions. However, teacher...
Article
Full-text available
This study presents a methodology for investigating teacher learning in and from practice based on discourses that are in constant flux and transformation. Conceptualizing teacher learning as a frame of meaning based on knowing and doing discourses, the ideas are illustrated through data collected from a secondary mathematics teacher conducting an...
Article
Full-text available
As a part of a larger study aiming at developing pre-service teachers’ pedagogical knowledge about mathematical modeling, this study investigates pre-service elementary mathematics teachers’ ways of thinking regarding rate of change in the context of a modeling task on population growth. The participants of the study were 9 prospective middle schoo...
Article
Full-text available
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future cla...
Article
Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage...
Article
Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students‟ mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers‟ knowledge to use modeling in mathematics education and how...
Article
The purpose of this study is to assess preservice teachers’ mathematical knowledge for teaching statistics (MKT-S) and identify the relationship between the components of this knowledge. For this purpose, MKT-S instrument consisting of two dimensions, ‘content knowledge’ (CK) and ‘pedagogical content knowledge’ (PCK) was developed, and applied to 6...
Conference Paper
Full-text available
The purpose of this study is to analyze the effects of using geometric figures for teaching identities in the form of (ax+b) n by the method of modelling on the success of students, as well as examining the opinions of students received within this framework. The study was conducted with 53 first year students selected by the method of convenience...
Article
Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies...
Article
Full-text available
Bu çalışmanın amacı, modelleme etkinlikleri bağlamında öğrenci çalışmalarını inceleyerek öğrencilerin düşünme biçimlerindeki hatalarını tespit eden lise matematik öğretmeni adaylarının, öğrencilerin bu hatalarına yönelik ne tür pedagojik yaklaşımlar sergilediklerini araştırmaktır. Çalışmanın verileri araştırmaya katılan 7 matematik öğretmen adayıyl...
Article
Full-text available
Researchers point out the importance of teachers’ knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students’ ways of thinking. This study investigated prospective secondary mathematics teachers’ interpretations of students’ thinking as manifested in students’ work that em...
Chapter
Full-text available
Bu bölümde matematik eğitiminin önemli araştırma alanlarından biri olan matematiksel modellemeye yönelik teorik yaklaşımlar ele alınmaktadır. Matematiksel modellemenin eğitimde kullanımına ilişkin ortak bir anlayış olmamakla birlikte, akademik çalışmalarda yaygın olarak kullanılan yaklaşımlar odaklanılan öncelikli öğretim hedefi kapsamında iki grub...
Book
Günlük Hayattan Modelleme Soruları; öğretmenler, öğretmen adayları, öğrenciler, günlük hayatta matematiği arayanlar ve matematiğe ilgi duyan herkes için bir kaynak kitap niteliğinde hazırlandı. “Günlük Hayattan Modelleme Soruları” kitabıyla; matematiği kendi içinde ve farklı disiplinlerle ilişkilendirme, matematiksel dili ve terminolojiyi kullanma,...
Article
The purpose of this study was to investigate the extent to which personality traits, motivation, academic risk-taking, and metacognition explain the mathematical creative ability of high school students. The participants were 217 9th-grade students that were exceptionally high achievers. The participants responded to a set of measures about persona...
Article
Full-text available
Awareness for and knowledge of students’ ways of thinking is an important component of teachers’ competence that should be gained before starting their career. The purpose of this study was to investigate pre-service secondary mathematics teachers’ views regarding the role of examining students’ work in understanding students’ ways of thinking with...
Article
Full-text available
This study attempts to investigate the performance of tenth-grade students in solving quadratic equations with one unknown, using symbolic equation and word-problem representations. The participants were 217 tenth-grade students, from three different public high schools. Data was collected through an open-ended questionnaire comprising eight symbol...
Article
The purpose of this study was to explore the effect of a technology-supported learning environment utilizing an interactive whiteboard (IWB) and NuCalc graphing software compared to a traditional direct instruction-based environment on student achievement in graphs of quadratic functions and attitudes towards mathematics and technology. Sixty-five...
Article
The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up, model-eliciting,...
Article
Full-text available
The purpose of this study was to investigate three second-year graduate students’ awareness and understanding of the relationships among the “big ideas” that underlie the concept of derivative through modeling tasks and Skemp’s distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up, model-eliciting,...
Conference Paper
Full-text available
Kovaryasyonel düşünme; fonksiyon, türev ve değişim oranı gibi matematiksel kavramların anlaşılması için önemli olup iki farklı niceliğin eş zamanlı değişiminin koordineli bir şekilde incelenmesini ifade eden bir kavramdır (Carlson, Larsen ve Lesh, 2003; Zeytun, Çetinkaya ve Erbaş, 2010). Kovaryasyonel düşünmede grafiksel temsillerin doğru oluşturul...
Article
Full-text available
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and...
Article
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and...
Chapter
Matematikteki temel öğrenme alanlarından biri olan Analizin (Calculus 1 ) en büyük hedeflerinden biri değişen nicelikleri, durumları ve olguları anlamak, yorumlamak ve ileriye yönelik tahmin ve hesaplamalarda bulunabilmektir. Bu hedeflere ulaşmada kullanılan en önemli yapı taşı ise analiz alanının temel kavramlarından olan türevdir. Türev, değişen...
Chapter
As teachers prepare to teach the Common Core State Standards for Mathematics (CCSSM), students’ exploration of patterns and relationships between numbers has gained more importance. Specifically, students’ conceptual understanding of numerical patterns is critical in middle school, as it lays a ground work for fostering mathematical thinking at all...
Article
The present study aimed to investigate students’ understanding of the function concept and their ability to classify relations as functions and non-functions. The participants of the study were 130 tenth grade industrial vocational high school students. The data were collected through a two-part test and semi-structured interviews with ten students...
Article
Problem statement: Contemporary global environmental problems have highlighted the importance of acting responsibly towards natural resources and the environment. The role of science education in shaping how people interact with the environment, therefore, has gained importance. The science education community has responded to this challenge by hel...
Article
The purpose of this study was to investigate the problem solving strategies, problem solving episodes, and metacognitions of five Turkish high school freshmen and explore the interplay of these on their problem solving success in mathematics. Participants worked on ten problems selected among the released mathematical literacy items used in Program...
Article
The purpose of this study was to investigate the effects of using a dynamic geometry environment (DGE) together with inquiry-based explorations on the sixth grade students’ achievements in polygons and congruency and similarity of polygons. Two groups of sixth grade students were selected for this study: an experimental group composed of 66 student...
Article
Full-text available
Teaching efficacy beliefs have attracted researchers' attention in recent decades because of its close association with and potential impact on the implementation of new ideas and skills in education. In the present study, we have explored the psychometric properties and construct validity of the Turkish adaptation of the Mathematics Teacher Effica...
Conference Paper
Full-text available
This study examined 10 th grade students' procedures for solving quadratic equations with one unknown. An open-ended test was designed and administered to 113 students in a high school in Antalya, Turkey. The data were analyzed in terms of the students' foci while they were answering the questions. The results revealed that factoring the quadratic...
Article
The purpose of this study is to describe teachers' knowledge about their students' algebraic thinking and to determine to what extent this knowledge essentially reflects students' ways of thinking. Three mathematics teachers and their 49 ninth grade students were selected as participants. In this study, students' algebraic thinking was determined t...
Article
Full-text available
The purpose of the study was to investigate students’ perceptions of the concept of functions in vocational high schools on industry. The participants were tenth grade students (n = 11) studying in the department of Computer Technology and Electrics and Electronics. A 10-item diagnostic test was designed to assess students’ understanding of the con...
Article
To take its due place in the world of education, Turkey has been through serious reform initiatives in the curriculums of various school subjects since 2003. The new Turkish elementary school curriculum was prepared considering the research studies conducted in Turkey and in other countries, as well as the educational systems of developed countries...
Article
Various studies suggest that covariational reasoning plays an important role on understanding the fundamental ideas of calculus and modeling dynamic functional events. The purpose of this study was to investigate a group of mathematics teachers' covariational reasoning abilities and predictions about their students. Data were collected through inte...
Article
Various studies suggest that covariational reasoning plays an important role on understanding the fundamental ideas of calculus and modeling dynamic functional events. The purpose of this study was to investigate a group of mathematics teachers' covariational reasoning abilities and predictions about their students. Data were collected through inte...
Article
The study investigates the effects of certain school characteristics on students’ mathematics performances in Turkey in the PISA 2006 while controlling for family background and demographic characteristics. Three models of Hierarchical Linear Modeling (HLM) are constructed. The results reveal that 55% of the variance is attributable to between-scho...
Article
The purpose of this study was to investigate student difficulties, common errors and misconceptions in solving simple linear algebraic equations within a group of students (n = 217) from four different schools. The results suggest that the students in lower achievement groups have conceptual problems and mal-rules, some of which might be considered...
Article
Full-text available
Problem Statement: International studies, such as the repeat of Trends in International Mathematics and Science Study and Programme for International Student Assessment, have shown that the mathematics achievements of Turkish students are lower than the international average. Geometry is an area of particular weakness. The use of dynamic computer e...
Article
The purpose of this study was to investigate the regional differences in students' awareness, perception, optimism and responsibility development toward environment. The data used for the study was obtained from the one produced by the Programme for International Student Assessment (PISA) 2006 and comprised of the Turkish sample of 4942 fifteen yea...
Article
Full-text available
Öğrencilerin temel cebirsel kavram ve işlemleri anlaması ve kullanması üzerine olan literatür, farklı okul ve sınıf seviyelerinde öğrencilerin birçok güçlüklerinin ve yanılgılarının olduğunu göstermektedir. Bu çalışmada, dört farklı okuldan bir grup öğrencinin (n = 217) basit doğrusal denklemlerin çözümünde karşılaştıkları güçlükler, yaptıkları ort...
Article
Full-text available
The mathematics education curriculum in Turkey is in the midst of a period of intensive reform. This article investigates the extent to which teachers implement the updated 6th grade mathematics curriculum through their self-reports and if there level of use differs according to the province where the school is located, teachers' gender, level of e...
Article
Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. It is particularly effective when students are encouraged to explore a single mathematics problem with multiple technologies. Using technology allows students to be creative in their problem-solving techniques, look at data in a variety...
Article
Ülkemizde ö�renci ba�arılarına yönelik uluslararası kar�ıla�tırmalı çalı�malar, ö�retim programlarını, ö�retmen yetkinliklerini de�erledirmeye yönelik incelemeler, neredeyse yok denecek kadar, azdır. Bu çalı�mada, uluslararası ö�renci ba�arısını belirlemeye yönelik Kassel Projesi Cebir Testi (KaPAT) 1997-98 ö�retim yılının son haftasında Ankara’nın...
Article
Full-text available
The use of technology provides an effective way for promoting multiple representations in problem solving and mathematics. Multiple representations allow students to experience different ways of thinking, develop better insights and understandings of problem situations, and increase comprehension about mathematical concepts. Even with all the benef...
Article
Full-text available
The purpose of this paper is to review the current state of doctoral programs in mathematics education in Turkish universities. In this context, this paper first provides brief background information about Turkish higher education system and teacher education policies. Then the major national initiatives towards future faculty development efforts a...
Article
ZET Teknoloji tabanlı yaklaşımlar öğrencilere verileri inceleyerek örüntüleri saptamaları yoluyla varsayımlar formüle etmeleri ve sonrasında bunları test ederek sonuçlar çıkarmaları ve bu sonuçların değişik şartlardaki anlamlılığını saptayarak genellemelerde bulunmalarına izin vermektedir. Öğrenciler teknoloji ile varsayımlarını doğrulamak için sem...
Article
Full-text available
Yapılan birçok çalışma göstermiştir ki, değişik okul ve sınıf düzeylerinde öğrencilerin temel Cebir kavramları (eşitlik çözümü, cebirsel ifadelerin kullanımı, problem çözme, ve değişken gibi birtakım temel cebir kavramlarını anlama) ile ilgili zorluk ve yanılgıları vardır. Bu çalışmada incelenen araştırma problemi, farklı okullardan bir grup Türk ö...
Article
Bu çalışmanın amacı, lise matematik öğretmenlerinin, öğrencilerinin cebirsel düşünme yapıları hakkındaki bilgi ve düşüncelerini ortaya çıkarmak ve bu bilginin gerçekte öğrencilerin düşünme yapılarını ne ölçüde yansıttığını belirlemektir. Araştırmanın katılımcıları, 49 dokuzuncu sınıf öğrencisi ve 3 matematik öğretmenidir. Çalışmada ilk olarak öğren...

Projects

Projects (2)
Archived project
The project was supported by the Turkish Scientific and Technical Research Institution (TUBITAK) to study the role of mathematical modeling in pre-service and in-service (secondary) mathematics teacher education. The purpose of this project was threefold: (i) to develop mathematical modeling tasks and activities that can be used with both secondary school students and pre-service and in-service teacher education programs; (ii) to develop an in-service mathematics teacher professional development program about mathematical modeling and to investigate how the program would affect teachers’ beliefs, knowledge, and practices; (iii) to develop an academic course for pre-service mathematics teachers and investigate how the course would affect pre-service teachers’ knowledge, competencies and attitudes in terms of mathematics, mathematical modeling and using mathematical modeling in mathematics education.
Archived project