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This study aimed to investigate seventh-grade students' visuospatial thinking processes in an art studio environment, where students were engaged with geometrically rich artworks. The students were asked to observe minimalist artworks, then create and critique their own and others' artworks based on the Studio Thinking Framework. Data were collected through interviews conducted with students, video recordings in the studio, and students' documents (sketches, artworks, and notes). The data were analyzed based on previous studies on spatial thinking and emergent data. The study's findings indicate that the Studio Thinking-based environment has the potential to elicit students' visuospatial thinking processes, mainly in recognizing shapes, decomposing and composing shapes, patterning, and transforming shapes rigidly and non-rigidly (scaling). The present study, which includes accounts of three studio works, suggests an emergent framework for the characterization of visuospatial thinking within a particular art-math-related environment. The findings of the study shed light on other studies on visual arts and mathematics education and on mathematical thinking and learning in informal learning settings.

Previous research claimed that integration of augmented reality on educational settings helps to improve academic achievement of students in collaborative learning environments, as well as to improve their retention and ability to translate this within other environments. Since augmented reality is still considered relatively novel technology in educational fields, there is an inherent need for research-based guides to design effective and feasible augmented reality tools for school-based learning. The main aim of this study was therefore to design and develop an augmented reality learning toolkit to foster spatial ability in middle school students using mobile devices. The study was conducted in two parts, as preliminary research and a prototyping phase. The findings guided the characteristics for designing an augmented reality learning toolkit with a set of spatial tasks aimed at middle school students. In light of the results, it can be inferred that the students were able to use this designed toolkit to perform their spatial ability through given spatial tasks since the students encountered no technical difficulties with the final toolkit prototype, and that they were able to use the toolkit assuredly. In conclusion, the study showed that augmented reality seemed helpful in enhancing the usage of mobile devices, not just for the reading of books, communication or playing games, but also as a support mechanism for the learning of mathematics. Thus, the augmented reality toolkit developed in this study presents a new way for students and/or teachers to use mobile devices in the learning and teaching of mathematics.

In school mathematics, representations of solid figures and three-dimensional geometric objects generally rely on two-dimensional projective representation modes on students’ textbooks. In learning environments, these representation modes create a kind of cognitive filter, which prevents students with low spatial ability to comprehend and envision three-dimensional objects. Studies showed that spatial ability could be improved by means of suitable concrete models and computer created models in learning settings. Thus, fostering students’ spatial ability helps to overcome and eliminate negative effects of this cognitive filter. However, some studies suggest that this cognitive filter may even occur while working with computer created objects since computers generally rely on two-dimensional digitizer panels on screen technology. On the other hand, augmented reality interface allows a new way of learning environment which could help to overcome this cognitive filter by providing unique representation modes and opportunities to foster students’ spatial ability. In this study, an intervention with an augmented reality interface to foster students’ spatial understandings were reported in terms students’ invented strategies for spatial concepts. In this sense, eight seventh graders worked on spatial tasks with an augmented reality interface in learning settings. Findings revealed that while proceeding on spatial tasks, students could invent, use and modify spatial strategies. Moreover, students’ spatial understanding was fostered as they progressed on tasks with the designed augmented reality interface. This study is a part of an educational design research which was focused on design and development a proper augmented reality tool to foster spatial ability of students. As a result of this study, with the help of combination of augmented reality interface and spatial tasks, teachers will be provided with a new tool to visualize mathematical concepts and students could be supported with this new tool as a new learning material.

To transform the knowledge and skills they develop through teacher education programmes into successful instructional practices, preservice teachers should strongly believe in their capabilities. T...

This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.

Mathematics education literature involves studies that sought a way of investigating the mode of reasoning in mathematics textbooks because textbooks are the main resource for teachers in planning their mathematics lessons. In this vein, this study aimed to analyze the ways of reasoning in mathematics textbooks that are currently used in five countries: Slovakia, Czech Republic, Italy, Norway, and Turkiye, as a part of a Horizon 2020 Project. We initially started with a framework that aimed to examine the effect of teachers’ participation in the lesson study on the improvement of students’ mathematical reasoning (Project LESSAM). However, as the textbook analysis of different countries proceeded, we realized that this framework would not solely be sufficient to address the types of reasoning with alternative tasks presented in those textbooks. Thus, our framework development followed four main steps: (1) starting with a proposed framework that focused on different types of reasoning (2) identification of reasoning and proof tasks among worked examples, (3) categorization of ways of reasoning through the proposed framework, and (4) developing new categories based on a review of existing frameworks, to cover and differentiate all types of reasoning in the worked examples. Hence, in this study, we aim to present the integrated framework that we developed to analyze the ways of reasoning in worked examples (the problems with explained solutions) in the above-mentioned countries’ textbooks. We also discuss future research agenda for analyzing mathematics textbooks with this integrated framework.

The purpose of this study was to investigate pre-service mathematics teachers’ self-efficacy beliefs about using concrete models in teaching mathematics. Participants were 31 junior pre-service middle school mathematics teachers. Six instructional sessions based on using concrete models were carried out during a three week period. Data were collected by a survey on pre-service teachers’ efficacy beliefs about using concrete models and semi-structured interviews. Data analysis demonstrated that the instruction had positive contributions on the pre-service teachers’ self-efficacy beliefs. In addition, results revealed that pre-service teachers had confidence in themselves about using concrete models both as learners and as teachers. Moreover, they believed that using concrete models would have positive consequences in teaching process and students’ learning. However, pre-service teachers had relatively low efficacies about classroom management.

This study aimed to investigate secondary mathematics teachers’ noticing of students’ mathematical thinking in the context of a professional development (PD) program utilizing modeling-based teacher investigations. The PD program was conducted with two groups of mathematics teachers from two public high schools. It included seven 1-month-long cycles, each consisting of an introductory meeting, the teachers’ classroom implementations of a model-eliciting activity (MEA), and a follow-up meeting focusing on the teachers’ collaborative investigation and discussion of students’ written work, including their strategies to solve the MEA. Findings suggested that participating in the PD program promoted the teachers’ noticing of students’ mathematical thinking, albeit differently, over time. We elaborated on the components of the PD program that might have influenced the teachers’ noticing of students’ mathematical thinking. Implications of the findings on teachers’ noticing for researchers, PD leaders, and teacher educators are discussed in terms of potential directions for future research and practice.

Problem Durumu: Anlamli ogrenmeye elverisli kosullar saglayan, gorsellik, geri bildirim ve gozden gecirmeye imkân sunan ogretim teknolojisi ortamlarinin ogrencilerin yeteneklerini elistirmek uzere tasarlanmasini saglayan teknolojinin matematigi gercek yasamla iliskilendiren PDO’ye entegrasyonu ogrencilerin daha iyi ogrenmeleri acisindan onemlidir. Fakat teknoloji ve PDO’nun ogrenciler uzerindeki etki veya faydalarinin tum yonleriyle derinlemesine inceleyen calisma pek bulunmamaktadir. Dolayisiyla, matematik ogretiminde PDO’nun ve teknoloji kullaniminin matematik basarisina ve ogrencilerin matematik dersine yonelik tutumlarina etkisinin altinda yatan sebeplerin aciga cikarilmasi matematik ogretimi acisindan yararli olacaktir. Arastirmanin Amaci: Bu calismanin amaci Teknoloji Destekli Probleme Dayali Ogrenme Uygulamalarinin (TPU)’nun ogrencilerin matematige yonelik tutumlari ve matematik basarilari uzerindeki etkisinin altinda yatan sebepleri belirlemektir. Arastirmanin Yontemi: Buyuk olcekli bir doktora arastirmasinin (Birinci Yazar, 2017) sadece nitel kismina odaklanan bir durum calismasi olarak gerceklestirilen bu arastirmada Ogrenci Gorusme Formu kullanilarak ogrencilerle gerceklestirilen yazili ve sozlu mulakatlarin analizleri yapilmistir. Arastirmada calisma grubu; Milli Egitim Bakanligina bagli olarak birinci yazar in gorev yaptigi, sinavla ogrenci alan ve esit agirlik alaninda egitim veren bir devlet lisesinde bulunan bir 9. Sinifin ogrencileri secilmistir. Fonksiyonlar konusunun ogretiminde teknoloji destekli probleme dayali ogrenme uygulamalari (TPU) adi altinda problem cozme ve teknolojiyi kullanarak matematigin gunluk hayattaki yerini ve anlamini gorebilecekleri bir icerikte birinci yazar tarafindan hazirlanan 12 etkinlik, calisma grubu ogrencilerine birinci yazar rehberliginde uygulanmistir. Calisma grubu ogrencilerinin teknoloji destekli probleme dayali ogrenme uygulamalari hakkinda dusuncelerini ayrintili bicimde algilamak icin birinci yazar tarafindan uzman gorusleri dogrultusunda bir Ogrenci Gorusme Formu duzenlenerek 7 soru icerecek bicimde son sekli verilmistir. Birinci yazar tarafindan gelistirilen bu form kullanilarak once ogrencilerin yazili gorusleri alinmistir. Daha sonra bu yazili gorusler incelenerek kendini ifade edebilen, kiz-erkek ve matematik basarisi dengeleri gozetilerek bu ogrencilerden amacli orneklemeden olcut ornekleme yontemi ile belirlenen 12 ogrenci ile okulda ozel bir odada mulakat yolu ile TPU hakkinda detayli gorusleri alinmistir. Arastirmanin Bulgulari : Ogrencilerin matematik dersine yonelik tutumlari ile TPU’nun iliskisi “Hoslanma” ve “Kullanislilik” alt boyutlari bazinda incelenmistir. “Hoslanma” boyutu ile TPU iliskisini aciklayan sebepler asagida siralanip ilgili ogrenci gorusleri verilmistir. TPU’nun hoslanma boyutu ile iliskisini aciklayan nedenler Grup Calismasi, TPU’nun ders isleyisini kolaylastirmasi, TPU’nun kisisel becerileri gelistirmesi, kendi kendine ogrenmenin dersi akici kilmasi ve teknolojinin dersi ilgi cekici hâle donusturmesi olarak ortaya cikmistir. “ Kullanislilik ” boyutunun uygulanan TPU ile iliskisini aciklayan etmenler dersi ogrenme istegini artirmasi, matematigi sevdirmesi ve matematigin kullanisliligini gormenin ogrencilere verdigi memnuniyet olarak ortaya cikmistir. TPU ile matematik dersi akademik basarisi iliskisini aciklayan on etmen asagidaki basliklar altindaki ogrenci gorusleriyle belirlenmistir. TPU ile matematik dersi basarisi iliskisini aciklayan etmenler; grup calismasi, grup calismasinin ogrenme zorluklari, sozlu ifade etme, gorsellik, teknolojinin kabullenilmemesi, teknolojiyle daha cok duyu organlarinin kullanilmasi, gunluk hayat uygulamalarinin iliski kurmada ve anlamada kolayliga sebep olmasi, Kesfederek, uygulayarak ogrenmenin anlamli ve hizli olmasi, Teknolojinin sagladigi isleyis kolayliginin zamani ust seviyedeki dusunme becerilerinin gelistirilmesine kullanmaya imkân tanimasi ve Kendi kendine ogrenme olarak belirlenmistir. Arastirmanin Sonuclari ve Onerileri: Oncelikle calisma grubunun ogrencileriyle yapilan yazili ve yuz yuze gorusmeler, uygulanan TPU’nun ogrencilerin matematik dersine yonelik tutumlarina etkisini nasil acikladigi incelenmistir. Ogrencilerin matematik dersine yonelik tutumlari ile TPU’nun iliskisinin incelendigi iki alt boyuttan biri olan Hoslanma boyutu ile TPU iliskisini aciklayan sebepler yukarida belirtilen bes baslik altinda, diger alt boyut olan Kullanislilik boyutunun uygulanan TPU ile iliskisini aciklayan etmenler ise 3 baslik altinda incelenmistir. Calismada ogrenci goruslerinin incelendigi diger bir boyut; TPU ile ogrencilerin matematik basarilari arasindaki iliskidir. Incelenen ogrenci gorusleri sonucunda TPU ile matematik dersi basarisi iliskisini aciklayan etmenler on baslik altinda incelenmistir. Bu calismada ogrencilerin TPU’yu ilgi cekici, anlamli ve eglenceli bulduklari belirlenmisti. Dolayisiyla, ogrenme motivasyonu, ogrenen bireyin, ogrenme etkinliklerini anlamli, ilgi cekici bulmasi ve bunlardan yarar saglamasi olarak dusunuldugunde TPU’nun ogrenci motivasyonunu etkileyip etkilemedigi bir motivasyon olcegi kullanilarak nicel olarak da arastirilabilir. Bununla birlikte, ogrencilerin matematik dersi fonksiyon konusundaki basarilari ile TPU iliskisini aciklayan bir etmenin teknolojinin kabullenilmemesi oldugu ve ogrencilerin teknolojiye adapte olmakta guclukler yasadiklarindan uygulamalari benimseyemedikleri belirlenmisti. Bu yuzden TPU calismasi oncesinde ogrencilerin bilgisayar hazir bulunusluk duzeyleri veya teknolojiye yonelik tutumlari belirlenip teknolojinin ogrenciler uzerindeki etkisi teknoloji gecmisleriyle karsilastirilarak irdelenebilir. Bu calisma sadece fonksiyon konusuyla sinirli oldugundan farkli matematik konularinda ve farkli seviyelerdeki siniflarda TPU benzeri uygulamalar kullanilarak tutum ve basariya etki eden faktorler daha genis bir yelpazede irdelenebilir. Bunun yani sira, calismamizda TPU’nun ogrenciler tarafindan benimsendigi ve faydali goruldugu belirlenmisti. Bu yuzden TPU ogretmenlere veya ogretmen adaylarina ders verilip bu uygulamalari gorev yaptiklari okullarda uygulamalari saglanmasi ogrenciler acisindan faydali olabilir. Ogrenciler akilda kaliciliga iliskin goruslerinde kendilerinin kesfederek, emek sarf ederek, gunluk hayatta uygulayarak ve kullanarak kalici ogrenme gerceklestirdiklerini ifade etmislerdir. TPU’nun akilda kalicilik sagladigi gorusu nicel olarak da arastirilabilir. Anahtar Kelimeler: Matematik egitimi, Geogebra, Gunluk hayat uygulamalari, Durum calismasi.

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 problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

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 that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students' ways of thinking. The researchers' conceptual development, on the other hand, involved realizing the critical aspect of the teacher role played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.

This study investigated how prospective teachers notice student mathematical thinking in a video-based learning environment and in analyzing students’ thinking when they conduct a research in their practice schools in the scope of a 14-week elective course program. Instructional process of the course had two phases. In the first phase, a group of eight prospective mathematics teachers analysed video cases related to students’ mathematical thinking. In the second phase, they explored actual students’ mathematical thinking through diagnostic interviews in their practice schools in order to conduct a small-scale research project. The results indicated that while prospective teachers tended to be more simplistic in analysing students’ thinking in their early video-case analyses, they came up with deeper analysis of student thinking by making sound inferences from data and proposing pedagogical strategies. Moreover, prospective teachers stated that micro-case videos functioned as a catalyst for enhancing their noticing of student thinking before conducting small-scale research projects.

This research provides the instructional exploration of analytic geometry pattern based on van Hiele thinking pattern, and the potential of GeoGebra effect on experimental group along with its nested group (high and low achievers) in comparison with control group in analytic geometry. To investigate the significant effect of GeoGebra, the two match groups were constructed on their previous grade-11 mathematics records with almost equal statistical background and with the same compatibility in the biological age. Further, six-week experiments of 22 lessons were prepared and two teaching methods (tradition vs DGS aided instructions) were tested. Three hypotheses were carried out i.e. Treatment does not significantly affect, the two groups in mathematical achievement mean scores and, the higher and low achievers of the two groups in mathematical achievement mean scores. To measure the treatment effect, t-test was used by SPSS. Analyses of the research revealed that experimental group performed well, while; GeoGebra was influential in favor of low achievers in comparison to control low achievers.

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, teachers' utilization of effective and higher-level questions is usually limited in traditional settings. The goal of this study is to investigate how secondary mathematics teachers' knowledge and skills of questioning change when they are engaged in professional development activities based on the modeling perspective. The program included five cycles each of which lasted a month. Each cycle consisted of meetings before and after the implementation of a model-eliciting activity and its implementation. The results showed that the professional development program had a positive effect on teachers' ability to ask qualitatively different questions in order to move students' thinking forward.

This study examines the interrelationships among students’ motivational beliefs (i.e. achievement goal orientations, perception of classroom goal structure, and self-efficacy), use of self-regulated learning strategies (i.e. elaboration, organization, and metacognitive self-regulation strategies), and achievement in mathematics, by proposing and testing a structural model. Participants were 1,019 seventh grade students, enrolled in public elementary schools in Ankara, Turkey. Self-report questionnaires and a mathematics test were administered to participants during their regular class periods. Results revealed that students’ perception of classroom goal structure was significantly related to their adoption of achievement goals. Among achievement goals, only mastery goal orientation was significantly related to use of self-regulated learning strategies and mathematics achievement. Among self-regulated learning strategies, only elaboration was significantly related to mathematics achievement. In addition, self-efficacy was associated with achievement goals, use of self-regulated learning strategies, and mathematics achievement. These results supported many of the hypothesized relationships, and offered additional clarification for the literature. Possible explanations are discussed regarding both the expected and unexpected outcomes.

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies developed by 2 prospective teachers. The results revealed that although the participants mostly used algebraic solutions in the PPB environment, they preferred geometric solutions in the GGB environment even though algebraic solutions were still possible (the software did not preclude them). Furthermore, different proofing strategies were developed in each environment. This suggests that changing the environment may prompt students to seek for additional solutions, which, in turn, results in a deeper understanding of the problem. As such, using both environments simultaneously in solving the same problems appears to bring about important benefits.

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 this knowledge evolves. The aim of this study is to investigate how teachers. pedagogical knowledge to use modeling in the classroom is formed and modified through professional development activities based on lesson study cycle from modeling perspective. The professional development program reported in this study included five monthly cycles consisted of meeting before the implementation, implementation of the activity and a follow up meeting. The participants were four in-service mathematics teachers. Results showed that the program provided opportunities for teachers to test, revise, and refine their knowledge. More specifically, teachers generated effective strategies for proper implementation of the modeling activities in the classroom.

This study investigated students’ scientific epistemological beliefs in relation to socio-economic status (SES) and gender. Data were obtained from 1,152 eight grade Turkish elementary school students using Scientific Epistemological Beliefs instrument. Canonical correlation analysis indicated that students with a working mother and educated parents as well as greater number of books at home together with a separate study room are more likely to have tentative views and less likely to have fixed views about science compared to students with unemployed mother, uneducated parents, less books at home, and no separate study room. Generally, results revealed while family SES correlated positively with tentative views, it was negatively associated with fixed views, implying that students from high SES family were more likely to believe that knowledge is uncertain and not handed down by authority compared to students from low SES family. This study, however, failed to indicate any relationship between father work-status, buying daily newspaper and epistemological beliefs. In addition, Multivariate Analysis of Variance indicated that boys more likely to have tentative beliefs compared to girls.

The purpose of this study was to investigate prospective mathematics teachers’ knowledge of common conceptions and misconceptions that sixth and seventh grade students had about multiplication of fractions. In addition, prospective teachers’ knowledge of the sources of these misconceptions and strategies they knew to overcome these misconceptions was examined. Data were collected from 17 Turkish prospective teachers at the end of the spring semester of the 2004–2005 academic year. A case study design was used in which data were collected through the Multiplication of Fractions Questionnaire and semi-structured interviews. The prospective teachers suggested many difficulties that elementary grade level students may have and stated that these difficulties stemmed from students’ lack of formal knowledge and rote memorization of the algorithms. In addition, the prospective teachers suggested many strategies that could be used to overcome these misconceptions or difficulties. These strategies could be grouped under three headings: strategies based on teaching methods, strategies based on formal knowledge of fractions, and strategies based on psychological constructs.

The purpose of this study was to compare pre‐service elementary teachers' sense of mathematics teaching efficacy beliefs in a Turkish university and in a major American university located in the Midwest. The data for this study were collected by means of the Mathematics Teaching Efficacy Beliefs Instrument. In the Turkish sample there were 141 pre‐service elementary teachers, and in the American sample there were 104 pre‐service elementary teachers. Results from the study indicate that pre‐service teachers in Turkey tend to have a stronger belief that teaching can influence student learning when compared with pre‐service teachers in the United States. However, a similar difference was not observed for personal mathematics teaching efficacy.

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 embodied solutions of mathematical modelling tasks. The data were collected from 25 prospective mathematics teachers enrolled in an undergraduate course through four 2-week-long cycles. Analysis of data revealed that the prospective teachers interpreted students’ thinking in four ways: describing, questioning, explaining, and comparing. Moreover, whereas some of the prospective teachers showed a tendency to increase their attention to the meaning of students’ ways of thinking more while they engaged in students’ work in depth over time and experience, some of them continued to focus on only judging the accuracy of students’ thinking. The implications of the findings for understanding and developing prospective teachers’ ways of interpreting students’ thinking are discussed.

SUMMARY The purpose of this paper is to discuss the problems of teacher education in Turkey and also to elaborate on the issues in the teacher education debate that we think are problematic. Our main focus will be on western influence and its consequences in building a relevant teacher education programme in Turkey. The irrelevancy between teacher education programmes and the realities of Turkish schools and the demand for a relevant theoretical base for teacher education were linked to western influence on the knowledge base and research traditions. The arguments in this paper were based on available literature and the authors' personal experiences in teacher education institutions. A background to and historical information on teacher education in Turkey are also included.

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 learning mathematics in terms of definitions of models and modeling, the theoretical backgrounds of modeling, and the nature of questions used in teaching modeling. This study focuses on two issues. The first section attempts to develop a unified perspective about mathematical modeling. The second section analyzes and discusses two approaches to the use of modeling in mathematics education, namely modeling as a means of teaching mathematics and modeling as an aim of teaching mathematics.

Ogretmenin sahip olmasi beklenen onemli yeterliliklerden birisi ogrenci dusunme sekilleri bilgisidir. Pedagojik alan bilgisinin bir alt boyutu olan bu bilginin ogretmenlere meslege baslamadan once kazandirilmasi onemlidir. Bu calismanin amaci matematiksel modelleme etkinliklerinin sinif ici uygulamalarindan elde edilen ogrenci cozum kâgitlari ve videolari incelemenin ogrenci dusunme sekillerini anlamaya olan katkisi konusunda matematik ogretmen adaylarinin dusuncelerini incelemektir. Calismanin katilimcilari ogretmen adaylarina donuk bir matematiksel modelleme dersine kayitli yirmi bes matematik ogretmen adayidir. Sekiz hafta suren calismanin verileri bireysel dusunce raporlari, birebir gorusmeler ve bir oz-degerlendirme anketi yoluyla toplanmistir. Verilerin analizleri, ogretmen adaylarinin ogrenci cozum kâgitlari ve video kesitlerini incelemenin ogrencilerin matematiksel dusunme sureclerinin farkina varma, tahmin edebilme, anlama ve yorumlamalarina yardim ettigini dusunduklerini ortaya cikarmistir. Bu calismanin sonuclari ogretmen egitimcilerine, ogretmen adaylarinin pedagojik alan bilgilerinin gelisimine destek saglamasi acisindan gercek sinif ortamlarindan alinmis ogrenci calisma urunlerinin kullanilmasini onermektedir. Anahtar Kelimeler : Pedagojik alan bilgisi, ogrenci dusunme sekilleri, ogretmen egitimi, ogrenci calismalari

If teachers interpret students' ways of thinking appropriately, they can make adequate instructional decisions before, during, and after teaching, and can develop their teaching with respect to stu...