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Papers by H.Bahadır YANIK

Özet Bu çalışmanın amacı göreve yeni başlayan ortaokul matematik öğretmenlerinin karşılaştıkları... more Özet
Bu çalışmanın amacı göreve yeni başlayan ortaokul matematik öğretmenlerinin karşılaştıkları zorlukları belirlemektir. Çalışma durum çalışması olarak tasarlanmış ve temel veri toplama aracı olarak görüşmelerden yararlanılmıştır. Çalışma kapsamında Türkiye'nin farklı bölgelerinde görev yapmakta olan 13 farklı üniversiteden mezun olmuş, toplam 23 ortaokul matematik öğretmeni ile görüşmeler gerçekleştirilmiştir. Görüşme verileri tematik analiz yöntemi kullanılarak analiz edilmiştir. Çalışma bulguları göreve yeni başlayan öğretmenlerin sınıf ve zaman yönetiminde, öğrencilere rehberlik yapmada, velilerle ilişkilerde ve okullarda yürütülen evrak işleri gibi konularda sorunlar yaşadıklarını göstermiştir. Ayrıca, öğretmenlerin bazı matematik konularını ve seçmeli dersleri etkili bir şekilde anlatmada, öğrenci merkezli yöntem ve teknikleri uygulayabilmede ve farklı seviyelerdeki öğrencilere ders anlatmada zorlandıkları belirlenmiştir. Bunun yanında, teknolojiyi matematik eğitimine entegre etmede, alternatif ölçme ve değerlendirme yaklaşımlarının kullanmada ve değerlendirmede, materyal hazırlamada ve beşinci sınıf öğrencilerine ders anlatmada öğretmenlerin çeşitli sorunlar yaşadıkları saptanmıştır.

Abstract
The purpose of this study was to identify challenges facing beginning middle school mathematics teachers. The study was designed as a case study and interviews were used as a major data collection tool. A total of 23 middle school mathematics teachers who are graduates of 13 different universities around Turkey was interviewed. Data were analyzed using thematic approach. The findings of the study showed that beginning teachers had problems in classroom and time management, guiding students, forming good parental relationships and dealing with school paper works. In addition, teacher had also problems in effective teaching of some mathematics content and elective courses, using student-centered methods and strategies, and working students with different learning abilities. Furthermore, teachers had problems in integrating technology into mathematics teaching, using alternative assessment and evaluation techniques, preparing instructional materials and working with fifth graders.

Using a dog’s paw as a basis for numerical representation, sixth grade students explored how to c... more Using a dog’s paw as a basis for numerical representation, sixth grade students explored how to count
and regroup using the dog’s four digital pads. Teachers can connect these base-4 explorations to the
conceptual meaning of place value and regrouping using base-10.

Scoliosis, the curvature of the spine, is a medical condition that often affects youth. This arti... more Scoliosis, the curvature of the spine, is a medical condition that often affects youth. This article provides students with an opportunity to explore the geometry behind the spine’s curvature. Students will first develop a method for measuring curvature, and then compare their method to the commonly used Cobb method.

Conference Presentations by H.Bahadır YANIK

Eğitime yönelik belirlenen hedeflere ulaşılabilmesi yolunda öğretmenlere önemli sorumluluklar yük... more Eğitime yönelik belirlenen hedeflere ulaşılabilmesi yolunda öğretmenlere önemli sorumluluklar yüklenmekte ve onlara karşı büyük beklentiler içerisine girilmektedir. Eğitim fakültelerinde farklı alanlarda farklı donanımlarla yetişen öğretmenlerin gerçek anlamda öğretmenlik mesleği ile tanışmaları mezuniyetlerinin ardından atamalarının yapıldığı okullarda gerçekleşmektedir. Yeni öğretmenlerden de deneyimli öğretmenler gibi birçok mesleki sorumluluğu yerine getirmeleri istenmektedir. Bu açıdan, öğretmenlik mesleğinin ilk yılları birçok öğretmen için zorlu ve stresli geçebilmektedir. Yapılan araştırmalarda (Harris ve Associates, Inc. 1991) mesleğinin ilk yılını tamamlayan birçok öğretmende öz güven kaybı yaşandığı belirlenmiştir. Uluslararası çalışmalarda (Ingersoll, 2001; Urban Teacher Collaborative, 2000) öğretmenlik mesleğin ilk yıllarının öğretmenler açısından kırılgan olduğu ve birçok öğretmenin bu yıllarda mesleği bırakma noktasına kadar gelebildiği belirlenmiştir. Bu nedenle, özellikle mesleğin ilk yıllarında öğretmenlerin yaşadıkları sorunların yakından incelenmesi önemlidir. Bu sorunların belirlenmesi öğretmen yetiştirme programlarının düzenlenmesi ve hizmet içi eğitimlere yönelik etkili projelerin geliştirilmesi açısından önem taşımaktadır. Bu çalışmanın amacı en fazla 3 yıllık mesleki tecrübeye sahip ortaokul matematik öğretmenlerinin yaşadıkları sorunlara yönelik görüşlerini tespit etmektir. Araştırmada, öğretmenlerin mesleğe girişte yaşadıkları sorunları ve deneyimlerini anlamak için olgubilim araştırma deseninden yararlanılmıştır. Araştırmanın ilk aşamasında Türkiye'nin farklı bölgelerinde görev yapmakta olan, 13 farklı üniversiteden mezun olmuş, en fazla üç yıllık tecrübeye sahip 23 ortaokul matematik öğretmeni ile görüşülmüştür. Bu aşamada öğretmenlerin mesleğe girişte yaşadıkları sorunlara yönelik veriler tematik olarak analiz edilerek ana temalar belirlenmiştir. İkinci aşamada ise 7 öğretmen ile görüşülerek derinlemesine bilgi elde etmek amaçlanmıştır. Bu çalışmada ilk aşamada elde edilen bulgulara yer verilmiştir. Veriler yarı yapılandırılmış görüşme tekniği ile toplanmıştır. Her bir katılımcı ile yaklaşık 40-70 dakika süren görüşmeler yapılmıştır. Veri analizi sonucunda öğretmenlerin genel ve matematik öğretimine yönelik çeşitli sorunlar yaşadıkları belirlenmiştir. Genel olarak öğretmenler sınıf yönetimi, rehberlik, zaman yönetimi, evrak işlerinin yoğunlukları, fiziksel alt yapı eksiklikleri ve velilerle ilişkiler gibi konularda yaşadıkları sıkıntılardan bahsetmişlerdir. Özellikle, öğretmenler kalabalık sınıflarda farklı düzeylerdeki öğrencilerle ilk defa yakından ilgilenmek durumunda kaldıklarını ve bu ortamın kendileri üzerinde baskı yarattığını belirtmişlerdir. Ayrıca sınıflarındaki özel eğitime gereksinim duyan öğrencilere yönelik nasıl bir yaklaşım sergileyecekleri ve nasıl bir eğitim vermeleri gerektiği konusunda zorlandıklarını ifade etmişlerdir. Zaman yönetimi konusunda fazlasıyla sıkıntı yaşadıklarını ifade eden öğretmenler çoğu zaman öğrettikleri konuları yüzeysel olarak geçmek zorunda kaldıklarını ifade etmişlerdir. Bunun yanında evrak işlerinin (zümre öğretmenler kurulu tutanağı, Şube öğretmenler kurulu tutanağı, rehberlik tutanakları, veli toplantı tutanakları gibi) yoğunluğuna da dikkat çeken bazı öğretmenler bu durumun okul ortamına uyum süreçlerini geciktirdiğini belirtmişlerdir. Ayrıca okullardaki fiziksel alt yapı

Mathematical modelling may be defined as a process of analyzing real life or realistic life situa... more Mathematical modelling may be defined as a process of analyzing real life or realistic life situations mathematically. The steps of this process constructed differently by different authors and in any way, while struggling with model eliciting tasks, there may happen turn backs and transitions through the steps. With group activities, carried on with 3 or 4 students, abilities such as organizing data, communication, using mathematics and verification may be developed. The purpose of the study was to define the views of prospective middle school mathematics teachers who solved model eliciting tasks in a mathematical modelling course. The data was collected from 27 prospective teachers through open ended questions. The findings discussed under three headings: (1) the definitions of prospective mathematics teachers about model eliciting tasks, (2) positive and negative views of prospective mathematics teachers to model eliciting tasks and (3) attitudes about using model eliciting tasks in their mathematics classrooms. The prospective mathematics teachers generally stated that model eliciting tasks were away from rote memorization approach, combined the abstract part of mathematics with real life, didactic and enjoyable. They stated that model eliciting tasks developed various mathematical skills such as problem solving, functional and relational thinking, algebraic thinking, mathematical thinking, making generalizations, questioning, analyzing and interpreting, They indicated that model eliciting problems provided opportunities to transfer real-life information to the problems and vice versa. The negative views of prospective mathematics teachers were that: Model eliciting problems were generally scary at first glance, long, challenging and difficult to define variables and they had no definite answer. The prospective teachers mostly indicated that they might use model eliciting problems in their classrooms. However, because of model eliciting tasks couldn't be applied to any subject, they might use them mostly in elective courses. While a few prospective teacher argued that because of tiring and taking time, model eliciting tasks caused negative attitude to mathematics so it shouldn't be used in mathematics classes. In conclusion, there were many different views about model eliciting problems. The prospective teachers generally agreed that model eliciting tasks provided various skills to students. However, the negative views generally focused on the challenge of the implementation process of model eliciting tasks.

Linear relationship is a crucial mathematical idea which forms a basis for many mathematics topic... more Linear relationship is a crucial mathematical idea which forms a basis for many mathematics topics, such as functions, derivatives and integrals. According to Turkish middle and high school mathematics curricula, it is expected for students to represent the linear relationship between two variables by using tables, graphs and algebraic expressions and comprehend the meaning of slope and rate of change. The purpose of this study was to examine how prospective middle school mathematics teachers conceive linear relationships. A total of 66 prospective teachers in their third year of the program in a public university participated in the study. Data were collected through a written instrument which required participants to provide examples and non-examples of a linear relationship and asked for a definition for it. The findings of the study suggested that the majority of prospective teachers considered positive correlations (i.e., both variables increasing or both variables decreasing) when thinking about the linear relationships. None of them mentioned about the possibility of negative correlations (i.e., one variable increasing the other decreasing or one variable decreasing the other increasing) when considering linear relationships. Overall findings suggested that prospective teachers had limited understanding about the concept of rate of change which hindered their understanding of linear relationships.

Fractions are one of the challenging topics for middle school students in mathematics. One reason... more Fractions are one of the challenging topics for middle school students in mathematics. One reason behind this difficulty might be related to representations. Fractions can be represented through various forms. Area models and number line models are often used by students to represent fractions. The purpose of this study was to investigate how middle school students represented proper fractions using these two models. Data were collected through a written instrument which was administered to 34 6th grade students. The instrument included 4 tasks. While two of the tasks required students to find the part of a whole, the other two tasks asked students to find the whole using the given parts on area and number line model. The data showed that while the majority of students were able to represent the proper fraction on the given area model, very few of them were able to locate fractions on a number line.

During the last few decades there has been considerable work in mathematics education that has ce... more During the last few decades there has been considerable work in mathematics education that has centered on applications and mathematical modelling. In education programs, there has been an increasing focus on implementation of model eliciting tasks to mathematics lessons. The purpose of this study was to reveal 6th and 7th grade students thoughts about model eliciting tasks. Firstly, the students were applied " Big Foot Problem " which is often place in literature, and secondly the view of students about problem is collected through open ended interview questions. Interview questions were applied to 30 6 th grade and 34 7 th grade students. The students were asked 1) how they felt on solving problems, 2) what is the different aspects of these problems from other examples in their classrooms, 3) how it would reflect on their learning if used this kind of problems in their classrooms, 4)which points they had difficulties most in implementation process 5) the methods to solve problem would work on similar cases or not, 6) the mathematical methods used in solving the problem can be associated with any subject in mathematics and 7) questions whether they have different proposals for the solution process of the problem. Students generally stated that they feel curious and excited throughout the study, they regard themselves as detectives and they were anxious at the beginning of the work but they said they were happy with the results closer. They also indicated that their work in this study provided them to work in groups and because of being a real life problem, it was different from other classical math problems. In addition, they implied that they made a research on this problem, they used calculators and rulers, used multi-step processes and had different results from each other. Such problems may develop problem-solving skills, research methods and operation skills. The difficulties students faced most were lack of time, difficulty of measurement and deciding a method to solve the problem. Finally, students proposed that it might be given more time, more clues and it might be increased this kind of problems.

The process of finding out mathematical rules embedded in real life or realistic life situations ... more The process of finding out mathematical rules embedded in real life or realistic life situations is defined " mathematical modelling " , and the physical and symbolic expression of these rules is defined as " model ". Model eliciting tasks provides opportunities to students to be aware of mathematical concepts and to develop the ability of overcoming these problems faced in real life. The purpose of this study was to explore a middle school mathematics teacher's experiences about using model eliciting tasks in his fifth grade class. The data collected through interviews and document analysis. The findings of the study suggested that initially while the teacher faced with various challenges in implementing model eliciting tasks in his classroom, later he was able to transform his classroom's environment into model exploration. The teacher stated that the most challenging issue he had to deal with was about transferring his classroom environment in a way that students' explore mathematical models. Also, because of getting used to the problems which had definite answers, it was difficult to perceive model eliciting problems with multiple solution paths. Furthermore, sometimes it was hard to keep down the student groups who were in interaction. Although the teacher faced various challenges, he indicated that if these challenges were overcome, applying model eliciting tasks might provide utilities. A well prepared context and group interactions might even provide uninterested students to involve in a problem. Furthermore, group interactions might uncover several creative ideas. He also stated that with model eliciting tasks, students would use mathematics in real life and they would be aware the need of mathematics in different disciplines. The mathematics teacher proposed to the teachers who wanted to apply model eliciting tasks in their classrooms that they should combine theory and practice of model eliciting tasks and use technology. As a result, although it is hard to get a habit of applying model eliciting tasks in classrooms, if accomplished, the students may acquire various skills at the end of this process.