Papers by Esra Bukova Güzel
The aim of the present study is to conceptualize the approaches displayed for validation of model... more The aim of the present study is to conceptualize the approaches displayed for validation of model and thought
processes provided in mathematical modeling process performed in technology-aided learning environment.
The participants of this grounded theory study were nineteen secondary school mathematics student teachers.
The data gathered from the video recordings received while participants were solving the given problems, the
written responses related to the solution of the problems, the GeoGebra solution files and the observation notes
taken by the researchers in the process of problem solving. The constant comparative analysis based on open,
axial, and selective coding methods were used for data analysis through the grounded theory. The five substeps
were emerged from data analyzing related to the process of the validation of model. It was determined
that these steps were covered by discussing the unexpected results in real-life situations, comparing the real
life results with the estimation based on the experiences or measurements, the problem data, the situations
given in video and pictures and the decision-making about the adequacy of the model. In this study, it was seen
that the technology-aided environment enriched the cognitive processes in validating step. With the help of this
research’s results, it was constructed a detailed description related to the cognitive processes which can be
displayed for validating of model in mathematical modeling. It was considered that the study would bring a different
perspective to the researchers towards the process of mathematical modeling.
Educational Sciences: Theory & Practice - 13(4) • 2499-2506
©2013 Educational Consultancy and Research Center
The aim of the present study is to conceptualize the approaches displayed for validation of model... more The aim of the present study is to conceptualize the approaches displayed for validation of model and thought aprocesses provided in mathematical modeling process performed in technology-aided learning environment.
The participants of this grounded theory study were nineteen secondary school mathematics student teachers.
The data gathered from the video recordings received while participants were solving the given problems, the
written responses related to the solution of the problems, the GeoGebra solution files and the observation notes
taken by the researchers in the process of problem solving. The constant comparative analysis based on open,
axial, and selective coding methods were used for data analysis through the grounded theory. The five sub-
steps were emerged from data analyzing related to the process of the validation of model. It was determined
that these steps were covered by discussing the unexpected results in real-life situations, comparing the real
life results with the estimation based on the experiences or measurements, the problem data, the situations
given in video and pictures and the decision-making about the adequacy of the model. In this study, it was seen
that the technology-aided environment enriched the cognitive processes in validating step. With the help of this
research’s results, it was constructed a detailed description related to the cognitive processes which can be
displayed for validating of model in mathematical modeling. It was considered that the study would bring a different perspective to the researchers towards the process of mathematical modeling.
The purpose of this study is to investigate the misconceptions emerging in mathematics student te... more The purpose of this study is to investigate the misconceptions emerging in mathematics student teachers’ limit instruction and the reflections of these misconceptions on their teaching. In this study, which used the case study design, regarding the limit concept, four senior mathematics student teachers’ four-hour limit instruction was examined within the context of misconceptions as described in the literature. Mathematics student teachers’ lesson plans, video recordings of the participants’ lessons in which they taught the concept of limitandaudiorecordingsofsemi-structured interviews were used to gather data.Participants carried their instruction mostly by demonstrating that the function’s limit is different than the function’svalueat x=a. However, since mathematics student teachers did not have adequate knowledge of misconceptions regarding the limit concept, some misconceptions emerged in their teaching process. Three of the participants made illustrations by making use of the meaning attributed to limit in daily language, and this situation caused students to perceive the limit concept as the maximum value to be reached and as a boundary not to be exceeded.
The purpose of this study is to introduce the Contingency unit of Knowledge Quartet, which is a f... more The purpose of this study is to introduce the Contingency unit of Knowledge Quartet, which is a framework used in assessing mathematics student teachers’ subject matter knowledge and pedagogical knowledge, address its significance and demonstrate examples from its reflections on classroom setting. The study initially covers the type of knowledge that teachers should possess and Knowledge Quartet, which enables examining and assessing subject matter knowledge and pedagogical knowledge together. Next, general information was given regarding knowledge units of this model and it was explained including contingency components. Finally, the importance of Contingency was mentioned and some examples in classroom setting were discussed. It is thought that through this study, awareness of mathematics student teachers can be made ensured with regards to situations that teachers may encounter and that are almost impossible to plan in advance.
(Bu çalışmanın amacı, matematik öğretmeni adaylarının alan ve alan öğretimi bilgilerinin değerlendirilmesinde kullanılan bir çerçeve olan Dörtlü Bilgi Modeli’nin Beklenmeyen Olaylar Bilgisi birimini tanıtmak, önemini belirtmek ve sınıf ortamına yansımalarından örnekler sunmaktır. Çalışmada, matematik öğretmenlerinin öğretimleri için gerekli olan alan ve alan öğretimi bilgilerini ayrıntılı olarak incelemeyi ve değerlendirmeyi mümkün kılan Dörtlü Bilgi Modeli’nin tanıtımına yer verilmiştir. Ardından söz konusu modele ait birimlere ilişkin genel bilgilendirme yapılmış ve bu birimlerden biri olan “Beklenmeyen Olaylar Bilgisi” detaylandırılmıştır. Son olarak “Beklenmeyen Olaylar Bilgisi”nin öneminden bahsedilmiş ve gerçek sınıf ortamlarından alınan kesitlerle bazı örnekler sunulmuştur. Sunulan çalışma ile matematik öğretmeni adaylarının önceden planlanması neredeyse imkansız olan ve öğretimlerinde karşılaşabilecekleri durumlara ilişkin farkındalıklarının sağlanacağı düşünülmektedir. )
The purpose of this study is to develop a scale to determine pre-service mathematics teachers' pe... more The purpose of this study is to develop a scale to determine pre-service mathematics teachers' perceptions related to their pedagogical content knowledge. Firstly, a preliminary perception scale of pedagogical content knowledge was constructed and then administered to 112 pre-service mathematics teachers who were enrolled in a mathematics teacher education programme. Exploratory and confirmatory factor analysis, item analysis, correlation analysis, internal consistency and descriptive statistic techniques were used to analyse the data. Then validity and reliability of the scale were investigated. The analyses resulted in the development of a five-factor scale of 17 items that was proved valid and reliable. We contend that the scale developed has the merit to contribute to pre-service teachers' self-awareness by revealing their perceptions regarding their pedagogical content knowledge.
![Research paper thumbnail of Matematiksel Modellemede GeoGebra Kullanımı: Boy-Ayak Uzunluğu Problemi [Using GeoGebra in Mathematical Modeling: The Height-Foot Length Problem]](https://attachments.academia-assets.com/35860143/thumbnails/1.jpg)
The integration of mathematical modeling with technology and the advantages of technology to mode... more The integration of mathematical modeling with technology and the advantages of technology to modeling process have become more important in today's fast-growing society. The studies about how the technology affects the mathematical modeling process and how to use the technology more effectively are of importance. The purpose of this study is to illustrate how to use GeoGebra in the process of mathematical modeling. In this study, GeoGebra was used in solution process of a problem designed in accordance with
mathematical modeling and the intended uses of GeoGebra were described in the mathematical modeling process. The solution of the Height-Foot Length Problem designed by the researchers was carried out taking into account the seven step modeling process. With this study, it was exemplified how the mathematics teachers will be able to use the mathematical modeling and the GeoGebra in their lessons. It is thought that GeoGebra will contribute to the uncovering and the development of modeling skills and will be provided
more conceptual and mathematical thinking by preventing losing in procedures.
Bu çalışmanın amacı, matematik öğretmeni adaylarının farklı modelleme türleri bağlamında oluşturu... more Bu çalışmanın amacı, matematik öğretmeni adaylarının farklı modelleme türleri bağlamında oluşturulmuş problemlere ilişkin çözümlerinden yola çıkarak matematiksel modelleme sürecinin basamaklarında kullandıkları gösterim şekillerini belirlemektir. Çalışma, Matematiksel Modelleme dersini alan on beş ortaöğretim matematik öğretmen adayıyla gerçekleştirilmiştir. Katılımcılar kendi istekleri doğrultusunda üçer kişilik beş çalışma grubuna ayrılmışlardır. Veriler, grupların altı matematiksel modelleme problemine ilişkin ayrıntılı çözümlerini içeren yazılı yanıt kâğıtları ve GeoGebra çözüm dosyaları yardımıyla toplanmıştır. Grupların modelleme problemlerinin çözümünde sözel, cebirsel, şekilsel, grafiksel, tablo ve dinamiksel gösterim şekillerinden yararlandıkları belirlenmiştir. Sürecin tüm basamaklarına göre gruplar en fazla sözel ve cebirsel gösterimleri kullanmışlardır. Problemin analizi basamağında sadece sözel gösterim kullanılırken, sistematik yapıyı kurma basamağında ise en fazla sözel ardından ise şekilsel gösterimden yararlanılmıştır. Matematikselleştirme, üst matematikselleştirme ve matematiksel analiz basamaklarında en çok kullanılan cebirsel ve ardından sözel gösterimler olmuştur. Yorumlama/değerlendirme ve modelin doğrulanması basamaklarında ise gruplar ağırlıklı olarak sözel ve ardından da cebirsel gösterimlerden yararlanmışlardır. Gösterim şekillerinin matematiksel modelleme sürecinin hangi basamaklarında niçin tercih edildiğine yönelik araştırmaların yapılması önerilmektedir.
The purpose of this case study is to examine the design process of the Model Eliciting Activity (... more The purpose of this case study is to examine the design process of the Model Eliciting Activity (MEA) named Obesity Problem designed by four mathematics teachers and the MEA itself in the framework of MEA designing principles. The data are the MEA and the transcriptions of the records videotaped in the design process. The records were analyzed using content analysis and the MEA was analyzed using document analysis. The MEA was completely appropriate for the reality, model construction, construct documentation and model generalization principles, and partially appropriate for the self evaluation principle. The effective prototype principle could not be identified. The teachers starting the design process from real life situations constructed a generalizable and appropriate model for the students.
![Research paper thumbnail of Öğrencilerin Kuyruklu Yıldız Problemi’ne İlişkin Çözüm Yaklaşımlarının Matematiksel Modelleme Süreci Çerçevesinde İncelenmesi [Examining Students’ Solutions Regarding the Comet Problem in the Frame of Mathematical Modeling Process]](https://attachments.academia-assets.com/35860176/thumbnails/1.jpg)
The purpose of the study is to examine students‟ solutions regarding the Comet Problem in the fra... more The purpose of the study is to examine students‟ solutions regarding the Comet Problem in the framework of mathematical modeling process. In the study conducted with ten secondary students, the data were collected through the written solutions to the Comet Problem solved by the students individually and the transcriptions of the video recordings including the students‟ think-alouds during the solution process. The rubric prepared by considering the seven-stage mathematical modeling process was used in the analysis of the problem. It was seen that the students‟ performances decreased gradually while going through the stages of the modeling process. The students did not display any approaches in the stage of the validation of the model. It is advised that students should be faced with much more mathematical modeling applications, and their approaches should be improved in the modeling process.
![Research paper thumbnail of Matematik Öğretmen Adaylarının Limit Kavramını Öğrenmelerinde Yapılandırmacı Öğrenme Ortamının Etkisinin Belirlenmesi [The Effect of a Constructivist Learning Environment on the Limit Concept among Mathematics Student Teachers]](https://attachments.academia-assets.com/36570297/thumbnails/1.jpg)
The purpose of this study is to design a constructivist learning environment that helps learning ... more The purpose of this study is to design a constructivist learning environment that helps learning the limit concept. The study is a pretest-posttest quasi-experimental research. The control and the experimental groups were chosen from the students attending a calculus course. Worksheets were used to assess students’ learning of the limit concept. As a result of data analysis, it was found that the constructivist learning environment provided positive contribution to learning of the limit concept. It was determined that the experimental group was more successful than the control group in seeing the relations between the limits and the real world. At the same time, experimental group had lesser difficulty in understanding the limits. However, both the experimental and the control groups had difficulty in applying the deltaepsilon approach. It is concluded that this study would guide when learning environment is design to construct mathematical concepts.
International Journal of Mathematical Education in Science and Technology, 2012
The purpose of this study is to determine prospective mathematics teachers’ views about using pro... more The purpose of this study is to determine prospective mathematics teachers’ views about using problem-based learning (PBL) in statistics teaching and to examine their thought processes. It is a qualitative study conducted with 15 prospective mathematics teachers from a state university in Turkey. The data were collected via participant observation and semi-structured interviews. To determine their thought processes, all PBL sessions and interviews were audio-taped. The analysis of the data suggests that the participants liked the PBL application. They had overall positive views regarding PBL, although there were some stated concerns regarding the applicability of PBL in Turkish schools due to insufficient means. The findings also suggest that PBL sessions enhanced their self-expressions; hence, their thought processes had developed in the course of PBL application. We hope that this study will contribute to future studies about the use of PBL method in statistics teaching.
Experience I-II and the Teaching Practice courses enabled to their acquisition of the professiona... more Experience I-II and the Teaching Practice courses enabled to their acquisition of the professional pre-practice experience. 36 mathematics student teachers from four different state universities in their last year of the Department of Secondary Mathematics Teacher Education in the 2006-2007 academic year participated. Data were collected using six open-ended questions oriented to the mathematics student teachers. The student teachers'
Buca Eğitim Fakültesi Dergisi, Jan 1, 2010
Özel durum çalışması niteliğindeki bu araştırmanın amacı, İzmir ili merkez ilçelerinden birinin İ... more Özel durum çalışması niteliğindeki bu araştırmanın amacı, İzmir ili merkez ilçelerinden birinin İlçe Milli Eğitim Müdürlüğü tarafından düzenlenen hizmet içi eğitim seminerine katılan matematik öğretmenlerinin öğrenme etkinliklerine yönelik görüşlerini ve deneyimlerini betimlemektir. Seminere farklı mesleki deneyime sahip ilk ve ortaöğretimin farklı sınıf seviyelerinde görev yapmakta olan on sekiz matematik öğretmeni katılmıştır. Katılımcılara seminer öncesinde öğrenme etkinliklerine ilişkin görüşlerini ve deneyimlerini belirlemeye yönelik sekiz adet açık uçlu sorunun yer aldığı bir görüş formu verilmiştir. Söz konusu form aracılığıyla yazılı olarak elde edilen veriler nitel olarak analiz edilmiş ve bulgular semineri gerçekleştiren ilk iki yazarın gözlem notları ile desteklenmiştir. Araştırmanın sonucunda öğretmenlerin etkinlik kavramına ilişkin görüş ve deneyimlerinin oldukça sınırlı olduğu görülmüştür. Bu çalışmanın matematik eğitimcilerine, matematik öğretmenlerine ve öğrenme etkinlikleri ile ilgili yapılacak araştırmalara yararlı bilgiler sağlayacağı ve yeni matematik öğretim programının etkin biçimde uygulanabilmesine katkıda bulunacağı düşünülmektedir.
Procedia-Social and …, Jan 1, 2010
The aim of this study is to determine the views and evaluations of high school mathematics studen... more The aim of this study is to determine the views and evaluations of high school mathematics student teachers regarding undergraduate courses aimed at developing mathematical pedagogical content knowledge, and to reveal their suggestions as to improve those courses. From four different state universities, in total 36 secondary school mathematics student teachers who were in their senior year participated in this study. The data were gathered through four open-ended questions asked to student teachers. Student teachers' responses were analyzed by means of content analysis. In the study, student teachers stated that these courses were necessary but there are some problems and limitations in the development of PCK. We hope that the study will contribute to the revision of courses aimed at developing pedagogical content knowledge in Turkey.
The purpose of this qualitative research is to examine the views of 21 secondary mathematics stud... more The purpose of this qualitative research is to examine the views of 21 secondary mathematics student teachers attending Mathematical Modelling Course regarding mathematical modelling in a state university in Turkey; reasons why they chose this course and their expectations from the course in question. For this reason, three open-ended questions were asked to the participants and they gave their answers in writing. These questions were related to their description of mathematical modelling, the reason why they chose this course and their expectations related to this course. The data obtained from responses to these questions were examined and categorized using content analysis. Data analysis showed that the participants generally defined mathematical modelling as making mathematical concepts more concrete, developing material, associating mathematics with real world and solving daily life problems. Among participants' reasons why they chose this course, it was pointed out that this course would fulfil the requirements of Secondary School Mathematics Curriculum. Participants' expectations related to this course are retention of mathematical knowledge, making mathematical concepts more concrete and more relevant to daily life; making their future students more active; contributing to their future teaching life.
International Journal of Mathematical Education in Science and Technology, 2011
The purpose of this study is to determine prospective mathematics teachers’ views about using pro... more The purpose of this study is to determine prospective mathematics teachers’ views about using problem-based learning (PBL) in statistics teaching and to examine their thought processes. It is a qualitative study conducted with 15 prospective mathematics teachers from a state university in Turkey. The data were collected via participant observation and semi-structured interviews. To determine their thought processes, all PBL sessions and interviews were audio-taped. The analysis of the data suggests that the participants liked the PBL application. They had overall positive views regarding PBL, although there were some stated concerns regarding the applicability of PBL in Turkish schools due to insufficient means. The findings also suggest that PBL sessions enhanced their self-expressions; hence, their thought processes had developed in the course of PBL application. We hope that this study will contribute to future studies about the use of PBL method in statistics teaching.
The purpose of the study is to determine the primary mathematics student teachers’ views related ... more The purpose of the study is to determine the primary mathematics student teachers’ views related to use instructional technology tools in course of the learning process and to reveal how the sample presentations towards different mathematical concepts affect their views. This is a qualitative study involving twelve mathematics students from a public university. The data gathered from two semi-structural interviews. The first one was realized in the beginning of the study. After that the representations prepared by the researchers were showed to the participants. These representations contain animations, Geometer’s Sketchpad activities, video-clips, spreadsheets, and power-point presentations. The last interview was realized at the end of these representations. The data from the interviews and content analyses were transcribed and read and reread to explore the major themes. Findings revealed that the views of the students changed in this process and they believed that the instructional technology tools should be used in their classroom.
The purpose of the study is to determine secondary prospective mathematics teachers' views relate... more The purpose of the study is to determine secondary prospective mathematics teachers' views related to using flash animations in mathematics lessons and to reveal how the sample presentations towards different mathematical concepts altered their views. This is a case study involving three secondary prospective mathematics teachers from a state university in Turkey. The data gathered from two semi-structural interviews. Findings revealed that these animations help understand mathematics meaningfully, relate mathematics and real world, visualization, and comprehend the importance of mathematics. The analysis of the data indicated that the sample presentations enhanced participants' views about using flash animations in mathematics lessons.
Procedia - Social and Behavioral Sciences, 2010
The aim of this study is to determine the views and evaluations of high school mathematics studen... more The aim of this study is to determine the views and evaluations of high school mathematics student teachers regarding undergraduate courses aimed at developing mathematical pedagogical content knowledge, and to reveal their suggestions as to improve those courses. From four different state universities, in total 36 secondary school mathematics student teachers who were in their senior year participated in this study. The data were gathered through four open-ended questions asked to student teachers. Student teachers' responses were analyzed by means of content analysis. In the study, student teachers stated that these courses were necessary but there are some problems and limitations in the development of PCK. We hope that the study will contribute to the revision of courses aimed at developing pedagogical content knowledge in Turkey.
Ürüne dönük düşünme, insanı diğer canlılardan ayıran en belirgin özelliğidir. Ancak her düşünce y... more Ürüne dönük düşünme, insanı diğer canlılardan ayıran en belirgin özelliğidir. Ancak her düşünce yararlıdır demek pek doğru bir varsayım olmaz. Düşüncenin yararlılığı, gereksinimlerin karşılanmasında kullanımı ve problemlerin çözümünde üretken olması ile ölçülür. Bu nitelikteki düşünmeye, kısaca Matematiksel Düşünme (MD) denir. Çalışma, özellikle matematik öğretmen adaylarının MD gelişimini ölçmeye yönlendirilmiştir. Araştırma iki aşamadan oluşmaktadır. İlk aşamada deneklerin MD gelişimini ölçme amaçlı araç geliştirilmiştir. İkinci aşamada ise oluşturulan ölçme aracı deneklere uygulanmış ve onların çözüm yaklaşımları, MD ölçütlerine uygun biçimde sınıflandırılarak değerlendirilmiştir. Analiz sonuçları, genel anlamıyla deneklerin MD gelişmişliğinin düşük düzeyde olduğunu ortaya çıkarmıştır. MD'nin düzeyi bakımındab gruplar arasında anlamlı farklılıklar gözlenmiştir.
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Papers by Esra Bukova Güzel
processes provided in mathematical modeling process performed in technology-aided learning environment.
The participants of this grounded theory study were nineteen secondary school mathematics student teachers.
The data gathered from the video recordings received while participants were solving the given problems, the
written responses related to the solution of the problems, the GeoGebra solution files and the observation notes
taken by the researchers in the process of problem solving. The constant comparative analysis based on open,
axial, and selective coding methods were used for data analysis through the grounded theory. The five substeps
were emerged from data analyzing related to the process of the validation of model. It was determined
that these steps were covered by discussing the unexpected results in real-life situations, comparing the real
life results with the estimation based on the experiences or measurements, the problem data, the situations
given in video and pictures and the decision-making about the adequacy of the model. In this study, it was seen
that the technology-aided environment enriched the cognitive processes in validating step. With the help of this
research’s results, it was constructed a detailed description related to the cognitive processes which can be
displayed for validating of model in mathematical modeling. It was considered that the study would bring a different
perspective to the researchers towards the process of mathematical modeling.
Educational Sciences: Theory & Practice - 13(4) • 2499-2506
©2013 Educational Consultancy and Research Center
The participants of this grounded theory study were nineteen secondary school mathematics student teachers.
The data gathered from the video recordings received while participants were solving the given problems, the
written responses related to the solution of the problems, the GeoGebra solution files and the observation notes
taken by the researchers in the process of problem solving. The constant comparative analysis based on open,
axial, and selective coding methods were used for data analysis through the grounded theory. The five sub-
steps were emerged from data analyzing related to the process of the validation of model. It was determined
that these steps were covered by discussing the unexpected results in real-life situations, comparing the real
life results with the estimation based on the experiences or measurements, the problem data, the situations
given in video and pictures and the decision-making about the adequacy of the model. In this study, it was seen
that the technology-aided environment enriched the cognitive processes in validating step. With the help of this
research’s results, it was constructed a detailed description related to the cognitive processes which can be
displayed for validating of model in mathematical modeling. It was considered that the study would bring a different perspective to the researchers towards the process of mathematical modeling.
(Bu çalışmanın amacı, matematik öğretmeni adaylarının alan ve alan öğretimi bilgilerinin değerlendirilmesinde kullanılan bir çerçeve olan Dörtlü Bilgi Modeli’nin Beklenmeyen Olaylar Bilgisi birimini tanıtmak, önemini belirtmek ve sınıf ortamına yansımalarından örnekler sunmaktır. Çalışmada, matematik öğretmenlerinin öğretimleri için gerekli olan alan ve alan öğretimi bilgilerini ayrıntılı olarak incelemeyi ve değerlendirmeyi mümkün kılan Dörtlü Bilgi Modeli’nin tanıtımına yer verilmiştir. Ardından söz konusu modele ait birimlere ilişkin genel bilgilendirme yapılmış ve bu birimlerden biri olan “Beklenmeyen Olaylar Bilgisi” detaylandırılmıştır. Son olarak “Beklenmeyen Olaylar Bilgisi”nin öneminden bahsedilmiş ve gerçek sınıf ortamlarından alınan kesitlerle bazı örnekler sunulmuştur. Sunulan çalışma ile matematik öğretmeni adaylarının önceden planlanması neredeyse imkansız olan ve öğretimlerinde karşılaşabilecekleri durumlara ilişkin farkındalıklarının sağlanacağı düşünülmektedir. )
mathematical modeling and the intended uses of GeoGebra were described in the mathematical modeling process. The solution of the Height-Foot Length Problem designed by the researchers was carried out taking into account the seven step modeling process. With this study, it was exemplified how the mathematics teachers will be able to use the mathematical modeling and the GeoGebra in their lessons. It is thought that GeoGebra will contribute to the uncovering and the development of modeling skills and will be provided
more conceptual and mathematical thinking by preventing losing in procedures.
processes provided in mathematical modeling process performed in technology-aided learning environment.
The participants of this grounded theory study were nineteen secondary school mathematics student teachers.
The data gathered from the video recordings received while participants were solving the given problems, the
written responses related to the solution of the problems, the GeoGebra solution files and the observation notes
taken by the researchers in the process of problem solving. The constant comparative analysis based on open,
axial, and selective coding methods were used for data analysis through the grounded theory. The five substeps
were emerged from data analyzing related to the process of the validation of model. It was determined
that these steps were covered by discussing the unexpected results in real-life situations, comparing the real
life results with the estimation based on the experiences or measurements, the problem data, the situations
given in video and pictures and the decision-making about the adequacy of the model. In this study, it was seen
that the technology-aided environment enriched the cognitive processes in validating step. With the help of this
research’s results, it was constructed a detailed description related to the cognitive processes which can be
displayed for validating of model in mathematical modeling. It was considered that the study would bring a different
perspective to the researchers towards the process of mathematical modeling.
Educational Sciences: Theory & Practice - 13(4) • 2499-2506
©2013 Educational Consultancy and Research Center
The participants of this grounded theory study were nineteen secondary school mathematics student teachers.
The data gathered from the video recordings received while participants were solving the given problems, the
written responses related to the solution of the problems, the GeoGebra solution files and the observation notes
taken by the researchers in the process of problem solving. The constant comparative analysis based on open,
axial, and selective coding methods were used for data analysis through the grounded theory. The five sub-
steps were emerged from data analyzing related to the process of the validation of model. It was determined
that these steps were covered by discussing the unexpected results in real-life situations, comparing the real
life results with the estimation based on the experiences or measurements, the problem data, the situations
given in video and pictures and the decision-making about the adequacy of the model. In this study, it was seen
that the technology-aided environment enriched the cognitive processes in validating step. With the help of this
research’s results, it was constructed a detailed description related to the cognitive processes which can be
displayed for validating of model in mathematical modeling. It was considered that the study would bring a different perspective to the researchers towards the process of mathematical modeling.
(Bu çalışmanın amacı, matematik öğretmeni adaylarının alan ve alan öğretimi bilgilerinin değerlendirilmesinde kullanılan bir çerçeve olan Dörtlü Bilgi Modeli’nin Beklenmeyen Olaylar Bilgisi birimini tanıtmak, önemini belirtmek ve sınıf ortamına yansımalarından örnekler sunmaktır. Çalışmada, matematik öğretmenlerinin öğretimleri için gerekli olan alan ve alan öğretimi bilgilerini ayrıntılı olarak incelemeyi ve değerlendirmeyi mümkün kılan Dörtlü Bilgi Modeli’nin tanıtımına yer verilmiştir. Ardından söz konusu modele ait birimlere ilişkin genel bilgilendirme yapılmış ve bu birimlerden biri olan “Beklenmeyen Olaylar Bilgisi” detaylandırılmıştır. Son olarak “Beklenmeyen Olaylar Bilgisi”nin öneminden bahsedilmiş ve gerçek sınıf ortamlarından alınan kesitlerle bazı örnekler sunulmuştur. Sunulan çalışma ile matematik öğretmeni adaylarının önceden planlanması neredeyse imkansız olan ve öğretimlerinde karşılaşabilecekleri durumlara ilişkin farkındalıklarının sağlanacağı düşünülmektedir. )
mathematical modeling and the intended uses of GeoGebra were described in the mathematical modeling process. The solution of the Height-Foot Length Problem designed by the researchers was carried out taking into account the seven step modeling process. With this study, it was exemplified how the mathematics teachers will be able to use the mathematical modeling and the GeoGebra in their lessons. It is thought that GeoGebra will contribute to the uncovering and the development of modeling skills and will be provided
more conceptual and mathematical thinking by preventing losing in procedures.