Bu çalışmanın amacı, ilköğretim matematik öğretmeni adaylarının farklı örüntü problemleri ile ilgili genelleme stratejilerini incelemek, genellemelerinin altında yatan gerekçelendirmeleri keşfetmek ve genelleme ile gerekçelendirmeleri arasındaki ilişkileri belirlemektir. Çalışma nitel araştırma desenlerinden olgubilim modeline göre tasarlanmıştır. Çalışma, Doğu Karadeniz Bölgesindeki bir üniversitenin İlköğretim Matematik Öğretmenliği programında öğrenim gören 4. sınıf öğretmen adayları ile yürütülmüştür. Veri toplama araçları, hem literatür hem de öğretim üyesi desteğiyle hazırlanan ve farklı çözüm stratejilerinin ve gerekçelendirme çeşitlerinin üretilebildiği lineer ve kuadratik örüntü problemleridir. Mülakatlar sonucu toplanan veriler araştırmanın kavramsal çerçevesi dâhilinde betimsel analiz tekniği kullanılarak çözümlenmiştir. Elde edilen sonuçlardan, öğretmen adaylarının en yaygın kullandığı strateji türü fonksiyonel strateji olmakla birlikte, içeriksel, yinelemeli, tahmin-kontrol ve karma stratejileri de kullanmışlardır. Öğretmen adaylarının çoğu gerekçelendirmelerini sayısal kontrol yoluyla doğrulama ile yapmışken, açıklama ve dışsal bilgi kaynağı yoluyla gerekçelendirme yapan öğretmen adayları da tespit edilmiştir.

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The aim of the research is to examine the perspectives of teachers and preservice teachers in regard with models, mathematical models and mathematical modelling process in different variables terms and to compare them. In this research that is having quantitative research design survey method, which is one of the descriptive research technic, survey method is used. Research is performed with 127 teacher and preservice teachers. It is benefitted from a different survey in the stage of data collection and open ended questions that is developed by the researcher. In the analysis of the data, descriptive and inferential statistical methods and content analysis method were used. As a result, views of the teachers and preservice teachers regarding (mathematical) models and mathematical modelling shows differences according to some variables, however, it is not found out most significant differences in the views of the teachers and preservice teachers in regard with these subjects.

The aim of this study is to determine the opinions and beliefs of secondary school mathematics teachers about the students' competencies to acquire mathematical content in the context of different types of problems and solutions. The study was conducted according to the descriptive research model from the quantitative research design. The sample of the research consists of 32 middle school mathematics teachers. In the data collection phase, literature supported questionnaires consisting of Likert and problem type questions and open-ended questionnaires developed by the researcher were used. Descriptive statistics and analysis methods were used in analysing the data. Teachers have stated that for students, algebraic problems are more difficult than arithmetic problems and verbal problems are more difficult than symbolic ones, the unknown quantities in the problem affect the level of difficulty of the problem and there are more strategies students can use. In addition, most teachers adopt the idea that story problems are more appropriate than symbolic problems in terms of new meanings, and that "algebra is the best" with symbol precedence view.