Öz: Bu çalışmada öğretmen adaylarının sonsuz kümelerin denkliği ile ilgili ispatlama yaklaşımlarının ve bu konu ile ilgili güçlüklerinin belirlenmesi amaçlanmıştır. Bu amaç doğrultusunda verilerin toplanması için açık uçlu sorular içeren bir form geliştirilmiş ve 121 matematik öğretmeni adayına uygulanmıştır. Elde edilen veriler içerik analizi ile incelenmiştir. İspatların sınıflanması için Blum ve Kirsch (1991) tarafından sunulan ispat şeması dikkate alınmıştır. Sonuçta öğretmen adaylarının gerçekleştirdikleri ispatlarda formal ve pre-formal yaklaşımları benimseyebildikleri tespit edilmiştir. Bununla birlikte pre-formal yaklaşıma sahip bireylerin ispatlama aktivitelerinde, formal bilgileri ile sezgilerini bir arada kullanabildikleri de görülmüştür. Diğer yandan öğretmen adaylarının ispatı oluşturamamalarına neden olan yanılgıları, bilgi eksiklikleri ve yöntemsel yetersizlikleri belirlenip özellikle yanılgılar, başlıklar halinde sunulmuştur.
The aim of this study is to examine middle school students" attitude towards mathematics in the context of their mathematic learning preferences using data mining which is data analysis methodology that has been successfully used in different areas including educational domains. "How do I actually learn?" questionnaire and attitude scale were applied to 702 middle school students studying in three different cities of Turkey. Demographic data (gender, grade level, parents" education level, pre-school education) were also gathered. Data mining techniques such as decision tree was implemented. Furthermore web graph was used for visualization of relationship between mathematic learning preference and attitude towards mathematics. Constructed decision tree models with C5.0 algorithm revealed that all of variables used in this study are related to the attitude towards mathematics but the most effective attribute is found as grade level. Using web graph, it was found that the strongest relationship was between reflective learning preference and positive level attitude towards mathematics.
In this study, using fuzzy-rough set and intuitionistic fuzzy set approaches, we propose a cognitive structural model for the concept of life for which a certain definition can not be made because of scientific uncertainty as well as moral, legal, and theological aspects. Total 191 first-year students from seven different high schools in a large western city in Turkey participated in the study. An open-ended conceptual understanding (CULC) test, developed by the researcher, was used for data collection. Semi-structured interviews were carried out with 14 students and their biology teachers to clarify ambiguous points in students' responses to the CULC test. The results of analyses indicated that students constructed the concept of life by associating it predominantly with 'human'. Motion appeared as the most frequently associated term with the concept of life. The results suggest that the life concept has been constructed using animistic-anthropocentric cognitive schemes. In the next step, we evaluated the data obtained from the CULC test using the fuzzy-rough set and intuitionistic fuzzy set theories. Consequently, we propose an 'animistic-anthropocentric structural model' about cognitive construction of the concept of life.
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