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.

ABSTRACT

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Although the emphases on the importance of proving in mathematics education literature, many studies show that undergraduates have difficulty in this regard. Having researchers discussed these difficulties in detail; many frameworks have been presented evaluating the proof from different perspectives. Being one of them the proof image, which takes into account both cognitive and affective factors in proving, was presented by Kidron and Dreyfus (2014) in the context of the theoretical framework of "abstraction in context". However, since the authors have not deepened the relationship between the proof image and formal knowledge, this article was intended to fill this gap. In this study, which is part of a larger doctoral thesis, descriptive method one of the qualitative methods was used. The participants of the study were three pre-service teachers selected via criterion sampling method among sophomore elementary school mathematics teacher candidates. In parallel with a course relating to Cantorian Set Theory, task-based individual interviews (Task I-II-III-IV) were conducted in the context of the equivalence of infinite sets. The subject of "infinity" had been chosen as the context of the study since it contains a process that goes from intuitive to formal. In the first task (Task I), the actions that the participants had performed without enough pre-knowledge was examined in terms of the proof image. In the second task (Task II) carried out after a course, in which basic knowledge was presented, the same question was asked to the participants again. Thus, the processes formed with the presence of formal knowledge were analysed. As a result of the descriptive analysis executed on the data of both tasks, it was determined that Ç, who was one of the participants, reached a proof image in the second task although she failed in the first task. Therefore, in this study, findings of her proving activity were shared. Consequently, formal knowledge has been identified to be directly related to each of the components of the proof image and, its main contributions have been listed as headings.

The aim of this chapter is to illustrate both uses of data mining methods and the way of these methods can be applied in education by using students' multiple intelligences. Data mining is a data analysis methodology that has been successfully used in different areas including the educational domain. In this context, in this study, an application of EDM will be illustrated by using multiple intelligence and some other variables (e.g., learning styles and personality types). The decision tree model was implemented using students' learning styles, multiple intelligences, and personality types to identify gifted students. The sample size was 735 middle school students. The constructed decision tree model with 70% validity revealed that examination of mathematically gifted students using data mining techniques may be possible if specific characteristics are included.

One of the general discussion in the studies about learning style is what degree of students whose learning style is determined, have other learning styles. In this context, the aim of this study is to determine the learning styles of prospective elementary mathematics teachers and to explore the relationships between these styles by using data mining techniques. Data mining can be defined as applications of different algorithms to identify patterns and relationships in a data set. For this purpose, Grasha-Reichmann Learning Styles Inventory was applied to 400 prospective elementary mathematics teachers at Dokuz Eylul University. Cronbach's alpha reliability coefficient of the scale was found as 0.83.Results show that more than 50% of female students have "independent'' learning style. At the same time students who have competitive learning style had the least number of students. The male students who have collaborative and dependent learning styles were the majority.. From Class 1 to Class 4, it was observed that the number of students who have individual learning styles was decreasing and the number of students who have cooperative learning styles was increasing. In network graph, it was found that one of the strongest relationships was between the students who have cooperative and independent learning style with high level. On the other hand the relationship between the students who have passive and independent learning style with low level was not seen in graph. The decision tree indicates that the most effective attribute is independent learning style to identify which level of the learning style students have. Besides in the Data mining, learning styles, Mathematics Education association rules model several rules are constructed with %75 confidence. Extended SummaryWith the transition to learner-centered education, approaches related to teaching and learning began to be questioned and developed in education system. The fundamental basis of the change is individual features of students and effect of these features to educational environment.Teachers can use individual differences in planning learning environments and processes (Tomlinson, 1997: 25). These individual differences consist of a lot of feature such as learning style. Kolb (1984) defines learning style as a preferred way of gathering information, whereas for Dunn (1984) learning style is an individual way of absorbing and retaining information or skills. Özer (1998) reported that teachers must know students' learning styles for effective learning.