The role of examples in the formation of concepts in mathematics

This research presents a brief survey of literature on the use of examples and generic examples in concept formation, and the observation of these theoretical ideas in a number of exam papers. Explanatory insight is given to c1arify the situations in the exam papers. By focusing on the students' answers and the definition given on generic example definition, mainly two suggestions arise for the usage of generic examples. Firstly, the sequence of the exemplification may be in the order of all the generic examples first andthen the practising examples. Secondly, while chosing the examples the non-parallel principle can be taken into consideration besides the parallel principle.
Hacettepe Üniversitesi Eğitim Fakültesi Dergisi


The Role of Metacognition in Facilitating Conceptual Change
Yürük, Nejla; Beeth, Michael E; Özdemir, Ömer Faruk (2003-03-31)
This paper describe the intertwined nature of metacognition and conceptual change and proposes a taxonomy that classifies the types of metacognitive knowledge and activities that are likely to influence the change in students' conceptions. The initial conceptual change model is introduced to provide background and context for the theoretical argument, and a summary of the other theoretical approaches is drawn to explain the change in students' conceptions. The definition of metacognition is presented along ...
The Heuristic role of questions in the formation of research programmes: Copernicus’s heliocentric system
Altuğ, Sezen; Bağçe, Samet; Department of Philosophy (2016)
The aim of this thesis is to develop a critical view about the notion of the heuristic in Lakatos’s methodology of research programmes. The heuristic is tried to be sterilized from its defects with an insight derived from different forms of theories dealing with questions. For that reason, a short survey which includes Socratic dialogues, Hintikka’s theory of interrogative games, van Fraassen’s theory of why-questions, and Laudan’s analogy between science and problem-solving activity is introduced. As a res...
The nature and development of interaction among components of pedagogical content knowledge in practicum
Aydın, Sevgi; Demirdogen, Betul; Akın Çelebi, Fatma; Kondakçı, Esen; Tarkin, Aysegul (2015-02-01)
This secondary analysis study focused on how interactions among preservice teachers' pedagogical content knowledge (PCK) components developed throughout a 14-week CoRe-based mentoringenriched practicum course, and the nature of those interactions. Data were collected from three preservice teachers, information-rich cases, by the use of content representation (CoRe) and semi-structured interviews. Content analysis and the constant comparative method were employed in the data analysis. Results revealed that t...
The Ontology of Contemporary Construction
Atakara, Cemil; Hürol, Yonca (Middle East Technical University, Faculty of Architecture, 2007)
The main aim of this study is to discuss the ontology of contemporary construction by considering the recent developments in structures. For this purpose, contemporary transparent surfaces of suspended glass systems are considered. These systems are compared with the framed structures of the modern, and Gothic structures in order to discuss the ontological differences between them. The three systems are compared according to the number of structural systems in the building, the type of structural mat...
The influence of the context of conditional probability problems on probabilistic thinking: A case study with teacher candidates
Olgun, Beyza; Işıksal Bostan, Mine (2019-12-21)
This study investigates the influence of the context of conditional probability problems on probabilistic thinking processes of mathematics teacher candidates. Data were collected from four mathematics teacher candidates through semi-structured clinical interviews. Teacher candidates were expected to solve and explain three conditional probability problems, which were selected based on specific contexts. The findings revealed that, when the context is related to a social issue such as health or justice, tha...
Citation Formats
B. Ubuz, “The role of examples in the formation of concepts in mathematics,” Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, p. –, 2000, Accessed: 00, 2021. [Online]. Available: