Browsing by Author "Yilmaz, Tugba Yulet"

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Relations Between the Functions of Proof and Social and Sociomathematical Norms: Reflections From the Kari̇de Model
(Turkish Education Assoc, 2025) Yilmaz, Tugba Yulet; Kose, Niluefer Yavuzsoy
In addition to demonstrating the validity of mathematical propositions through proof, it also reveals functions such as explanation, discovery, systematization, and communication. It is essential to utilize all proof functions to transform it into a meaningful and profound mathematical activity in classrooms. Since mathematical proof and reasoning are social processes, teaching proof at the middle school level, particularly in demonstrating its importance and necessity, is influenced by certain norms. Therefore, teachers' consideration of proof's functions and the social and socio-mathematical norms supports students' reasoning processes. In this context, this study aims to reveal the functions of proof, social and socio-mathematical norms, and the relationship between these functions and norms within a learning environment that enables students to solve proof problems through interaction. The study participants comprised 7th-grade students attending a public middle school in the Central Anatolia Region. Since uncovering proof functions and establishing norms require long-term interaction in an authentic learning environment, the teaching experiment method was adopted in this study. The findings were presented by analyzing the video and audio recordings and worksheets obtained from the 12-week teaching process. The study results revealed that the classroom community developed shared norms regarding discussion, problem-solving, justification, and collaboration. These social and socio-mathematical norms guided students' participation in discussions and enhanced the quality of their contributions. Additionally, the study revealed that norms and functions of proof were intertwined in dialogues and that the norms across different themes and the functions of proof were interconnected. In the study, it was determined that the norms in the themes of discussion and collaboration mainly supported the communication function of proof, while the norms in the themes of justification and problem-solving mainly supported the verification, explanation, discovery, and systematization functions of proof. It is recommended that studies focus on the social aspect of proof to demonstrate how social and socio-mathematical norms and the functions of proof support each other at different grade levels.
Understanding Pre-Service Teachers Perceptions of the Ideal Learning Environment for Mathematical Activities Through Drawings
(Mdpi, 2025) Yilmaz, Tugba Yulet; Gok, Mustafa
Mathematical activities, which have the potential to engage students cognitively, are an essential component of modern educational approaches. The design of learning environments that facilitate the full realization of the potential of mathematical activities is as crucial as the activities themselves. Well-designed physical, social, and emotional learning environments significantly contribute to students' holistic development. Pre-service teachers' perceptions regarding the ideal learning environment for mathematical activities can shape the quality of learning environments they will create professionally. This study explores the perceptions of pre-service primary school teachers and pre-service elementary mathematics teachers regarding the ideal learning environment for mathematical activities through their drawings and related reflections. This study employs a qualitative case study design, and data were collected through freehand drawings depicting ideal learning environments and semi-structured interviews with pre-service teachers. The analysis reveals five prominent components of the ideal learning environment for mathematical activities: purpose, instructional methods and techniques, teacher-student roles, seating arrangements, and interrelations among these components. The findings indicate differences in perceptions between pre-service primary school teachers and pre-service elementary mathematics teachers. Additionally, the results highlight that these components are interrelated within the learning environment, with the purpose component serving as a guiding factor for the others.