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- MakaleAçık Erişim2026Thinking Through Russell’s Paradox: Logical, Epistemological, and Pedagogical Transformations in Pre-Service Teachers
Aksakalli, Ayhan
This study examines how the paradoxical structure of set theory introduced by Bertrand Russell affects the thinking skills and pedagogical awareness of pre-service teachers. Conducted within a qualitative research framework, the study involved 30 mathematics education students enrolled in the faculty of education at a public university. The participants engaged in a multilayered instructional process structured around Russell’s Paradox. Observation notes, individual reflection forms, group discussions, and focus group interviews were used as data collection tools, and the obtained data were analyzed through thematic analysis. The findings reveal that the paradox generated transformations in pre-service teachers at the levels of conceptual rupture, logical reorganization, and pedagogical awareness. It was observed that Russell’s Paradox became not only a theoretical logical construct but also a powerful learning tool that triggered epistemological inquiry. In this context, the study suggests that paradoxes may offer significant contributions to teacher education by fostering critical thinking, developing strategies for coping with contradiction, and supporting the construction of teacher identity.
- MakaleAçık Erişim2018The Metacognitive Skills Performed by 6th-8th Grade Gifted Students during the Problem-Solving Process: Gümüşhane Sample
Öztürk, Mesut; Akkan, Yaşar; Kaplan, Abdullah
The fact that the gifted students perform their problem-solving activities by using their metacognitive skills will reinforce their ability to correlate among the mathematical concepts as well as developing their understanding and learning mathematics in depth. For this reason, the purpose of this study is to determine and compare the metacognitive skills performed by 6th-8th grade gifted students at the time of their problem-solving process. The case study, one of the qualitative research models, has been used in this study. The data in this study conducted with nine gifted secondary school students were collected by using a think- aloud protocol (interview forms) along with the observation forms. A thematic analysis was performed by making use of the studies in the literature. It was ascertained as the result of the study that the gifted students at different learning levels has exhibited metacognitive skills in all of the problem-solving steps and that the number of the metacognitive skills performed during the problem- solving processes generally increased as the learning levels of the students developed. Moreover, it was also determined that the students, in all of the problem-solving steps, generally felt confident, reviewed their targets and self-evaluated/self-checked at every step of this process.
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