Abstract

The purpose of this study is to address the ways in which mathematically gifted students reason when faced with both confirming and contradicting examples for a mathematical statement. By addressing this issue, this study aims to investigate the types of examples, generalizations and justifications that students construct after confronting confirming and contradicting examples for the statements. Eight students who enrolled in a Science and Art Center volunteered to participate in a semi-structured individual interview. The results indicated that the types and the purposes of suggested examples varied among the students. Research investigating student reasoning suggests that students’ justification schemes reflect their current view of the collection of examples that are considered as sufficient for the validation of a mathematical generalization. This study revealed that the types of examples were informative regarding the types of generalizations and arguments that were constructed by the students.

Keywords: Example types, Generalizations, Gifted students, Justifications, Mathematical reasoning

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Copyright © 2025 The Author(s). This is an open access article distributed under the Creative Commons Attribution License (CC BY), which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is properly cited.

How to cite

Zeybek Şimşek, Z., & Kılıçoğlu, E. (2025). Investigating Student Reasoning When Faced with a Mathematical Statement that Contains both Confirming and Contradicting Examples. Education and Science, 50(222), 45-66. https://doi.org/10.15390/EB.2025.12962