Research Information System
Thinking Skills and Creativity, vol.59, 2026 (SSCI, Scopus)
This study aims to investigate how proficient prospective mathematics teachers are in evaluating the truth value of statements that are true in Euclidean geometry in terms of non-Euclidean geometries. In addition, this study seeks to portray the strategies prospective mathematics teachers used during the inductive reasoning process as they evaluate the truth value of statements in terms of non-Euclidean geometries. To this end, 106 participants were asked to evaluate the truth value of six statements, which are true in Euclidean geometry, in terms of elliptic and hyperbolic geometries, and explain their reasoning. Through this comparative and evaluative task, participants were naturally engaged in an inductive reasoning process. According to the findings, at least a quarter of the participants presented incorrect answers for every statement. The strategies observed during the inductive reasoning process were classified under thirteen categories: visualizing geometry surface/concept(s) in the statement, drawing by considering geometry surface/concept(s) in the statement, drawing without explanation, considering the definition of the main concept in the statement, presenting/aiming to present a counterexample/countercase, stating the absence of a counterexample/countercase, pointing a similarity/difference with Euclidean geometry, associating with the fifth postulate, generalizing, relating to another discipline, considering the cases necessary for the statement to be true, offering the presence of various cases based on the predicate of the statement, and identifying a specific relation between the concepts of the statement.