This study aimed at investigating two main issues related to counterexample construction: the appropriateness of counterexamples and the types of arguments that are often used when refuting a false conjecture. Twelve pre-service elementary teachers who demonstrated a wide range of reasoning skills participated in this study. The data revealed…

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

The Van Hiele theory asserts that there exist five hierarchical levels of geometric thinking that a successful learner passes through. The purpose of the study described in this paper was to investigate the geometric understanding and misconceptions in students in the fourth through eighth grades who have been identified as gifted. The students…