Examining Students’ Generalizations of the Tangent Concept: A Theoretical Perspective

Abstract

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 this study, we examine students’ understanding of the tangent concept from the viewpoint of generalization. The findings of the study reveal differences in students’ generalizations regarding the tangent concept. We discuss the causes of these differences and provide a theory to account for them. In light of the results, some suggestions are made for improving the teaching of the concept of a tangent.

Keywords:

• Calculus teaching
• concept image
• mathematical generalization
• tangent concept

Additional information

Notes on contributors

Erdem Çekmez

Erdem Çekmez is an Assistant Professor in the Secondary Mathematics Education Department at Karadeniz Technical University. He has been awarded a Ph.D. in Mathematics Education. His research interests lie in the learning and teaching of calculus, learning theories, and computer-based mathematics education.

Adnan Baki

Adnan Baki is a Professor of Mathematics Education at Karadeniz Technical University. He became the chairman of the Turkish Mathematics Educators Organization in 2012. He is the Editor-in-Chief of the Turkish Journal of Computer and Mathematics Education. His research and teaching interest lie in the philosophy of mathematics and mathematics education, instructional technology in mathematics education, and history of mathematics.