Teaching Mathematics and its Applications Advance Access originally published online on October 1, 2007
Teaching Mathematics and its Applications 2008 27(1):1-10; doi:10.1093/teamat/hrm014
| ||||||||||||||||||||||||||||||||||||||||||||||||
Bridging the gap between mathematical conjecture and proof through computer-supported cognitive conflicts
Address for correspondence: Ming-Puu Chen, No. 162, Sec.1, Ho-ping East Road, Taipei, Taiwan 10610. E-mail: mpchen{at}ntnu.edu.tw
Submitted June 2006; accepted July 2007
In many mathematical problems, students can feel that the universality of a conjecture or a formula is validated by their experiment and experience. In contrast, students generally do not feel that deductive explanations strengthen their conviction that a conjecture or a formula is true. In order to cope up with students’ conviction based only on empirical experience and to create a need for deductive explanations, we developed a problem-solving activity with technology support intended to cause cognitive conflict. In this article, we describe the process conducted for this activity that led students to contradictions between conjectures and findings. The teacher could create familiar problem-solving situations and use students’ naïve inductive approaches to make students think mathematically and establish the necessity for proof via computer support.
Chun-Yi Lee is Doctoral candidate of the Graduate Institute of Information and Computer Education at National Taiwan Normal University. He received his MA degree in the Degree Program of E-Learning from National Chiao-Tung University and with a bachelor degree in Mathematics from National Kaoh-Siung Normal University.
Ming-Puu Chen is Professor of the Graduate Institute of Information and Computer Education at National Taiwan Normal University. He received his PhD. and MA degrees in Educational Technology from University of Northern Colorado, USA.