Students’ Errors in Solving Problem: A Case Study based on the Concept “Didactical Contract”

Abstract

In this study, we used a type of “undefined problem ” in analytic geometry in space and analogical reasoning as tools to find out students’ errors in learning mathematics; here, we defined an undefined problem in geometry as a problem that has the infinite number of objects satisfying the insufficient conditions of the problem. Participants were 309 grade 12th students in schools of Vietnam, in which the students were assigned to one undefined problem to solve. The results showed that students revealed many errors in solving undefined problems in geometry and the use of analogical reasoning was one of causes of their errors.