“Didactical Contract” As a Tool for Finding out Students’ Errors in Solving Problem: An Illustration in Analytic Geometry

Abstract

In this study, we used the concept “didactical contract”, which was introduced by Guy Brousseau in 1980, as a tool for finding out the errors of students. In order to illustrate this approach, we used the type of a task: “In the space Oxyz, write the general equation of a plane (P) passing through point A(xₒ, yₒ, zₒ) and parallel to two straight lines: (d₁) and (d₂) ((di) and (d₂) are not parallel to each other)” which was mentioned in mathematics textbooks of Vietnam. We formulated the hypothesis H: there exists a rule of didactical contract: When solving the problem, students don’t verify whether (d1) and (d₂) are parallel or not; therefore, students will commit errors in the case of (d₁) and (d₂) are parallel. The results of study showed that many students committed errors in solving the exercise because of the above didactical contract.