Investigation of Students' Preconceptions and Difficulties with the Vector Direction Concept at a Mexican University

In this paper, we investigate common preconceptions that Mexican university students have with the concept of direction of a vector. Students entering a large private Mexican university were tested before receiving instruction related to vectors in an introductory physics class. In the first part we present students' difficulties with the direction concept of a vector due to the use of two conventions in the Mexican system. The common convention of direction in the American system conflicts with a convention of this property as it is composed of two separate properties: direction as the line of action and sense as which of the two ways the vector points along that line. Both conventions are regularly used in the Mexican educational system and students use one or the other without doing it explicitly. In the second part, based on the work of Nguyen and Meltzer [I], we designed problems in which students are asked for direction of a vector without indicating any particular convention, and problems in which students are asked for direction of a vector indicating the line of action convention. We analyze preconceptions of direction in the first type of problems (investigating in depth the ones detected by Nguyen and Meltzer), and preconceptions of direction and sense in the second type of problems. At the end we compare responses of students in the two types of problems.