Cognitive construction of vector space R 2

Abstract

We present background information on the validation of a cognitive model for the lear ning of the vector space R 2 . As a result, we highlight the role played by the association of a pai r of real numbers t o a homogeneous l i near equat ion (with t wo unknowns) to induce an algebraic st r uct ure to the solution set. Furthermore, we present evidence of how the use of a parameter to write a solution of a homogeneous linear equation, is an important factor that highlights the product of a solution by a scalar as an operation that is associated with the solution set of a homogeneous linear equation. All of this has a close connection with the construction of the vector space R 2 .