## 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} .

Translated title of the contribution | Cognitive construction of vector space R ^{2} |
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Original language | Spanish |

Pages (from-to) | 57-86 |

Number of pages | 30 |

Journal | Revista Latinoamericana de Investigacion en Matematica Educativa |

Volume | 21 |

Issue number | 1 |

DOIs | |

State | Published - 1 Mar 2018 |