The Cartesian Plane in Fifth Grade students: its Re-signification on a Specific Situation

Abstract We report the results of a research on the re-signification of the Cartesian plane in a group of fifth-grade students of a Chilean school. The corresponding mathematical school discourse lacks meaningful teaching situations to introduce and to understand the use of that plane, and rather fosters a prescribed mathematics, that you do not need to build. That re-signification was evidenced through the design of a specific situation promoting the need of building the Cartesian plane. In the arguments and discussion held, the group evidenced building orthogonal axes, and the notions of distance, origin, and location of points considering rectangular coordinates摘要 本研究报告了智利某小学五年级学生群体对笛卡尔平面（Cartesian plane）开展意义重构的研究成果。当前的学校数学话语体系缺少能够引导学生认识并理解笛卡尔平面使用方法的富有意义的教学情境，反而催生了无需学生自主建构的规定性数学教学模式。本研究通过设计一项可激发学生建构笛卡尔平面内在需求的特定教学情境，验证了该意义重构过程的有效性。在后续开展的论证与讨论环节中，该学生群体展现出了正交坐标轴（orthogonal axes）的建构能力，并掌握了结合直角坐标系理解距离、原点及点的位置等相关概念。