Teaching the Solutions of Equation in view of Symmetry

- Journal title : Communications of Mathematical Education
- Volume 29, Issue 4, 2015, pp.699-722
- Publisher : Korea Society of Mathematical Education
- DOI : 10.7468/jksmee.2015.29.4.699

Title & Authors

Teaching the Solutions of Equation in view of Symmetry

Kim, Ji Hong; Kim, Boo Yoon; Chung, Young Woo;

Kim, Ji Hong; Kim, Boo Yoon; Chung, Young Woo;

Abstract

Based on Lagrange`s general theory of algebraic equations, by applying the solution of the equation using the relationship between roots and coefficients to the high school 1st grade class, the purpose of this study is to recognize the significance of symmetry associated with the solution of the equation. Symmetry is the core idea of Lagrange`s general theory of algebraic equations, and the relationship between roots and coefficients is an important means in the solution. Through the lesson, students recognized the significance of learning about the relationship between roots and coefficients, and understanded the idea of symmetry and were interested in new solutions. These studies gives not only the local experience of solutions of the equations dealing in school mathematics, but the systematics experience of general theory of algebraic equations by the didactical organization, and should be understood the connections between knowledges related to the solutions of the equation in a viewpoint of the mathematical history.

Keywords

equation;symmetry;resolvent;the relationship between roots and coefficients;

Language

Korean

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