A Study on Physics-Mathematics Convergence Teaching-Learning Strategies Using Newton’s ‘Invention of Figures for Reflection’

The purpose of this study is to propose a teaching and learning program for gifted students using the history of science. In ｢Waste Book｣, Isaac Newton presented three pictures and equations under the title of ‘Invention of figures for reflection’, this study proposed the three step program for teaching and learning using Newton’s work. The first step is the proof of Newton’s equations. The second and third steps are mathematical proofs of three questions about reflection in conic curves and physics proofs using Fermat’s principle. The three questions about reflection of conic curve are: 1. Does a ray parallel to the optical axis travel toward the focal point after reflecting in a parabola. 2. Does a ray traveling toward a focus travel toward the other focus after reflecting off the hyperbola? 3. Does a ray from a focus travel to the other focus after reflecting off the ellipse? etc. Additionally, the applications for gifted education were discussed through the relevance of the curriculum, the convergence of physics and mathematics, and the proofs through experiments.