Teaching mathematical concepts based on the principle of "Consistency in Explanation"

Abstract

This paper explores the importance and methods of achieving "self-consistency" in the teaching of mathematical concepts. It first emphasizes the central role of mathematical concepts in learning mathematics and, through the example of teaching the eccentricity of an ellipse, points out the complexity of understanding mathematical concepts. Then, by exploring the history of "eccentricity," the paper demonstrates the human conventions and historical development behind mathematical concepts, highlighting the need for teachers to delve into the origins and meanings of concepts in their teaching. The paper proposes four strategies to achieve "self-consistency": sorting out the history of mathematical development, finding applications of mathematics in daily life, rebuilding connections between mathematical knowledge, and utilizing perspectives from other disciplines. Finally, the paper argues that "self-consistency" is not only a teaching method but also a teaching philosophy, aimed at helping students gain a deep understanding of mathematical concepts.