Beyond Memorization: Advocating Derivation and Proof in School Mathematics

Abstract

This paper advocates for the teaching and emphasis of derivation and proof in school mathematics as
a means to foster deeper conceptual understanding and reduce overreliance on rote memorization. By examining
the derivation of key geometric formulas-such as the volumes of a cylinder, cone, prism, and pyramid, as well as
the shortest distance between two points on a sphere in latitude and longitude-it demonstrates how students can
engage meaningfully with mathematical ideas. Through logical reasoning, spatial visualization, and mathematical
connections, derivation empowers learners to appreciate mathematics as a coherent and purposeful discipline.
The paper calls for an instructional shift toward reasoning-based learning in school curricula to cultivate critical
thinking and lasting comprehension.