WHY PRE-TEACHING: A GEOMETRIC EXPLANATION

Abstract

Traditionally, subjects are taught in sequential order: e.g., first, students study algebra, then they use the knowledge of algebra to study the basis ideas of calculus. In this traditional scheme, teachers usually do not explain any calculus ideas before students are ready - since they believe that this would only confuse students. However, lately, empirical evidence has shows that, contrary to this common belief, pre-teaching - when students get a brief introduction to the forthcoming new topic before this topic starts - helps students learn. In this paper, we provide a geometric explanation for this unexpected empitical phenomenon.