Method for Teaching the Derivation of an Equation on the Principle of Leverage: Focusing on Redescription of Internal Representations

Abstract

This study developed teaching aids to help students with the derivation of an equation on the principle of leverage. The aim was to use the teaching aids to redescribe internal representations that arose and were molded in pupils and to derive an external representation, namely, an equation on the principle of leverage, which is a mathematical expression. As a result, first, use of the “grid expression” arose and formed internal area representations during data interpretation. Next, employment of “block expression” and “area representation” arose and formed internal area representations as well. Additionally, the internal area representations were redescribed (converted and integrated) and the right-hand side of a lever balanced with the left-hand side was expressed as external representations. Use of these grid, block, and area expressions allowed transfer between internal representations. Pupils were able to generate and form internal area representations, and then convert and integrate them. In other words, they were able to redescribe the generated and formed internal representations and interpret data as external representations, i.e., “the mass of weights x number of ticks=a constant.”