How secondary level teachers and students impose personal structure on fractional expressions and equations-an expert-novice study

摘要

While an algebraic expression is typically assigned a regular structure, this article introduces the concept of personal structure (Strukturierung); here, the structuring of an algebraic expression is understood as the act of forming relationships between its parts. This concept is used for the analysis of interviews in which experts and novices talk about the personal structures they produced when looking at fractional expressions and equations. The results show, firstly, that experts will structure a given fractional expression in various different ways. Secondly, four categories have been identified: structuring can mean that an expression is made more visually straightforward, changed, reinterpreted or classified. This is meaningful for negotiating the appropriateness of the personal structures in teaching algebra.