Insights into the School Mathematics Tradition from Solving Linear Equations

In this article, we explore how the solving of linear equations is represented in English­-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for solving linear equations. Teachers' reactions to correct student solutions that do not follow this canonical method suggest its centrality to school algebra instruction. We reflect on these observations using the notions of didactical transposition, instructional exchange, and a metaphorical alchemy that creates school subjects from disciplinary knowledge.