Unveiling structure in linear equations: discerning and disregarding critical aspects

Journal article, 2026

Recognizing what is algebraically relevant in equations could potentially help students solve them more efficiently. In a research project involving 16-year-old students, a lesson was planned, analyzed, and modified in three cycles, using variation theory to explore which aspects of linear equations are decisive in making students aware of the structure of the equations. The results highlight the necessity to help students direct their attention to specific aspects of linear equations (e.g., the combination of operations), but also to aspects that are irrelevant for the algebraic structure (e.g., the numbers, the unknown's notation, and their positions relative to the equality sign and to commutative operations). The results contribute to research by highlighting that awareness of algebraic structure is not merely a set of operational skills, but an ability that relates to a specific mathematical content and develops through students experiencing critical aspects of that content.