Difficulties in learning linear equations in Secondary Education

Abstract

This study identifies the main difficulties in learning linear equations in secondary education through a narrative review. The findings reveal a multifactorial problem involving: (1) cognitive components (prior arithmetic deficits, variable polysemy), (2) didactic approaches (emphasis on mechanical algorithms), and (3) attitudinal factors (low motivation). Research by Socas (2008) and Barría-Chavarría (2010) shows that persistent errors (confusion of inverses, misuse of algebraic properties) stem from decontextualized teaching that prioritizes procedures over conceptual understanding. These limitations create a cumulative effect that hinders performance in advanced mathematics and increases dropout risk. Evidence-based solutions are proposed: (1) visual representations (algebraic balances) for concept abstraction (Duval, 2006), (2) contextualization of real-world problems, and (3) gamification to enhance engagement. Integrated implementation—combined with teacher training in error diagnosis—could significantly reduce these difficulties (Radatz, 1979). Addressing these challenges is crucial for ensuring educational equity and STEM access, requiring policies that balance mathematical rigor with innovative, student-centered pedagogies.