Design of a didactic sequence to address frequent errors in 2×2 linear equation systems at U.E. Gonzalo Zaldumbide

Abstract

Introduction: solving 2×2 systems of linear equations is an essential topic in high school; however, students frequently make errors in both conceptual understanding and algebraic procedures. This teaching sequence aims to address these difficulties through active activities, error analysis, and the use of digital resources, with the goal of fostering logical reasoning, participation, and learning in the classroom. Objective: to design a teaching sequence based on error analysis and the use of digital tools to address the most frequent difficulties in solving 2×2 systems of linear equations in the first year of high school at the Gonzalo Zaldumbide Educational Unit. Methodology: the study employed a quantitative, applied approach with a descriptive scope and a cross-sectional, non-experimental design, following research and development methodology. The purposive, non-probability sample consisted of 24 mathematics students and teachers. The information was obtained through a diagnostic pedagogical test, a teacher perception questionnaire with a Likert scale, and a validation form based on expert criteria. The data were processed using descriptive statistics, percentages, means, standard deviation, Cronbach's alpha, and the Content Validity Index (CVI). Results: the diagnosis revealed major difficulties in the procedural dimension, followed by the verification-representational one. A 12-session sequence was designed, structured into four modules (substitution, elimination, reduction, and graphical method with GeoGebra). Specialists validated its relevance and applicability with a CVI of 0.80. Conclusion: the designed sequence constitutes a coherent and feasible methodological alternative to address conceptual, procedural, and representational errors in linear systems. General area of ​​study: Education. Specific area of ​​study: Education. Type of study: Original.