A Binational COIL Matrix-Cryptography Challenge to Teach Invertibility and SDG 4 in Engineering Education

Abstract

This qualitative case study examines a binational Collaborative Online International Learning (COIL) experience that uses matrix cryptography to teach matrix inversion in engineering education while connecting disciplinary work to SDG 4 (Quality Education). Forty undergraduates from two Latin American universities (Mexico and Chile) collaborated in mixed teams (n = 9) to decrypt a plaintext encoded with a 10×10 key matrix using Python, MATLAB, and Excel, and then produced an evidence–action memo linking the decrypted message to SDG 4 targets and proposing feasible on-campus actions with indicators. Data included team reports (n = 9), recorded presentations, and individual reflections (n = 40). An inductive codebook thematic analysis supported by Atlas.ti yielded three interrelated dimensions: (i) technical (71 coded segments), with cross-tool validation achieved by 100% of teams; (ii) pedagogical (59 coded segments), with explicit SDG 4 linkage in all team reports; and (iii) emotional–collaborative (63 coded segments), highlighting intercultural motivation and joint problem solving across sources. To provide post hoc evidence of conceptual understanding, we applied a Rubric for Conceptual Understanding of Invertibility (RCCI) to team artifacts: 78% of teams provided complete justification of invertibility conditions, and 67% demonstrated systematic error diagnosis and correction. Although no objective pre/post tests were administered, the findings suggest that cryptography-based COIL tasks can strengthen procedural autonomy, conceptual justification, and socially grounded relevance in linear algebra.