Application of the Ontosemiotic Approach in Linear Algebra: Modeling and Cryptography through Software Development
DOI:
https://doi.org/10.70939/revistadiged.v2i1.28Keywords:
linear algebra, mathematics education, ontosemiotic approach, computational modeling, cryptographyAbstract
OBJECTIVE: To apply the ontosemiotic approach to mathematical cognition and instruction to design a didactic proposal that integrates Linear Algebra content with technological tools, facilitating its understanding and functionality in Systems Engineering contexts. METHOD: A qualitative approach was adopted through a didactic intervention design based on the principles of the ontosemiotic approach. The proposal was implemented with a group of second-year university students in Systems Engineering, who participated in a didactic sequence structured in three phases: epistemic configuration, computational modeling, and cryptographic application. Data collection included student-produced work, performance records, metacognitive reflections, and analysis of the developed software. RESULTS: A significant improvement was observed in the functional understanding of mathematical objects such as matrices, determinants, linear transformations, and systems of equations. Students successfully integrated theoretical knowledge with computational applications by developing a program capable of solving algebraic problems and executing basic encryption processes. A fluent transition among symbolic, operational, and computational representations was evidenced, along with a meaningful reconfiguration of mathematical knowledge. CONCLUSION: The use of the ontosemiotic approach as a didactic guide fostered meaningful learning by linking theory and practice within a technologically relevant environment. The proposal proves to be replicable in other technological subjects requiring integration between abstract thinking and the functional application of mathematical knowledge.
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