Conference Agenda

This study presents the implementation and evaluation of an educational strategy based on experiential learning and the regulated use of artificial intelligence tools as support for mathematical reasoning in a Differential Equations course for engineering students. The study was conducted using a comparative quasi-experimental design, in which three groups taught by the same instructor were analyzed: one control group following a traditional instructional approach and two experimental groups that incorporated contextualized activities in real engineering scenarios and the controlled use of artificial intelligence as cognitive scaffolding. The assessment of academic performance and disciplinary competencies was designed in alignment with the learning objectives and institutional competency frameworks of the course, using instruments integrated into the regular evaluation process. The results show consistent differences in favor of the experimental groups in both final grades and criteria associated with complex problem solving, mathematical modeling, and solution interpretation. The analysis suggests that the integration of experiential learning and the regulated use of artificial intelligence promotes a more applied understanding of mathematical concepts, while maintaining students as active agents in the learning process. Overall, the study provides empirical evidence on the feasibility of pedagogical approaches aligned with Education 6.0 in foundational mathematics courses for engineering within Latin American contexts.

In this paper, the concept of artificial prime numbers, previously defined on subsets of the positive integers, is extended to more general algebraic structures, such as integral domains, Euclidean domains, and rings of algebraic integers. A generalized definition of artificial primality is introduced, based exclusively on the internal divisibility relations of a given set, incorporating the notion of associated elements. Particular cases in the Gaussian integers ℤ[i] and in non-factorial rings are analyzed, establishing the relationship between artificial primes, irreducible elements, and algebraic primes. Furthermore, fundamental properties, generalized sieving procedures, and constructive methods are discussed, as well as possible applications in pure mathematics, computation, engineering, and STEM education. This approach provides a contextual view of primality, independent of unique factorization, and broadens the conceptual framework of applied number theory.

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.

In this work, a comprehensive numerical analysis of the oscillating pendulum model is undertaken. The numerical integration of nonlinear ordinary differential equations constitutes
an essential complement to the analytical and qualitative study of their solutions and, in numerous instances, represents the only viable approach for obtaining meaningful insight into
their dynamical behavior.
This study systematically presents and examines the principal numerical integration methods for ordinary differential equations. The primary objective is to evaluate and compare these methods in the context of the oscillating pendulum model, particularly in regimes where closed-form analytical solutions are not attainable. In addition, fundamental issues such as error
estimation, convergence, and numerical stability are rigorously addressed. Finally, computational simulations were conducted using MATLAB to illustrate and analyze the resulting numerical solutions.