Resolución de problemas y pensamiento lógico-matemático a través de metodologías activas y plataformas tecnológicas en la educación básica.

The development of mathematical problem solving and logical-mathematical thinking is a core component of the basic education curriculum; however, traditional instructional approaches continue to show limitations in fostering deep and sustained learning in these competencies. In this context, the aim of this study was to analyze the impact of integrating active methodologies mediated by technological platforms on the development of mathematical problem solving and logical-mathematical thinking in basic education students. The study adopted a mixed-methods approach with a quasi-experimental design, including an experimental group and a control group. The sample consisted of 78 students aged between 9 and 11 years from a public educational institution. The pedagogical intervention lasted eight weeks and integrated problem-based learning strategies, gamified activities, and the use of interactive technological platforms, including mathematical visualization tools such as GeoGebra. Data were collected through standardized tests assessing mathematical problem solving and logical-mathematical reasoning, as well as classroom observations and semi-structured interviews. Quantitative data were analyzed using inferential statistical techniques, including ANCOVA, while qualitative data were examined through thematic analysis. The results revealed statistically significant improvements in mathematical problem solving and logical-mathematical thinking in the experimental group, with large effect sizes. A significant increase in academic motivation and engagement was also observed, along with positive associations between motivational variables and mathematical performance. In conclusion, the pedagogically intentional integration of active methodologies and technological platforms represents an effective approach to strengthening mathematics learning in basic education, provided that it is supported by sound instructional design and adequate teacher training.