arXiv subjects

Felix De la Cruz Serrano

Publications and source records attributed to Felix De la Cruz Serrano.

3 recordsLinked to original sources

arXiv2026

Open Mathematical Tasks as a Didactic Response to Generative Artificial Intelligence in Post-AI Contexts

The widespread availability of generative artificial intelligence tools poses new challenges for school mathematics education, particularly regarding the formative role of traditional mathematical tasks. In post-AI educational contexts, many activities can be solved automatically, without engaging students in interpretation, decision-making, or mathematical validation processes. This study analyzes a secondary school classroom experience in which open mathematical tasks are implemented as a didactic response to this scenario, aiming to sustain students' mathematical activity. Adopting a qualitative and descriptive-interpretative approach, the study examines the forms of mathematical work that emerge during task resolution, mediated by the didactic regulation device COMPAS. The analysis is structured around four analytical axes: open task design in post-AI contexts, students' mathematical agency, human-AI complementarity, and modeling and validation practices. The findings suggest that, under explicit didactic regulation, students retain epistemic control over mathematical activity, even in the presence of generative artificial intelligence.

math.HO↗

arXiv2026

Footprints of the Walking of Numbers: A Dynamic Visualization Task for Understanding Decimal Numbers in Secondary Education

The study of decimal numbers in secondary education is often approached from algorithmic perspectives, which limits students' understanding of their structure. This paper presents the task Footprints of the Walking of Numbers, a dynamic visualization proposal aimed at supporting the understanding of decimal numbers through the exploration of their infinite decimal expansions. The task is based on assigning vectors to the decimal digits from 0 to 9, so that the sequence of digits of a number generates a dynamic geometric path in the plane. Through the use of GeoGebra as a visualization environment, students can observe, compare, and interpret traces associated with different types of numbers, such as terminating decimals, repeating decimals, and irrational numbers, identifying visual regularities linked to their decimal behavior. The analysis is developed from a theoretical-didactical perspective, using the Mathematical Working Space as an interpretative lens to characterize the potential of the task design. In addition, the paper discusses the punctual use of generative AI tools exclusively as instrumental support for computation, without shifting the focus away from mathematical reasoning.

math.HO↗

arXiv2025

Impacto del Enfoque Matematicas en Tres Actos en la Educacion Matematica

The "Mathematics in Three Acts" approach, proposed by Dan Meyer, aims to transform the teaching of mathematics through a model that encourages active student participation, fostering creativity, problem-solving, and metacognition. This study explores the implementation of this approach in a mathematics contest for secondary school students, evaluating its impact on various key competencies. Aspects such as mathematical creativity, problem-solving skills, metacognitive abilities, and students' perceptions of mathematics are examined. The results show that the approach contributes to the development of creative skills, improves understanding and problem-solving abilities, and increases student motivation and confidence. However, areas for improvement are also identified, particularly in the justification of procedures and cognitive flexibility. This study highlights the effectiveness of the "Mathematics in Three Acts" approach as an innovative methodology that fosters more meaningful, reflective, and autonomous learning, suggesting its potential to transform mathematics teaching in diverse educational contexts.

math.HO↗