Teaching combinatorial paradoxes at the intersection of digital culture and algorithmic thinking

Abstract

Abstract. This research addresses the growing need to integrate sophisticated computational thinking into teacher training. We perform a critical pedagogical and computational analysis of the LearningApps platform. The study determines which specific learning theories (e.g., behaviorist vs. constructivist) its underlying algorithmic templates support, and proposes methodologically sound strategies for future educators to leverage this structure for differentiated, complex learning outcomes. Combinatorial paradoxes and probability curiosities can be effectively applied to the development of algorithmic thinking and digital culture, as they help learners recognize logical inconsistencies, intuitive fallacies, and the importance of systematic reasoning. The aim of this research is to explore how such paradoxes can be used to enhance critical and algorithmic thinking in mathematics and computer science education. Classic paradoxes, such as the Monty Hall problem and the Chevalier de Méré paradox, serve as excellent tools for developing probabilistic reasoning, logical deduction, and awareness of cognitive biases [1][2]. Wijayatunga [2] demonstrated that using such paradoxes improves students’ critical thinking skills, especially when applied in interactive and digital learning environments. Similarly, Rezvanifard, Radmehr, and Drake [3] found that incorporating paradoxes and sophisms into higher education enhances students’ reflective thinking and strengthens their ability to decompose and analyze problems algorithmically. Tillema [4], through an empirical study of secondary school students, showed that visual and 3D combinatorial structures significantly foster abstraction and logical organization.