The teaching guiding activity in the elaboration of conceptual connections in number systems within the continuing education of teachers who teach mathematics

Abstract

Mathematics is a dynamic human construction, influenced by historical and cultural contexts, rather than a static and decontextualized body of knowledge. D’Ambrósio (1999) and Miguel (1997) emphasize that its traditional teaching, detached from its origins, limits students’ understanding. The history of mathematics reveals its cultural diversity, evolution, and practical applications, which are essential to demystify it and present it as a constantly developing language. This study investigates how the Teaching Guiding Activity (AOE), based on Vygotsky’s (2005) historical-cultural theory, can mediate the learning of number systems. The activity “Letter to Professor Ori,” which explores a fictitious base-four system, was applied to eight master’s students in Mathematics Education. The results showed: (1) diversity of strategies (some used formal methods, others intuitive solutions); (2) error as a pedagogical tool, helping to revisit concepts such as place value; and (3) the effectiveness of the AOE in integrating historical context and learning. It is concluded that the historical-cultural approach and the AOE make mathematics teaching more dynamic, overcoming mechanization and promoting a deeper conceptual understanding. The research reinforces the importance of training teachers capable of connecting mathematical rigor with creativity and cultural context, transforming mathematics into a critical and emancipatory tool.