Marlene Ballestas Rodríguez

The article explores the mathematical connections activated by Colombian university students when solving a problem involving the construction of frequency distribution tables. This study arose because the literature and teaching experience reveal difficulties in statistics in finding the range and determining the number and size of classes, which are essential aspects for creating frequency tables with grouped data. Grounded in the networking between the extended theory of connections, the onto-semiotic approach, and levels of table reading, A qualitative methodology was implemented with 28 students who completed the task and actively participated in the class. The findings reveal that students activated mainly procedural, part-whole, implication, and different representation connections to construct grouped frequency tables, progressing from data organization to statistical interpretation. These connections supported the articulation of mathematical practices, primary objects, and semiotic functions, evidencing a structured but predominantly procedural understanding. However, students’ comprehension was largely situated at level 1 and level 2 (reading the data and reading within the data), with limited evidence of higher-order reasoning such as inference or critical analysis. Only a small proportion of responses reached level 3, and no evidence of level 4 was identified. These results indicate that, although students successfully complete statistical procedures, their understanding remains incipient. This highlights the need for instructional approaches that foster deeper reasoning and critical statistical literacy through the activation of meaningful mathematical connections.