A study on the representations and generalization strategies of numerical sequences among secondary school students

Algebraic thinking in secondary education has been widely studied through the exploration of patterns. This study aimed to identify the representations developed by secondary school students to express a numerical sequence and to describe the strategies they employed for its generalization. To this end, a questionnaire was administered to 25 students aged 14 to 15, who were asked to represent four different numerical sequences. The results revealed four levels of representation: pre-structural, emerging, partially structured, and fully structured. Similarly, it was found that the strategies varied according to the type of task. In immediate and near generalization, students primarily relied on counting and additive operations, whereas in distant generalization, the strategies diversified, with the correspondence strategy being the most frequently used. Finally, it was evident that the representations produced by the students themselves served as an essential resource that facilitated the construction of their generalizations.