Interdisciplinary Conceptualizations of Variables and Parameters Through Narratives

The concepts of variable and parameter are fundamental for mathematical activity but are also challenging to rigorously introduce at a didactic level. In this paper, we discuss findings from an 11th-grade class interdisciplinary project involving mathematics and linguistics, promoting a conceptual approach to the learning of variables and parameters through narratives. We analyze the written productions of 22 Italian students across two tasks: the first aimed at exploring differences in the meaning of variables and parameters while employing a logico–scientific or narrative mode of thinking; the second involved a meta-reflection on the methodological tools used in the disciplines involved. Students’ productions were qualitatively analyzed using content analysis and thematic analysis, respectively. The analysis enables an elaboration on students’ understanding of the different roles of variables and parameters and of their epistemic features. Students’ conceptualizations of variables and parameters went beyond formal description, drawing on a variety of real-world situations. Moreover, the meta-reflection on the methodological tools shows new awareness of students’ understanding of disciplinary concepts. These findings suggest that interdisciplinary approaches involving mathematics and linguistics can effectively support the conceptual understanding of algebraic notions in secondary school. We therefore recommend further research exploring the integration of narrative contexts and cross-disciplinary collaborations in mathematics teaching.