An international comparative study of the role of mathematical argumentation in primary school inquiry approaches

Mathematical argumentation is widely considered central to inquiry-oriented mathematics teaching, yet inquiry approaches organise mathematical validation in substantially different ways across educational contexts. This paper investigates how mathematical argumentation is organised within inquiry-oriented primary mathematics teaching in Japan and Denmark. The study adopts a theory-driven international comparative design based on two Grade 4 mathematics lessons centred on arithmetic tasks. Drawing on the Anthropological Theory of the Didactic, the analysis combines economic and ecological perspectives to examine both the development of classroom praxeologies and the broader institutional conditions shaping these developments. Balacheff’s distinctions between forms of validation are used to analyse how students’ mathematical techniques are validated in classroom interaction. The economic analysis shows that both classrooms engaged students in
inquiry-oriented mathematical activity and supported the production of multiple techniques. However, the lessons differed substantially in how techniques became connected to mathematical validation. In the Japanese lesson, students’ strategies were progressively related to explicit mathematical properties and symbolic generalisation through repeated comparison and justification. In the Danish lesson,
validation remained primarily operational and procedural, with legitimacy grounded mainly in successful transformations between multiplication and division expressions. The ecological analysis suggests that these differences are related to broader institutional conditions. Whereas the Japanese context reflects a relatively coherent instructional infrastructure connecting curriculum, textbooks, and professional practices, the Danish context reflects a more decentralised ecology characterised by
local interpretation and professional autonomy.