A cognitive-pedagogical taxonomy of 3D modelling and printing activities in mathematics education: implications for digital creation

Digital creation activities can support learning through making, but their pedagogical value depends on how tasks organise cognitive engagement, learner autonomy, and participant roles. This study develops an empirically grounded taxonomy of three-dimensional modelling and printing (3DMP) activities in mathematics education. Drawing on the Interactive, Constructive, Active, and Passive (ICAP) framework, learner autonomy, and the distribution of teacher and learner roles, we analysed 119 activities from 38 learning designs using cluster analysis. The analysis identified four pedagogical profiles: Passive Demonstrations, Guided Explorations, Learner Modelling and Making, and Conceptual Co-Design. The profiles differed in their dominant ICAP modes, levels of learner autonomy, design roles, and pedagogical objectives, showing that autonomy, artefact production, collaboration, and cognitive engagement are related but non-equivalent aspects of 3DMP activity design. The taxonomy contextualises ICAP alongside autonomy and role distribution within 3DMP mathematics education, providing a multidimensional lens for comparing creation activities and a practical heuristic for activity design. Although these dimensions may also be relevant to other digital-creation technologies, the transferability of the four-profile structure requires independent empirical validation.