The secondary–tertiary mathematics transition: a visionary research agenda for the field

The secondary–tertiary mathematics transition remains a persistent challenge across educational systems. Despite decades of research, reforms often oscillate between deficit narratives (‘students are underprepared’) and narrow curriculum fixes (‘more algebra, more rigour’). In this paper, I argue for a different framing: the transition is a shared design problem distributed across institutions, curricula, pedagogies and assessments. I synthesize key lines of work: early studies on proof, formalization and advanced mathematical thinking; institutional analyses emphasizing didactical contract and discontinuities in mathematical organizations; and more recent socio-cultural, socio-political and affect-oriented research examining belonging, identity, norms and equity. I identify unresolved issues, including theory fragmentation, limited comparative curricular evidence, weak causal claims about interventions at scale, and insufficient attention to diverse student pathways and service mathematics. I propose a future research agenda structured around (i) theory networking, (ii) curriculum–assessment coherence, (iii) design-based and programmatic intervention research, (iv) equitable participation and identity-safe teaching, (v) cross-institutional teacher education, (vi) data infrastructures for transition monitoring and (vii) international and intra-national comparative studies. The argument is intentionally visionary: we need to move from diagnosing transition ‘problems’ to designing transition ‘handovers’ with shared responsibility and stronger evidence.