Navigating Boundaries between Physics and Mathematics Education: Bridging Secondary School and University, Research and Practice

This dissertation investigates how the intertwined learning of physics and mathematics can be effectively supported across secondary and early university education. Although mathematics provides essential tools for physics, students often struggle to transfer and integrate knowledge across the two domains. The study addressed four guiding questions: (RQ1) the relationship between students’ performance and confidence, (RQ2) possible gender-based differences, (RQ3) the role of teacher learning communities (TLCs) in shaping instructional practices and student outcomes, and (RQ4) the potential of theoretical frameworks to inform the design of interdisciplinary activities. A design-based methodology combined the refinement of diagnostic instruments with classroom interventions. The Test of Calculus and Vectors in Mathematics and Physics (TCV-MP) was revised, and the Physics Inventory of Quantitative Literacy (PIQL) was translated and validated in Italian; both were extended with confidence ratings to analyse calibration between perceived confidence and actual performance. Two TLC-based interventions—FisicaMente al Liceo (2022/23) and Let’s Interplay! (2024/25)—engaged teachers in collaborative design and classroom experimentation, embedding these tools in authentic contexts. Results show that students achieved statistically significant gains in test performance, accompanied by a systematic improvement in calibration between confidence and competence. In the second intervention, the gender achievement gap narrowed; however, confidence disparities remained more resistant to change, underscoring the need for sustained attention. Teachers emphasized that TLCs fostered a shift from valuing interdisciplinarity in principle to enacting it in practice, overcoming some systemic institutional barriers. Theoretically, the integration of Uhden’s modelling cycle, the Family Resemblance Approach, and boundary crossing provided a coherent framework for both analysing practices and designing instructional materials. A distinctive contribution of this work lies in showing how these perspectives can be brought together to produce concrete, classroom-ready activities that directly improved student outcomes. Overall, this dissertation contributes validated assessment tools, empirical evidence of learning gains, and a theoretically grounded approach for fostering physics-mathematics integration. It demonstrates that systematic focus on confidence, interdisciplinarity, and teacher collaboration can generate tangible improvements in student learning and teacher practice, strengthening the bridge between school and university, and between research and classroom practice.