This study investigates how structural alignment between mathematics teaching and vocational welding practice can support student engagement and strengthen the perceived relevance of mathematics. The research examines an interdisciplinary intervention in Danish vocational education, where mathematics and welding teachers collaboratively designed modules linking trigonometric calculations to practical workshop tasks. Using Cultural–Historical Activity Theory (CHAT), the mathematics classroom and the welding workshop are analysed as interacting activity systems. The analysis draws on video observations, field notes, and interviews with teachers and students. The findings show that interdisciplinary collaboration reorganised relations between classroom and workshop practices by aligning artefacts, division of labour, and shared objectives across learning environments. Students reported improved understanding of how mathematics is applied in vocational practice, increased precision in workshop tasks, and more positive attitudes towards mathematics.

Given a compact quantum metric space (A, L), we prove that the domain of L coincides with A if and only if A is finite dimensional. We then show how one can explicitly build many quantum metrics with distinct domains on infinite-dimensional AF algebras. In the last section, we provide a strategy for calculating the distance between certain states in these quantum metrics, which allow us to calculate the distance between pure states in these quantum metrics on the quantized interval and on the Cantor space.

Background. Attrition from STEM programs remains a persistent challenge for universities globally. To better support student success and socio-academic integration, universities have developed a range of curricular and co-curricular resources. Much emphasis has been placed on the benefits of these resources; however, less is known about how students recognize, access, and realize these benefits. Guided by a capital-mediated agency model, this asset-based focus group study examined how university-provided resources support undergraduate STEM students’ use of capital. We conducted four parallel focus groups with 21 students at a Norwegian university and analyzed narratives using thematic analysis. Results. Students described using both curricular and co-curricular resources to build personal/emotional, social, and human resource capital that helped them navigate academic and personal challenges. Curricular resources, including mandatory assignments, fieldwork, and laboratory activities, supported disciplinary training and opportunities to develop relationships with peers. Co-curricular resources, including tutoring rooms and student organizations, similarly provided academic and emotional support. Although students often initially accessed resources to address academic challenges, they frequently described emergent social benefits. Recognition of these social benefits appeared to link resource use with decisions to invest in them. Across participants’ accounts, social capital and sense of belonging appeared to operate reciprocally: relationships formed through resource engagement fostered belonging, while belonging strengthened students’ willingness and capacity to continue engaging with peers, resources, and their academic communities. Conclusions. These findings extend the capital-mediated agency model by identifying students’ recognition of resource benefits as a meaningful process linking their use to investment. They also position students’ sense of belonging as an emergent and reciprocal outcome of engagement with both primarily academic and social resources. For institutions and instructors, the findings suggest that simply providing resources may be insufficient and that students must be able to recognize their relevance, access them, and use them in ways that generate meaningful academic and, critically, social outcomes. Designing and evaluating university resources to support these processes and build social capital may create learning environments that better support student agency, resilience, belonging, and persistence in STEM.