In this essay, I propose the use of itinerant encounter spaces as educative agents for teaching time studies experientially. My work is informed by an arts-based methodology, conducted as part of a PhD, which used a mobile shepherd's hut as host for instances of temporal reflexivity. This specific wooden caravan, a venue for shared and introspective stillness, invites participants to embrace non-linearity within formal educational environments that are generally structured by calendars, clocks and bells. By offering unaudited room and time for reflective activities such as storytelling and subjective mapping, I encouraged my research participants, student teachers in Scotland, to nurture the temporalities of self-care that may or may not be part of their personal journeys into ‘meaningful teaching’ during an Initial Teacher Education (ITE) programme. My role was to open up an extracurricular atmosphere which disrupted the temporal standardisations required by many curricular designs for modular fit in university degrees. Curating a vehicle for methodological acts of temporal dissensus offered me insights into teaching time beyond a focus on input and outcomes. The prevailing instrumental logic in formal education rarely acknowledges itinerancy as a dynamic sphere for the pedagogical encounter. My session plans were loosely structured by the provision of a ‘shelter in public’ as a gesture of hospitality and not by a fixed schedule of activities or content to be delivered. This gave research participants the chance to narrate their own intrinsically perceived student teacher trajectories. The improvisation through public pedagogy and the ‘vagueness’ of indirect pedagogy cultivated playful detours. I suggest taking steps aside from dominant curricular formats and explore further how time studies can be taught through the coexistence of movement and stillness, as temporal reflexivity on wheels.