In the beginning of the 21st century, models have emerged to describe and develop undergraduate research and inquiry-based learning. This article discusses four examples of modelling didactical issues around this topic. The aim of the first part is to scrutinize the epistemological and didactical purposes of these four models. As essential dimensions of undergraduate research and inquiry- based learning are neglected, two alternative models are developed in the second part. The first of these puts the coordination of theory and evidence at the centre and determines three different horizons of significance in the field of science. In relation to these horizons, the second new model highlights the broader societal context of scientific practices. The role of research and science in society is recognized here, on the one hand as an affirmative process of institutionalization of approved knowledge, and on the other, as practices of criticizing and breaking away from established forms of knowing, testing, evaluating, and approving. Concomitantly, the education (‘Bildung’) of students through and within scientific practices of research and inquiry-based learning (Humboldt’s ‘Bildung durch Wissenschaft’) is interpreted against the backdrop of two opposing trajectories, which influence students’ ambitions to engage with problems of science. ... mehrIn relation to this, higher education didactics need to distinguish between long-term and short-term goals. It is argued that the latter concretizes the former. This understanding of teaching is corroborated against the backdrop of the concept of learning as ‘enculturation’ in science. The argumentation refers back to insights by Lev S. Vygotsky, Ludwik Fleck and Michael Polanyi.