While it is clear that engagement between students and instructors positively affects learning outcomes, a number of factors make such engagement difficult to achieve in large-enrollment introductory courses. This has led to pessimism among some education professionals regarding the degree of engagement possible in these courses. In this paper we challenge this pessimistic outlook through a case study involving a large-enrollment introductory, general education, STEM college course. Several pedagogical approaches related to social constructivist theory offer possibilities for increasing student engagement in the learning process, but they may be difficult to implement, particularly in environments yielding little or no reward for classroom innovation. Here, we present an approach to developing an engaging learning environment by hybridizing aspects from a range of pedagogical approaches varying from the didactic (e.g. traditional lecture) to the more constructivist (e.g. peer instruction, project-based learning). We describe the course in question and our pedagogical approach, provide evidence for its effectiveness, and discuss contextual factors affecting the development of our approach and its adoption to other subjects and institutions. We also discuss important remaining challenges regarding the adoption of our approach and similar practices.