Some 35 years ago, Gerard K. O'Neill used the large context of space travel with his undergraduate physics students. A Canadian physics teacher, Art Stinner, independently arrived at a similar notion in a more limited but, therefore, more generally useful sense, which he referred to as the "large context problem" approach. At a slightly earlier time the large context problem type of approach had already been used in the study of medicine, pioneered by McMaster Medical School. And the Faculty of Education at the University of Calgary currently uses a large context problem method to deliver its entire curriculum. These approaches are four distinct ways of presenting large context problems to students. This paper will discuss these approaches historically, look at their grounds and their applications, weigh their successes and characterize their limitations. It will try to see what they take most deeply for granted as viable approaches to teaching science, both theoretical and applied. Finally, it will relate these approaches to the constructivist prejudices of our own time, suggesting their relation to earlier forms of philosophical idealism.