We discuss opportunities to integrate STEM across both formal and informal settings. Our reflections begin with looking back to "Making Science Matter: Collaborations Between Informal Science Education Organizations and Schools," an influential report published by the Center for Advancement of Informal Science Education (CAISE) in 2010. We expand the arguments in that report to address integrating STEM education in formal and informal education particularly in the light of the growth of interest in teaching about 'wicked problems'. We discuss several issues that we believe need to be taken into account in developing closer formal/informal collaboration, and trace how they have emerged since the term STEM was first used in the 1960s. We conclude that a significant challenge, that is often overlooked, is that the term STEM has several different meanings and that institutions in formal and informal settings may have different outcomes in mind when collaborating with each other. The implications are that discussing the meaning and purpose of STEM are an essential first step in any collaboration between formal and informal institutions.