This article argues that sociotechnical imaginaries, defined as collectively held, institutionally stabilized, and publicly performed visions of desirable sociotechnical futures, are significantly connected to visions, policies, and projects of educating citizens. These visions, policies, and projects -- or educational imaginaries -- constitute ways to problematize, negotiate and ultimately govern citizens and citizenship at the intersection between technology and education. This article presents a model which conceptualizes and analyzes educational imaginaries, and specifically introduces the notion (and method) of 'problematizations' into these imaginaries. The model, consisting of four key components -- technology, problematizations, collective actors, and target populations -- is exemplified through a genealogy of the education of the 'digitalized citizen'.