Conventional Slumber is where the Hero's Journey begins.  The traveler often finds his or her conventional thinking or beliefs challenged.  This stage is often called Unenlightened Slumber, intimating that the traveler is not very aware of what is going on or what needs to be changed in a larger sense.  Another way to look at Conventional Slumber is that the traveler is "asleep" to bigger issues or problems, and needs to wake up to new demands and needs.
    This stage is common for adolescents, in that they are waking up from sheltered childhood, or they are asleep to their issues and problems.  Adolescents often wake up all of a sudden, looking at the world through new eyes or as blank portrait to be filled in.  While that dynamic is a common adolescent developmental trait, staying stuck in out-dated or detrimental thinking and belief systems will only inhibit their chance for a productive and healthy life.  For example, an addicted teen who still believes that he can smoke marijuana and drink socially is asleep to his real problems, and unless he wakes up to the reality of needing to be clean and sober, his slumber will keep him restricted throughout his life.
    In using the Hero's Journey as a treatment model, if this is where a teen is stuck, you don't bother to work them at further levels until they get this stage handled.  Thus, the Hero's Journey helps show you where to work with a particular youth.  If and when the traveler wakes up from conventional thinking, the next stage is the Call to Adventure.