The other aspect of shinnantam is derived from the context of the Shema: learning the mitzvot. This involves talking about Torah all day long, when you arise in the morning and when you walk about during the day and also before going to bed.
The third part of the Shema (Numbers 15) explains that men have a special need when it comes to education. They have a weakness in that their eyes will constantly be drawn towards women. So Torah says they must wear tzitzit so their eyes won't wander. If eyes wandered back in ancient times when women covered themselves in modest garments, how much more will male eyes wander in today's culture in which women reveal their figures?
In mentioning this, Torah addresses a specific need for men (and women) to have guidance when it comes to relational matters. And so Judaism developed an entire culture to respond to this need. Very specific guidelines are provided to men and women, explaining what is expected. Gender roles are clearly established. There's no confusion about when or how to date. When the man is financially stable, it's time to date. The "how" to dating is established by the community. Everyone makes sure that the men and women are never alone together (yichud)--and even the classrooms are segregated according to gender. The men and women do not touch prior to marriage (shomer negiah). The length of the courtship is typically very short---there's no dating for years on end. The dating is purposeful and marriage-oriented. And, by the way, all of these things also protect women. These communities don't have to worry about things like date-rape, teen pregnancy, emotionally tumultuous break-ups--they eliminate these things by making sure single men and women are never alone together.
Perhaps the keenest insight in Jewish education is that gentile entertainments should be forbidden. This is because, just like children, young adults learn from observing. Whatever they see will become normative. So if young adults are allowed to watch a lot of movies depicting premarital sex as something casual, this becomes their norm. Judaism prevents this by establishing clear standards: no gentile entertainments.
To sum up, shinnantam is about communal learning (chavrutot) with the focus of guiding men and women toward healthy relationships.
Some traditional Christian schools probably share these values in certain ways. But in my experience they fall short. The good news is that, with the growth of the Hebrew Roots movement, Christian school systems may eventually get exposed to the Jewish approach. My hope for the Hebrew Roots movement is that it will truly become a counter-cultural force.