Personally I think that compass and paper map should be taught and mastered first, and be the habitual reference.
The danger is that new pilots naturally want to use GPS gizmos in their cockpits - because they are much easier, and involve no maths - so they jump straight to those before properly learning compass and map.
Compass direction is vital for ones's situational awareness - for dead reckoning or lining up on the correct runway, or flying a raw data ILS, or tracking an NDB.
Use of a paper map is important for identifying prohibited airspace, military areas or high ground that a GPS device might ignore if you get airborne and then input a direct-to command.
We can all think of garbage in garbage out situations that we ourselves have created or experienced with our car satnavs or aircraft FMS. A solid grounding in compass and paper map is important for situational awareness and gross error checking.
If all else suddenly fails; e.g. an electrical power failure; pilots need to be able to drop straight onto Heading, V/S and Altitude to get them home. this needs to be instinctive rather than them having to try to work out how to read and use a compass during a major power failure whilst airborne.