Sometimes I giggle a little when students request "core" in class. Yoga IS core! Everything we do in flow requires mad strength from your core muscles. That being said, it is super important that students know how to use their core, which is where the "Lay on your back and do crunches" approach does come in handy.
There are two things I think students "forget" about when they are doing their more "blatant" core work.
1. BREATH
The breath is SO important here. Think "Inhale, Extend" and "Exhale, Exert". So if you were doing a "basic crunch" you would inhale to lower your head, and exhale to lift your chest up.
2. CONTROL
Keep control of your low belly. If your low back is arched away from the floor and your ribs are flared, misalignment is bound to happen. In 100% of core work, the low belly should be pressing down towards the mat, ESPECIALLY on the exhale.
Core work is great for back problems, balance problems, hypermobility and much more. So you should try to incorporate strengthening your core into your daily or weekly routine to avoid discomfort and difficulties down the road.